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RELATION BETWEEN COST, QUALITY, AND RISK IN PORTLAND CEMENT CONCRETE PAVEMENT CONSTRUCTION By SOFIA MARGARITA VIDALIS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005 Copyright 2005 by Sofia Margarita Vidalis I would like to dedicate this dissertation to my supporting parents, Pavlos I. and Klere Vidalis and to my brother Joseph A. Vidalis. ACKNOWLEDGMENTS It is a great pleasure for me to thank and acknowledge the many individuals who assisted me and supported me during the course of my doctorial program. I begin by expressing my gratitude to Dr. Fazil T. Najafi, my advisory committee chairman, for his continuing encouragement, patience, and support throughout my studies at the University of Florida. I will always be grateful for lessons learned under his tutelage. I am greatly indebted to Mr. Peter A. Kopac, P.E., Research Engineer for the Federal Highway Administration, who helped me select this research topic and contribute toward fulfilling some of the FHWA research needs. I would like to thank him for his invaluable assistance, patience, advice, and critique throughout this research. In addition, I would like to thank him and the FHWA for funding Dr. Nasir G. Gharaibeh's visit to the University of Florida for his assistance. I want to express my gratitude to Dr. Nasir G. Gharaibeh, from University of Texas, El Paso, for assisting me on a program (analyzes risk and expected profit associated with performancerelated specifications) that he and J. Stefanski and M.I. Darter developed that became an excellent starting point for this research. I would also like to thank the rest of my committee members, Dr. Mang Tia, Dr. Andrew Boyd, and Dr. Ian Flood, for their support, guidance, and help in accomplishing my work. I would have not been able to reach this milestone if not for their advice, guidance, and support. I would like to thank Dr. Iordanis Petsas, from the University of Scranton, for all his support and help during my doctorate. I would also like to extend my thanks to all of my friends for their support in the progress and completion of my study. Finally, I express my deepest gratitude to my parents and my brother for their love and support and for many sacrifices they have provided me with the opportunities that enabled me to pursue my higher education at the University of Florida. I will always be grateful for everything they have done and owe them a debt that can never be repaid. TABLE OF CONTENTS A C K N O W L E D G M E N T S ................................................................................................. iv LIST OF TABLES ......... ....................................................... ix L IST O F FIG U R E S .... ...... ...................... ........................ .. ....... .............. xii ABSTRACT ........ .............. ............. ... ..... .......... .......... xv CHAPTER 1 IN TR OD U CTION ............................................... .. ......................... .. 1.1 B background ......... ...... ................................................................... ........... 1 1.2 Problem Statem ent...... .. ............................ .. .............. ................ .2 1.3 O bjectiv es .................................................................... 3 1.4 Scope..................................................... . 3 1.5 R research A approach .................................. ..............................................4 1.5.1 T ask 1: L literature R eview ....................................................... 4 1.5.2 Task 2: Data Collection ............................................... ........................... 1.5.3 T ask 3: D ata A analysis ..................... .................................. ... ..... 1.5.4 Task 4: Computer Program Development ...................... ............... 1.5.5 Task 5: Interpretation of Computer Program Output ................................6 1.6 Practical A applications .......................................................... .............6 2 LITERATURE REVIEW .................... ...................... ........... ...............7 2.1 Introduction ............ ..................................................... ............... 2.2. Highway Pavement Construction Specifications..................................7 2.2.1 Prescriptive Specifications ........................................ ........ ............... 8 2.2.2 Quality Assurance Specifications........... .......................... ...............9 2.2.3 Perform ance Related Specifications .............................. ..................... 10 2.3 Variability in Highway Pavement Construction.............................. ..............11 2.3.1 R andom Sam pling ................................................................. ............... 11 2.3.1.1 Pure R andom Sam pling......................................... ............... 12 2.3.1.2 Stratified Sam pling...................................... ......................... 13 2.4 Acceptance Schedule ......................................... .................... 13 2.4.1 A attributes A acceptance Plan ............................................. ............... 14 2.4.2 Variables Acceptance Plan ...... .............. .. .................. ............... 14 2.5 Pay A djustm ent............... ........................................... ... ...... .... 15 2.6 Acceptance Quality Characteristics ....................................... ...............16 2.6.1 Slab Thickness .................. ........................... .. .. .... .. ........ .... 18 2.6.2 Strength ................................ ....................... ..... .... ...... 18 2.6.3 Surface Sm oothness......................................................... ............... 20 2.6.3.1 Profile index .................. ..................... ........ .. .... .. .. ...... .... 23 2.6.3.2 International Roughness Index.......................................................24 2.6.3.3 Comparison of Profile Index with International Roughness Index..27 2.7 Diam ond Grinding ......... ................... .......... ......... .. ... ..... ...... .. 28 2.8 R elated R research ............................................ ................... .. .... .. 28 3 DATA COLLECTION AND ANALYSIS..................... ...... ............... 31 3.1 Introduction ............... ............... ...............31 3.2 Questionnaire Development ............. ... ................. .................. 31 3.2.1 Concrete Contractor Respondents ................................... ............... ..34 3.2.2 State Highway Agency Respondents................ .............................35 3.2.3 Desired Number of Acceptance Quality Characteristics Cost Responses..35 3.3 Contractor's Bidding Decision M aking...... .......... ...................................... 38 3.4 State Highway Agency's Cost Estimating Procedures.......................................42 3.5 Concrete Pavement Acceptance Quality Characteristics Change in Cost............43 4 STATISTICAL AND MATHEMATICAL METHODS UNDERLYING TARGET QUALITY IN HIGHWAY CONCRETE CONSTRUCTION..................46 4.1 Introduction....................................................................... ....... ...... 46 4.2 Variability M measures in PCC Pavements............... ............................................46 4.3 Quality M measures ................ ................ ..................... ............ 48 4.3.1 Percent W within L im its........................................................................ .. ...49 4.3.2 Quality Index .................. ............................ .... .. .. .. ........ .... 50 4.4 Pay A djustm ents ....................................... ............... .............. 52 4 .4 .1 P ay F actor ............................................... ........ ....... 52 4.4.2 C om posite P ay F actor.................................................................... ....... 55 4.5 M ethods for Selecting Target Quality ...................................... ............... 56 4.5.1 D eterm inistic M ethod ........................................................................ .. ...56 4.5.2 Probabilistic M ethod ......................................... ............... 60 4.6 Evaluating Probabilities of Risks in Concrete Pavement Construction ..............61 5 COMPUTER PROGRAMMING AND ANALYIS............... ....... .........67 5 .1 In tro d u ctio n ............ ...... .......... ......... ...... ............ ................ 6 7 5.2 Purpose of Com puter Program ........................................ ........................ 67 5.2.1 Computer Program Development....................... ...................... 67 5.2.2 M onte Carlo M ethod ............................................................................ 71 5.3 Program Structure ................... ........... ........ ................ .............. 72 5.4 Computer Program Output Variability ...................................... ............... 75 5.5 Probabilistic O ptim ization for Profit ........................................ .....................79 5.5 Deterministic vs. Probabilistic Approach..........................................................84 6 CONCLUSIONS AND RECOMMENDATIONS ............................................. 92 6 .1 Sum m ary and F finding s .............................................................. .....................92 6.2 C onclu sions ............................. ................ ................................93 6.3 Recommendations for Future Research.....................................................94 APPENDIX A STA TISTICAL TABLES ........................................................................... 96 B CONCRETE CONTRACTOR QUESTIONNAIRE...............................................104 C STATE HIGHWAY AGENCY QUESTIONNAIRE ..............................................115 D COST OF ACCEPTANCE QUALITY CHARACTERISTICS.............................134 E COMPUTER PROGRAM (MICROS/VISUAL BASIC) SCRIPTING CODE.......141 F COMPUTER SOFTWARE PROGRAM (PROB.O.PROF) MANUAL................ 197 F.1 System Requirements and Recommendations .................................................. 197 F .2 Softw are Installation................................................. .............................. 197 F.3 Starting the Softw are ............. .......................... .................................197 F.4 Input Data ................................. ............................... ........ 199 F .5 O u tp u t D ata .................................................................................................. 2 0 2 LIST OF REFERENCES ......... ......... ..... ............... ..................................... 206 B IO G R A PH ICA L SK ETCH ......... ................. ...................................... .....................211 LIST OF TABLES Table p 21. Summary of IRIPI Relationships with a 2.5ft (0.76m) Moving Average Sm oothing Filter ................................................ ................. 28 31. Summary of the Required Number of Samples for Relative Incremental Cost for E ach A Q C ........................................................................... 4 0 32. Average AQCs and Incremental Change in Cost from Respondents......................45 33. Average AQCs and Revised Incremental Change in Cost ......................................45 41. AASHTO Price Adjustment Factors for Smoothness .............................................54 42. AQC Values and their Measures for Deterministic Example Problem.....................58 43. Deterministic Method for Selecting Target Quality Levels .............................. 65 51. A Q C P properties U sed ........................................................................ ...................75 52. Variability in AQC Combinations................................................ ..................... 78 53. Prob.O.Prof Output for Individual AQC Acceptance Plans .................................87 54. Prob.O.Prof Ranking of HighestProfit Target AQC Value Combinations for W eighted A average M ethod ............................................. ............................. 88 55. Prob.O.Prof Ranking of HighestProfit Target AQC Value Combinations for Average M ethod ................ ............. ........................................... 88 56. Prob.O.Prof Ranking of HighestProfit Target AQC Value Combinations for Sum m action M ethod .............................. .. .......... ...... ........ .. ............... 89 57. Prob.O.Prof Ranking of HighestProfit Target AQC Value Combinations for Product M ethod .............................. .............. ................ .. ........ .... 90 58. Deterministic and Prob.O.Prob Average Output ................................................91 A1. Percent W within Limits For a Sample Size of 3 .................................. ............... 96 A2. Percent W within Limits for a Sample Size of 4 ................................ ...... ............ ...97 A3. Percent Within Limits for a Sample Size of 5 ........................ ..................98 A4. percent W within Limits for a Sample Size of 6 ................................. ............... 99 A5. Percent Within Limits for a Sample Size of 7 ........... ........................................ 100 A6. Percent W within Limits for a Sample Size of 8 ............................... ............... .101 A7. Percent Within Limits for a Sample Size of 9 ........... ........................................ 102 A8. Area (A) Under the Standard Normal Curve From oo to z (A)............................103 B1. Concrete Contractor's Responses (Questions 1 11).............................................110 B2. Concrete Contractor's Responses (Questions 12 15d)............... .... ...............110 B3. Concrete Contractor's Responses (Questions 15e 15h)............... ...............111 B4. Concrete Contractor's Responses (Questions 15i 15j) .............. ......................111 B5. Concrete Contractor's Responses (Questions 15k 151) ............ ...................112 C1. State Highway Agencies' Responses (Questions 1 4c) ...................................119 C2. State Highway Agencies' Responses (Questions 4d 4f) ................... ...............120 C3. State Highway Agencies' Responses (Questions 4g 4h)....................................121 C4. State Highway Agencies' Responses (Questions 4i 4j)............... ...................122 C5. State Highway Agencies' Responses (Question 4k)...............................................123 C6. State Highway Agencies' Responses (Question 41)..............................................124 C7. Price Adjustment Schedule from 0.0 Blanking Band Special Provision...............128 C8. Profile Index Adjusted Pay for the State of Kansas.............................................. 129 C9. Profile Index Adjusted Pay for the State of South Dakota .....................................132 D 1. Thickness Costs per Square Y ard.................................................. ..... .......... 134 D 1. Thickness Costs per Square Y ard (Cont.)..................................... ..................... 135 D1. Thickness Costs per Square Yard (Cont.)..................................... ............... 136 D 2. Strength Costs per Square Y ard........................................ ........................... 137 D2. Strength Costs per Square Yard (Cont.) ...................................... ............... 138 D3. Smoothness Costs per Square Yard.................................................................139 D3. Smoothness Costs per Square Yard (Cont.) ...........................................................140 LIST OF FIGURES Figure page 21. Elements of an Ideal Quality Assurance System ......................................................8 22. QA Programs for PCC Paving......... ...................................... 11 23. Examples of Pure and Stratified Random Sampling ...........................................12 24. State DOT Concrete Pavement Incentive and Disincentive Pay Adjustment Practices (A C PA 1999) ................................................ ............................... 17 25. Concrete Com pressive Strength Test .............................................. ............... 19 26. ThirdPoint Flexural Strength Test....................................... .......................... 20 27. Center Point Flexural Strength Test ........................................ ....................... 21 28. Percent of Different Measuring Devices Used in the United States........................22 29. The California Profilograph (CalTrans, 2000) ................................. ............... 22 210. California Profilograph 0.2inch Blanking Band Trace (ACPA, 1990)................23 211. Types of Profiles from Profilograms (AASHTO, 2004)............ ................25 212. Lightweight Profilometer (Sayers and Karamihas, 1998).............. ... .............26 213. HighSpeed Profilometer (Sayers and Karamihas, 1998) .....................................26 31. Concrete Cement Pavement Types Built......................................... ............... 32 32. Jointed Plain Concrete Pavement Overhead and Side Views (ACPA, 2005) ............33 33. Percent of Contractors that Use a Formal Technique to Win a Bid .........................39 34. Method used to Handle Uncertainty in Pricing Quality in JPC Pavement.................41 35. M ethod used for Job Related Contingency .................................................. ...... 41 36. Method Used to Calculate Cost for Jointed Plain Concrete Cement Projects............42 37. Cost Estimation Procedures that is Independent/Dependent of Quality...................43 38. Understanding of Cost Associated with Incremental Change of AQC ...................44 41. P percent W within L im its......................................................................... .................. 49 42. Three Examples of Symmetric Beta Distributions...............................................51 43. Deterministic M odel ................................................................ ......... 64 4 4 P rob ab ilistic M odel........... ..... .................................................................... ................ 66 51. Variation of Average Thickness Depending on Number of Lots Used....................69 52. Variation of Strength Pay Adjustment Depending on Number of Lots ...................70 53. Variation of Smoothness Pay Adjustment Depending on Number of Lots ...............72 54. Com puter Program Flow Chart ............................................................................ 76 54. Computer Program Flow Chart (Continued)...........................................................77 55. Profit versus Risk Probability for Number One Rank..............................................80 56. Profit versus Risk Probability for Number Two Rank ............................................80 57. Profit versus Risk Probability for Number Three Rank .............. ..........................81 F1. Disable/Enable Macros Message Box ............................................. ...............198 F2. The Five Buttons Used in the Software Program.....................................................198 F 3 S each T o o l..................................................................... 19 9 F4. Input the Number of AQCs for Analysis..............................................................199 F5. Message Box if Number of AQCs is Not Entered ............................199 F 6 T sickness Input B ox ......................................................................... .................. 200 F 7. Strength Input B ox ........................... .......................... .... ......... .... ..... ...... 20 1 F 8. Sm oothness Input B ox............................................................................. ........ 202 F 9. T sickness O utput T able......................................... .............................................203 F 10. Strength O utput T able ........................................ .............................................203 F 11. Sm oothness O utput T able ........................................................... .....................203 F12. Cap and Composite Pay Factor Inputs ...................................... ............... 204 F13. Composite Pay Factor Drop Box of Different Methods Used .............................204 F14. Combinations of Target AQCs for Different Risks.............................................205 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy RELATION BETWEEN COST, QUALITY, AND RISK IN PORTLAND CEMENT CONCRETE PAVEMENT CONSTRUCTION By Sofia Margarita Vidalis December 2005 Chair: Dr. Fazil T. Najafi Major Department: Civil and Coastal Engineering In highway cement concrete pavement construction, the contractor decides what levels of quality to target under statistical quality assurance specifications. The selection of appropriate target quality levels affects both the probability of being awarded a project and the subsequent profit margin. Contractors are currently using the deterministic approach in selecting combined target acceptance quality characteristics. This approach does not take risk and probabilities into consideration. A new procedure using the probabilistic approach has been addressed. This probabilistic approach has been developed into a computer program that calculates the risks and probabilities in selecting the overall target quality. This proposed procedure and accompanying computer program can help a contractor select target quality levels that will maximize profit in a specific situation. It will also assist state highway agencies in validating their quality assurance specifications and pay adjustment provisions. Based on the analysis conducted, it was found that the deterministic and probabilistic methods do not necessarily identify the same optimal target values. The difference in answers between the two methods can mean a significant difference in profit. The proposed procedure is an improvement because it relies on computer simulation to replace timeconsuming trial and error. CHAPTER 1 INTRODUCTION 1.1 Background During 1956, the move toward Quality Assurance/Quality Control (QA/QC) acceptance plans in highway pavements began with the American Association of State Highway and Transportation Officials (AASHTO) Road Test. The test was an experiment designed principally to determine the effect of variations in traffic loadings on different pavement cross sections. Among the findings was that there was far greater variability in materials and construction than engineers at the time realized, which led to the conclusion that highway concrete specifications must be improved (Burati et al., 1995). In a standard construction contract, the State Highway Agency (SHA) specifies the quality level of construction and material the contractor must deliver. Quality levels can be described for use within methods specifications or statistical QA specifications. The quality level under methods specifications is described in terms of specific materials, equipment, and procedures the contractor must employ. This approach to construction specification development is predicated on the assumptions that the SHA fully understands the relationships between the construction process and the quality of the product, and is the primary repository of the technical knowledge needed to link the two (Chamberlin, 1995). In this case, contractors will only need to deliver the minimum acceptable quality level specified. Thus, contractors typically have no incentive to deliver a greater quality level under these specifications. On the other hand, the quality level under statistical QA specifications explicitly describes only the desired sample statistic and not the desired constructed product. Contractors are not provided a specific quality level to target during construction under these specifications either. Contractors are left to determine their own target quality. Although they can be innovative in determining these levels, they still need a guidance for economic evaluations in the cost of quality. Choosing a target quality is important to both the SHA as well as the contractor. The probability of a contractor being awarded a project and his/her subsequent profit margin are affected by this process. It is important for SHAs to have a better understanding of how and why contractors select target quality levels. These levels will ultimately provide insight on the cost and performance of the constructed concrete pavement. 1.2 Problem Statement A questionnaire was sent out to numerous SHAs and concrete contractors regarding the cost of highway concrete pavement acceptance quality characteristics (AQC) such as slab thickness, compressive strength, and surface smoothness. This questionnaire revealed that the majority of SHAs are not aware of the cost of AQCs and so they leave it up to the contractor to estimate them. This is because most SHAs' cost estimating procedures are independent of quality requirements. This means that the cost estimating procedure does not allow estimators to differentiate pavement construction costs with respect to the measure of quality. The main objective of concrete contractors, as profit seeking firms, is to make a profit. That profit is to a large degree dependent on the target quality level, which in turn is very much influenced by the specifications. SHAs need to monitor the process of how contractors react to the QA specifications and associated pay adjustment provisions. In addition, SHAs need to know if the specifications encourage the contractors to maintain a proper balance between high quality/high performance and low cost. All of the above mentioned important issues are analyzed in the next section. 1.3 Objectives The objectives of this research are as follows: * Compare the differences and similarities of the current deterministicc method) and a new (probabilistic) method used to predict estimated quality. * Develop guidelines from the new method for concrete contractors in selecting target quality levels that will achieve maximum profit. * Incorporate probabilities and risk percentiles in targeting the composite AQCs that maximize profit. * Assess whether SHAs acceptance plans and pay adjustment systems encourage construction that offers an optimal balance between quality and cost such as to result in lowest lifecycle cost. * Develop a computer program that will help concrete contractors and SHAs evaluate the economic consequences of AASHTOrecommended QA specifications for strength, thickness, and smoothness. Specifically, this program will aid concrete contractors in targeting AQC levels to achieve maximum profit. This will provide the SHA a means to check whether the contractor's optimum target values (target values that maximize profit) are reasonably close to what may be considered optimum from the SHA's point of view (target values that minimize life cycle cost). 1.4 Scope The main goal of this research is to determine the effects of different target AQC combinations so as to maximize the contractor's end profit. In addition, it will also provide types of contractor risk percentiles involved in the design phase of Portland Cement Concrete (PCC) pavement construction. Risk factors can vary depending on how confident a contractor is in achieving the specified construction and quality of the material achieved. This study was limited to concrete pavement construction with only three types of AQCs: slab thickness, compressive strength, and surface smoothness. The questionnaire was developed in order to understand the following: * The change in cost, as a percentage, of each incremental change in the numerical value of an AQC. * The contractor's and SHA's understanding of economic evaluations in the change of cost of the numerical value of an AQC. * The methods that concrete contractors and SHAs use to price AQC. The questionnaire provided input to the development of a computer software to aid contractors and SHAs in PCC pavement construction work. This software program probes various quality levels that could be employed. It identifies the contractor's optimum target quality based on the risk the contractor is willing to take. Ultimately, this assists contractors with bidding and operating strategies. Moreover, this assists SHAs with developing and validating specifications and the contained pay adjustment systems. 1.5 Research Approach The research approach that was followed in order to fulfill the research objectives mentioned in Subheading 1.3 is described in the following task: 1.5.1 Task 1: Literature Review This task consisted of a literature search on the following: * Concrete pavement AQCs * Types of QA/QC concrete pavement construction specifications (e.g., AASHTO, state specifications, etc.) * Current methods used to perform economic evaluations * Pay adjustment procedures for AQCs * Previous research reports 1.5.2 Task 2: Data Collection This task was conducted to understand the cost associated with each AQC. The following steps were used to accomplish this task: * Send a questionnaire to SHAs and concrete contractors on each AQC's economic evaluations in the initial construction of concrete pavements. * Collect results of related studies on AQC economic evaluations in the initial construction of concrete pavements. 1.5.3 Task 3: Data Analysis This task includes an analysis of the following: * The data collected from the questionnaire sent to SHAs and concrete contractors. * The data collected from pastrelated studies. * Current procedures and methods (e.g., deterministic approach and probabilistic approach) used to calculate pay adjustment costs for each AQC. 1.5.4 Task 4: Computer Program Development A spreadsheet computer program that uses Macros/Visual Basic was developed based from the data obtained from the questionnaire, current pay adjustment procedures, and AASHTO specifications. This software was used as a tool to relate cost, quality, and risk in PCC pavement construction. The design value, lower specification limit, standard deviation, number of samples taken per lot, and incremental cost percentage for each AQC are among the inputs in the computer program. Monte Carlo simulation was used in the computer program to simulate sampling from the various AQC populations. It also combined statistical methods (e.g., mean, standard deviation, and probabilities) to calculate the pay factor at each trial AQC target value. The result represents the contractor's expected pay and profit for each target AQC at a specific risk probability. The profits are then ranked in descending order and the three most profitable AQC target value combinations are identified for each of the four risk probabilities. In this case, the contractor can choose the best combination suited for him/her that will maximize his/her profit and apply that to a bid. 1.5.5 Task 5: Interpretation of Computer Program Output This task was conducted to understand the economic evaluations of the relationship between cost, quality, and risk. The following was interpreted: * The difference of profit between AQC target values alone and AQC target values once the composite pay equation is taken into account. * How risk plays a part in the overall profit. * Recommendations for improvement of current QA/QC specifications. * Recommendations and future research possibilities for additions to the computer program. 1.6 Practical Applications The results from this study will assist concrete contractors with intelligently setting target quality levels, to maximize their profit. In addition, it will also assist SHAs in validating their quality assurance specifications and pay adjustment provisions. The new method, along with the computer program, can be used to assist in the development of new and improved QA/QC specifications that will have significant economic advantage for SHAs and concrete contractors. Ultimately, this will not only have a positive impact on the agencies and contractors but also on the general public. CHAPTER 2 LITERATURE REVIEW 2.1 Introduction The quality of highways has always been a major concern to highway engineers and contractors. During the past 50 years, the highway construction industry has been evolving toward a Quality Assurance (QA) model as seen in Figure 21. According to this model, the SHA describes the highway pavement desired through design drawings and specifications that include quality assurance characteristics, quality levels and tolerances, acceptance sampling and testing schemes, and acceptance criteria. The contractor creates the highway pavement by establishing a process for manufacturing/constructing the product and by exercising control over the quality of the output. The contractual agreement is then structured in a way that assures an equitable distribution of risk between the contractor's expectation of fair compensation and the SHA's expectation of reasonable quality (Chamberlin, 1995). 2.2. Highway Pavement Construction Specifications Concrete highway construction utilizes a wide variety of materials. The control of the quality of these materials and the methods by which they are used is a major concern of the highway practitioner throughout the planning, design, and construction stages of a project. The specific requirements for governing both the quality and utilization of materials are set up in the form of specifications. A construction specification should be practical for implementation purposes and should be developed with the goal of achieving a highquality constructed pavement at a reasonable price that will result in the lowest lifecycle cost. SHA Contractor Quality Characteristics Manufacturing Process and Levels Acce Quality Control Plan Acceptance Criteria S oThe Product  Compensation Figure 21. Elements of an Ideal Quality Assurance System Specifications for highway construction materials and elements have taken different forms through the years as construction managers and highway agencies have adopted better methods of measuring compliance. These methods have typically been labeled as either prescriptive, QA, or performance (Chamberlin, 1995). 2.2.1 Prescriptive Specifications The traditional specifications used are known as method specifications, also called prescriptive specifications. According to this specification, the contractor is provided with specific details on concrete pavement materials, design type, and method of construction. This specification does not provide the lowbid contractor any flexibility in making decisions about the design and process of the pavement construction. This does not give any incentives to use better methods or materials that will result in improving the quality of the specified methods and materials of the highway pavement. Contractors who use this specification rely greatly on their engineering judgment, their intuition, and their past experience. The contractor is responsible for the endresult of the project and its control parameters. Another major weakness associated with this specification is that it may not always produce the desired endresult even when it is properly followed. The reason is that it relies on past experiences achieved under conditions that may not be replicated in a new situation (Chamberlin, 1995; Solaimaniam et al., 1998). 2.2.2 Quality Assurance Specifications Since the AASHTO Road Test in 1956, the discovery of the magnitude of variability in the quality of highway construction has raised concerns about the need for its improvement. The improvement has taken place as an evolution in quality assurance specifications. In QA specifications, the desired quality level, and the decisions to reach the desired quality are based on statistical principles. The SHA is responsible for describing the level of quality desired in the end product as well as the procedures that will be used to judge quality and acceptance. QA specifications can be easily enforced because there is a clear separation of responsibilities for control and acceptance. Moreover, this specification can be easily applied because pay adjustment for defective work is predetermined and thus, there is no need for negotiations. The contractor working under quality assurance specifications typically has a positive/negative pay adjustment provision. This provides the contractor with incentives to achieve higher quality that can be more profitable. Under the earlier prescriptive specifications, a contractor's bid was often influenced by the reputation of the engineer who was in charge of acceptance of the end product. Unlike the historical data collected in conjunction with prescriptive specifications that have been notoriously unreliable, quality assurance specifications produce useful data obtained with valid random sampling procedures. The obtained data can be further analyzed to develop better specifications for the future (Weed, 1996a). 2.2.3 Performance Related Specifications Later in the 1980s, the Federal Highway Administration (FHWA), National Cooperative Highway Research Program (NCHRP), and State Highway Research Program (SHRP) integrated the development of relationships between construction quality measures and performance. This integration came to be known as Performance Related Specifications (PRS) (Chamberlin, 1995). PRS improved quality assurance specifications by describing the desired levels of key materials and construction acceptance quality characteristics (AQCs). These characteristics, through PRS, have been found to correlate with fundamental engineering properties that predict performance (Hoerner et al., 2000). Quality characteristics include material and construction variables that are under the control of the contractor and that are used for acceptance by the agency. These AQCs include means and standard deviations of slab thickness, concrete strength, entrained air content, and initial roughness (Darter et al., 1993). The primary component of a PerformanceRelated specification is the collection of prediction models that are used to determine the probable lifecycle cost (LCC) of the asdesigned and asconstructed pavements. An increasing number of SHAs are using QC/QA specifications compared to material and methods specifications. Although SHAs are increasingly using QC/QA specifications, the methods and procedures that constitute the QA programs of SHAs differ significantly. Figure 22 shows that the majority of SHAs use QA programs with the contractor controlling quality and the agencyperforming acceptance (16 out of 40 responses) (Hughes, 2005). 18 16 14 S12 SC S10 . 8 6 c, 4 4 0 6 2 z 0 Materials and Agency QC and ContractorQC Contractror QC Methods Acceptance and Agency and Acceptance Acceptance Figure 22. QA Programs for PCC Paving 2.3 Variability in Highway Pavement Construction Since the Road Test findings were reported, both the FHWA and various State DOTs have conducted many studies on typical variability in highway construction. Variation exists in all material and constructionrelated acceptance quality characteristics (AQC's) such as aggregate gradation, cylinder and beam strength, air content, slump, water/cement ratio, permeability, pavement thickness, and smoothness. The factors that influence this variability may be due to the period of time, distance, area, or quantity of material over which the variability is measured (Hughes, 1996). Due to the inconsistency in highway construction, different types of sampling and acceptance plans had to be implemented to develop QC procedures and requirements. 2.3.1 Random Sampling Sampling is one of the most important features in QC/QA specifications. Quality Assurance Specifications use methods such as random sampling and lotbylot testing to determine if the operations are producing an acceptable product (Burati et al., 2002). In sampling, one needs to know the point of sampling (where to sample), what technique to use, number of samples, and the time and production rate of sampling. If sampling is done inappropriately, a bias in test results may be introduced that cannot be detected or accounted for. The primary objectives in statistical sampling are to obtain a random sample which has the same probability of being taken as any other sample of material and a sufficient number of samples to adequately characterize the material. (Newcomb and Epps, 2001). This random sampling method can be used for quality assurance testing that allows every member of the population (lot) to have an equal opportunity of being selected as a sample. There are two types of random sampling: pure and stratified, as seen in Figure 23. Pure Random Sampling S  Lot Stratified a Random S 0 Sampling Sublot Sublot Sublot Sublot Sublot 1 2 3 4 5 Figure 23. Examples of Pure and Stratified Random Sampling 2.3.1.1 Pure Random Sampling The more fundamental method of random sampling is also known as pure random sampling. This allows the samples to be selected in an unbiased manner, based entirely on chance. A drawback of pure random sampling is that the samples occasionally tend to be clustered in the same location. Although this method of sampling is valid from a statistical point of view, the samples may be spaced such that they do not adequately represent a lot (Pathomvanich, 2002). 2.3.1.2 Stratified Sampling The stratified sampling method is designed to eliminate the clustering problem and spreads the sampling locations more uniformly throughout the work (Weed, 1989). This method ensures that the specimens for the sample are obtained throughout the lot, and are not concentrated in one portion or section of the lot. Therefore, most SHAs use stratified random sampling for their acceptance plan. A lot is also known as the population. It is a specific quantity of similar material, construction, or units of product, subjected to either an acceptance or process control decision (TRC, 2005). The determination of lot size is primarily an economic decision. It is recommended that the lot length be set equal to one day's production. A lot can be stratified into a number of sublots equal to the sample size to be selected from the lot. Typically, sublots have approximately equal surface area. One core is randomly selected from within each sublot. This ensures that each portion of the lot has the same chance of being selected while, at the same time, ensuring that the sample is spread out over the entire lot (Hoerner et al., 1999; Burati et al.,1995). In order to test the sampling method for acceptance, different types of acceptance plans are specified. 2.4 Acceptance Schedule An acceptance plan plays an important role in QA specifications. The plan specifies how many measurements are needed and how the accept versus reject (including pay adjustment) decision is made based on measured data (Chang and Hsie, 1995). There are two types of statistical acceptance plans in quality assurance specifications: attributes and variables. 2.4.1 Attributes Acceptance Plan An attributes acceptance plan is a procedure where the acceptability of a lot of material or construction is evaluated by noting the presence or absence of some quality characteristic in each of the units or samples in the group under consideration and counting how many units do or do not possess this quality characteristic. The inspection does not provide information regarding the average quality level and the variability of a quality characteristic. Therefore, there generally are no clues in regard to the type of corrective action that should be taken (TRC, 2005; Chang and Hsie, 1995). 2.4.2 Variables Acceptance Plan A variables acceptance plan is a procedure where the quality is evaluated by measuring the numerical magnitude of a quality characteristic for each of the units or samples in the group under consideration and computing statistics such as the average and the standard deviation of the group. This type of sampling procedure is more suitable for developing adjusted pay schedules to deal with the intermediate levels of quality. Attribute sampling is much less efficient than variable sampling because to obtain a certain buyer's risk or seller's risk, the number of samples needed for attribute sampling may be 30% greater than the number needed for variable sampling (Weed, 1989). There are two cases in variable sampling: one where the standard deviation is known and the other where it is not known. The standard deviationknown acceptance plan is appropriate when the process has been running for some time and when a state of statistical control exists with respect to process variability. However, in most highway construction situations, the true standard deviation, c, is not known. With the standard deviation unknown (and the mean unknown), the beta distribution is used to estimate the percent within limits (PWL) of the AQC (TRC, 2005). The beta distribution is a statistical method used for modeling random probabilities and proportions. The PWL is the amount of material or workmanship determined statistically to be within a boundary or boundaries, upper and/or lower limit, commonly used to determine acceptability (AASHTO, 1996b). These methods are discussed more in detail in Chapter 4. 2.5 Pay Adjustment A pay adjustment plan is used to determine the overall pay for a submitted lot of material or construction. In order to do this, it requires that the SHA establishes a acceptable quality level (AQL) and a rejectable quality level (RQL). Work that meets the level of quality defined as acceptable is eligible for 100% payment. Work that fails to meet the desired quality level but that is not sufficiently deficient to warrant removal and replacement typically receives some degree of pay reduction (Weed, 1996a). A pay factor in the specifications is used to adjust the contractor's pay according to the level of quality actually achieved. This is either added or subtracted from the contractor's payment for a unit of work. To receive full payment or more, the contractor is required to perform all work to a standard above the AQL. In terms of statistical quality assurance methods, this is typically specified as 90% within limits. By contrast, all work at a level below the RQL is totally unacceptable and must be removed and replaced. In terms of statistical quality assurance, this is typically specified as 50% within limits (Schexnayder and Ohrn, 1997). Contractor pay incentives serve at least two objectives: (1) they encourage the contractor to construct pavements with significantly improved performance while at the same time maintaining costs at reasonable levels; and (2) they provide a rational alternative for dealing with marginally inadequate/adequate construction (Deacon et al., 2001). Under the incentive pay concept, a contractor receives a bonus as a reward for providing superior quality and has a bidding advantage over contractors with poor quality control. Although the pay adjustment approach to highway quality assurance is now widely used, there is not yet a consistency of practice regarding the magnitude of pay adjustment judged appropriate for varying levels of AQCs as seen in Figure 24. Figure 24 indicates that there are more incentive and disincentive pay adjustments for smoothness than thickness and strength. 2.6 Acceptance Quality Characteristics Acceptance quality characteristics (AQCs) are measured for acceptance purposes. The AQCs that are considered in this study are concrete slab thickness, compressive strength, and surface smoothness. These AQCs are used in this research because they are used in the American Association of State Highway Transportation Officials (AASHTO) guide specifications and are easily associated with cost. They are also single sided, which means that they consist of a maximum or a minimum value and not both. Several other quality characteristics (e.g., air content, aggregate gradation, slump, dowel placement, tie bar placement) are important but are not considered in this study. This is because there is no incentive/disincentive percent pay given in the AASHTO guide specifications. In addition, some quality characteristics such as slump and aggregate gradation are typically controlled on a conventional acceptance or rejection criteria (Diwan et al., 2003). The SHA is responsible for determining the acceptability of the material produced. Acceptance of the material is based on the inspection of the construction, monitoring of the contractor's QC Program, acceptance test results, and comparison of the acceptance test results to the quality control test results (AASHTO, 1996). The following are the three AQCs used in this research, which include an explanation of how they are measured in the construction field pertaining to AASHTO's guidelines. Concrete Slab Thickness Concrete Compressive Strength Dsincentives Only 24% Incentives Only 0%O Dsincentives Only 18% Both 10% Concrete Initial Smoothness Incentives Only 10% 6% NbneINA 40% Figure 24. State DOT Concrete Pavement Incentive and Disincentive Pay Adjustment Practices (ACPA, 1999) Incentives Only 0%/ 2.6.1 Slab Thickness AASHTO's Quality Assurance Guide Specification provides an acceptable quality level for thickness. The pavement thickness is determined from an analysis of measurements made on cores. The cores should have a diameter at least three times the maximum size of the coarse aggregate in the concrete and a length as close to twice the diameter as possible (Kosmatka and Panarese, 1988). The slab thickness at a cored location is recorded to the nearest 0.1 inch (in), as the average of three caliper measurements along the core length. The total length of the paving lane in linear feet (ft) in the highway proper will be divided into sublots of 500 feet (0.1 mile (mi)), each. A sublot of pavement represented by a core deficient by more than one inch is not accepted. Cores from the balance of the pavement sublots are analyzed to determine the average and standard deviation of the pavement thickness. When evaluated in accordance with the Quality Level Analysis, the percent within limits (PWL) shall be at least 90%. A thickness measurement for each sublot is determined by taking a number of core borings at random locations in the sublot. Thus, the thickness sample size is the sum of the number of core borings at random locations per sublot (AASHTO, 1996b; Gharaibeh et al., 2001). 2.6.2 Strength Strength is not always the most important characteristic of concrete quality, but it is the one that is most often measured. It is assumed to be indicative of the watercement ratio and, accordingly, an indicator of durability (Darter et al., 1998). There are three types of testing used to measure strength: compressive, flexural, and tensile. The computer program only focuses on compressive and flexural testing. Compressive strength testing is the most common quality attribute measured on paving projects today (ACPA, 2004a). The compressive strength of concrete pavement is determined by testing cores that are taken in the same manner as the analysis of pavement thickness but in this test a load is applied on top, see Figure 25. Two replicates are considered as one sample in a pavement sublot. The strength for each sublot sample is determined by the ASTM C39 or AASHTO T22 standard test method for compressive strength of cylindrical concrete specimens (Kosmatka and Panarese, 1988). The compressive strength average and standard deviation of a number of cylinder casts from a sample of concrete pavement from the sublot is calculated. It should be at least 28 days old but less than 90 days old when the cores are obtained. The concrete pavement is considered acceptable if the PWL is 90% or greater (AASHTO, 1996b). Figure 25. Concrete Compressive Strength Test The flexural strength for each sublot sample can be determined by two tests: the thirdpoint loading or the centerpoint loading. The flexural strength is measured by loading 6 x 6inch (150 x 15mm) concrete beams with a span length (L) at least three times the depth (d). The thirdpoint loading flexural strength test is determined by the ASTM C78 or AASHTO T97 standard test method. In this method half of the load is applied at each third of the span length, see Figure 26. The maximum stress is present over the center onethird portion of the beam. Head of Testing Machine /2 Load 1/ Load Ii d=L/3 L/3 Span Length = L Figure 26. ThirdPoint Flexural Strength Test The ASTM C293 or AASHTO T177 standard test method determines the center point loading. In this method the entire load is applied at the center span, see Figure 27. The maximum stress will be present only at the center of the beam therefore; the modulus of rupture will be greater than the thirdpoint loading (AASHTO, 1996a). The flexural strength or normalweight concrete is often approximated as 7.5 to 10 times the square root of the compressive strength (Kosmatka and Panarese, 1988). The flexural strength conversion that was used in this dissertation uses the average of nine times the square root of the compressive strength. 2.6.3 Surface Smoothness Initial pavement smoothness is a key factor in the longterm performance. The smoother a pavement is built the smoother it stays over time, resulting in lower maintenance costs, decrease in traveling costs, and more comfort and safety for the traveling public. State highway agencies recognized the importance of initial pavement smoothness in the 1960s, and began developing and implementing smoothness specifications (Smith et al, 1997). There are many devices that measure pavement smoothness such as the Mays Meter, Rainhart Profilograph, NonContact Profilograph, California Profilograph, and Straight Edge. Past national surveys indicated that the majority of state highway agencies use the California Profilograph (76%), as seen in Figure 28 (ACPA, 1999; Ksaibati et al., 1996). Head of Testing Machine Load Smd=L/3 i<. L/2 ,m , >I L/2 Span Length = L Figure 27. Center Point Flexural Strength Test The California Profilograph is a 25footlong rolling straightedge with a recording wheel at the center of the frame, as seen in Figure 29. The sensing wheel moves freely in the vertical direction and records its motion on graph paper. The recorded profile is termed a profilograph trace and is developed on a scale of oneinch equals 25 feet longitudinally and oneinch equals one inch vertically. Its measurement is a series of numbers representing elevation (AASHTO, 1996b, ACPA, 1990). Noncontact Ms Profilometer 2% N/A 2% 6% Rainhart Profilograph 8% Straightedge California Profilograph 6% 76% Figure 28. Percent of Different Measuring Devices Used in the United States REVOLVING DRUM CABLE TO PROFILE WHEEL" 4 MULTIPLE OR SINGLE RECORDER AXLE WHEEL CABLE ASSEMBLY "T FLEXIBLE SHAFT Figure 29. The California Profilograph (CalTrans, 2000) Every device measures the smoothness differently. For example, the California and Rainhart Profilographs calculate smoothness using the profile index (PI), but still the test results between them are not identical. Studies show that the California model indicates larger deviations than the Rainhart (ACPA, 1990). The Noncontact calculates RDING PEN \ CHART DRIVE MECHANISM PAPER STORAGE FLEXIBLE SHAFT WTO DRIVE UNIT \ RECOIL SPRI NG smoothness with another method called the International Roughness Index (IRI) (Smith et al., 2002; ACPA, 2002). 2.6.3.1 Profile index A PI is a summary number calculated from the many numbers that make up a profile. A large majority of States (39 out of 50 total) used the profile index with a blanking band (BB) of 0.2 inch (Plo.2) (5 mm, PIs) to calculate the smoothness (ACPA, 2004b). One advantage is that any valid profiler can measure a PI. A blanking band is a plastic scale 1.7 inches wide and 21.12 inches long representing a length of 0.1 miles on the profilograph trace (one inch equals 25 feet horizontal scale). Figure 210 shows an example of a California Profilograph reading with a Plo.2nch of 8 in/mile (Waalkes, 2001; ACPA, 1990). A satch Line A Lines scribed 0.1" apart on plastic scale Blanking Band 0.2" A 00 2/10 A 12.12" = 0.1 mile (Horizontal Scale 1" = 25')  Match Line 0.5/1 1/1u 0.5/1 i A Total count for this segment (0.1 mile) is 8 tenths (PI0 = 8 inches/mile) Figure 210. California Profilograph 0.2inch Blanking Band Trace (ACPA, 1990) On each side of this band are parallel scribed lines 0.1 inches apart that serve as a scale to measure the size of deviations of the profile line outside an opaque band that is located at the midpoint of the running length of the BB. These deviations are known as scallops shown in Figure 211 A. An advantage of the BB is that it helped engineers and contractors calculate the profile index quickly and accurately. A twotenths inch BB was initially used to ignore the bumps within 0.2inch of the average. Some SHAs have moved away from the 0.2inch BB because it can hide bumps that cause surface chatter, which can be annoying to the driving public. In this case, they have moved toward the 0.0inch BB (the middle line in the opaque strip) or the 0.1inch BB (Waalkes, 2001; ACPA, 1990). Short portions of the profile line that are visible outside the BB are not included in the count unless it is 0.03 inch or more on the profilograph trace as seen in Figure 211 B. There are also some special conditions where the profile line is not included in the count. If the profilograph encounters rock or dirt on the pavement, the profile line creates a spike that is not included in the count. In addition, doublepeaked scallops that do not go back into the blanking band are only counted once at the highest peak. These special conditions are shown in Figure 211 C and D (ACPA, 1990). 2.6.3.2 International Roughness Index An International Roughness Index (IRI) is a number computed from a profilograph trace that is measured by a laser instead of a wheel riding on the surface. Almost every automated road profiling system includes software to calculate this statistic. IRI was developed and tested by the World Bank in the 1970s through the 1980s. Some devices that use the IRI are known as noncontact profilometers (e.g. Lightweight and High Speed Profilers). They consist of an integrated set of vertical displacement sensors, vertical accelerometers, and analog computer equipment mounted in a vehicle equipped with distancemeasuring instrument that can be operated at certain speeds, see Figures 2 12 through 213. The Lightweight and HighSpeed Profilers are able to measure the smoothness traveling at higher speeds than the California Profilograph. (AASHTO, 2004). The HighSpeed Profiler uses the inertial reference system, which measures and computes longitudinal profile by using accelerometers placed on the body of the measuring vehicle to measure the vehicle body motion. The relative displacement between the accelerometer and the pavement profile is measured with either a "contact" or a "noncontact" sensor system (Sayers and Karamihas, 1998). Typical Condi Scallops are shown in the cross hatched sections d m U II II_ Rock or dirt on the pavement (not counted) Small projections that are not included in the count ....... ... ... ""  .. ,,r 4 II Special Conditions Double peaked scallop (only highest part counted) Figure 211. Types of Profiles from Profilograms (AASHTO, 2004)  rr I  ~ ~~   3 _~ il ~II Computer Laser Figure 212. Lightweight Profilometer (Sayers and Karamihas, 1998) Computer S3. Speed Distance 1. Inertial Accelerometer 2. Height relative to reference (laser, optical, or ultrasonic sensor) Figure 213. HighSpeed Profilometer (Sayers and Karamihas, 1998) IRI may also be expressed in inches per mile. There is only a small percentage of SHAs that are using NonContact Profilometers. Even though they are the state of the art, there have been studies that indicate most profilometers do not do a very good job of measuring smoothness on coarse concrete textures. The problem is that the profilers pick up the texturing which a car cannot feel, thus giving a higher number that is not accurately reflective of the pavement's smoothness. There is continuing research on new profilers that can do multiple traces and compute both IRI and PI values (AASHTO, 2004). 2.6.3.3 Comparison of Profile Index with International Roughness Index The use of inertial profilers has remained limited in initial construction acceptance testing due to their higher cost and constraints on timeliness of testing. Thus, in many agencies, initial pavement smoothness has been measured one way (PI) and smoothness over time has been measured another way (IRI). The research reported in this dissertation included both PI and IRI. The PI was included because of the majority of SHAs still use the California Profilograph device, and because it is specified in AASHTO's specifications. IRI calculations were included because it is evident that IRI will become the statistic of choice in future smoothness specifications (Smith et al., 2002). Although both indexes relate well to highway user response to roughness, their correlation to each other is not as strong because different roughness components (e.g., bumps and dips) are amplified or attenuated in computing each index. Studies show that the most significant differences between the two relate to the reference profiles from which the two indexes are computed, the type of sensors used, and the degree and type of wavelength filtering (moving average or thirdorder Butterworth) performed to produce the index values. Various studies have also found that the correlation of PI and IRI becomes progressively higher with the application of smaller and smaller BB widths (Hoerner et al., 2000). The LongTerm Pavement Performance (LTPP) program established the relationship between IRI and three different variations of the PI statistic: PI0.2inch (PIsmm), PI0.1inch (PI2.5mm), and PIo.o. As mentioned above, the research reported in this dissertation applies to the AASHTO guide specifications, which only specify Pay Factors (PF) for PIo.2inch. Based on a standard filtering routine (2.5ft [0.76m] moving average smoothing filter) and the application of the three different variations of the PI statistic, the PItoIRI conversion equations were developed as seen in Table 21 (FHWA, 1993; Hoerner et al., 2000). Table 21. Summary of IRIPI Relationships with a 2.5ft (0.76m) Moving Average Smoothing Filter Linear Regression Equation In/mile m/km IR = (2.625 x PIO 2 ,,h )+ 75.541 IRI = (2.625 x PI5 m) +1.192 IRI= (2.240 x PIo inh) + 58.163 IR= (2.240 x P25 m) +0.917 IRI = (2.233 x PIo ) + 25.557 IRI = (2.233 x PI))+ 0.403 2.7 Diamond Grinding Diamond grinding is a concrete pavement restoration technique that corrects irregularities such as faulting and roughness on concrete pavements. It is a costeffective treatment. On the average, it costs between $1.70 and $6.70 per square yard ($2.00 and $8.00 per square meter). An increase in the cost can depend on many factors including aggregate, PCC mix properties, average depth of removal, and smoothness requirements. As the increased competition in diamond grinding grows and as diamond blade performance improvements are made, the lower the cost (Correa and Bing, 2001). Because of the minimal cost associated with spotgrinding new pavements, (in comparison to overall construction costs), this research does not take into account the cost of spotgrinding any identified rough locations that the contractor needs to correct as required by the AASHTO guide specifications. 2.8 Related Research To control the quality of construction, highway agencies have developed quality assurance methods or programs based on statistical sampling and procedures to ensure that the work is in accordance with the acceptance plans and specifications. The current method used today by many SHAs is embodied in AASHTO's guide QA acceptance plans. As mentioned throughout this chapter, those plans only evaluate concrete pavement thickness, strength, and surface smoothness. A computer simulation software program, COMPSIM, was developed on Quality Management to provide guidance on the use of practical and effective quality assurance procedures for highway construction projects. This program does the following: * Analyze both pass/fail and pay adjustment acceptance procedures * Construct operating characteristic curves * Plot control charts * Experiment with computer simulation * Perform statistical comparisons of data sets * Demonstrate the unreliability of decisions based on a single test result * Explore the effectiveness of stratified random sampling (Weed, 1996b). The program employs PWL as a quality measure but it does not allow the user to work with more than one AQC at the same time. In other words, it only calculates one PF at a time. A pay adjustment factor assigns a pay in percentage for the estimated quality level of a given quality characteristic (TRC, 2005). A method was developed for analyzing risks and expected profit associated with PRS. The method was applied to a concrete paving project on 1295 in Jacksonville, Florida under Level A (simplified level) PRS. The method was based on Monte Carlo Simulation and probabilities. The specifications did not use PWL as a quality measure, and the method did not go so far as to consider the effect of the composite pay equation. In addition, it did not simulate enough samples for each AQC to get a close enough output every time it was simulated (Gharaibeh et al., 2002). This research became an excellent starting point from which to make modifications and improvements necessary to meet the needs of contractor and SHAs working under the AASHTOtype QA specifications. The Innovative Pavement Research Foundation (IPRF) developed a methodology for comparing the impact of various PCC pavement design features on cost and performance. In addition, a computer software tool was developed for comparing and evaluating tradeoffs in assessing the relative performance benefits and costs of various PCC design features. Questionnaires were sent out to concrete contractors and SHAs to collect cost and performance data for the computer software tool that was developed (Hoerner et al., 2004). The IPRF strength cost data was used in this research because the smoothness costs that were gathered from the questionnaires from this research were not deemed to be as accurate. These three developed methods (Weed's, Gharaibeh's, and IPRF's) taken separately each serve different purposes. Together however, they became an excellent starting point from which to make modifications and improvements necessary to meet the objectives identified in this dissertation. CHAPTER 3 DATA COLLECTION AND ANALYSIS 3.1 Introduction Due to the many variables in concrete pavements, it is difficult to establish the exact cost associated with individual AQCs. The cost of thickness and strength depends on the cost of the material used (e.g., cement, aggregate, sand, admixtures, water, ground granulated blastfurnace slag, and fly ash). The cost of smoothness depends primarily on the time and effort taken to make the pavement smoother. Since cost depends on many variables (such as the equipment, materials, and procedures the contractor uses) it can be difficult to achieve the same cost in different projects. On any given project, however, if one disregards the effect of inspection, the following can be said: an increase in the contractor's target quality level increases the initial construction cost, and a decrease in the contractor's target quality level decreases the initial construction cost. A data collection effort was required to obtain information necessary to assess the cost associated with individual AQC quality. This chapter describes each of the primary data collection activities and how the collected data were used to develop the software program. 3.2 Questionnaire Development Once concrete pavement AQCs were identified, questionnaire surveys were developed. A request for participation along with the questionnaire was electronically mailed, snail mailed, or faxed to 50 SHAs and 40 PCC Contractors. The purpose of the questionnaire was to better understand: The degree to which contractor's consider construction quality in their bid strategy The SHA's cost estimating procedures How SHAs and concrete contractors price quality There were two similar questionnaires, one for contractor respondents and one for SHA respondents. Each questionnaire was divided into two parts. The first part contained questions about bidding decisions and cost estimating procedures. The second part was designed to discreetly obtain AQC cost information with respect to Jointed Plain Concrete Pavement (JPCC). There are different types of concrete pavements such as Jointed Reinforced Concrete Pavement (JRCP) and Continuously Reinforced Concrete Pavement (CRCP) but the majority of the SHAs build JPCPs (68%), Figure 31 (ACPA, 1999). 80% 70% 60% 50% 40% 30% 20% 10% 0% JPCP JRCP CRCP Figure 31. Concrete Cement Pavement Types Built A JPCP is shown in Figure 32. The joints are usually spaced at intervals of 1323 feet (47 meters (m)), although some specifications require a maximum spacing of 15 feet (4.6 m), such as this case (Atkins, 2003). Overhead View Side View Epoxy Coated Dowel Bars (Embedded at Transverse Joints) Figure 32. Jointed Plain Concrete Pavement Overhead and Side Views (ACPA, 2005) The questions in the second part of the questionnaires related to the following JPCP construction situation: * Four lane highway divided * Five mile length, few horizontal and vertical curves * New construction, no traffic control * Rural area * Epoxy coated dowels * 15 feet transverse joint spacing * Standard thickness used in the state * Standard strength requirement used in the state * Standard smoothness requirement used in the state * Routine bidding situation for contractor (e.g., typical number of competing contractors, contractor is neither desperate for work nor overloaded with work, etc.) The concrete contractors and SHAs were asked to answer cost questions based on the assumption that the above pavement construction situation was applicable. Moreover, they were asked additional information on the tests and/or machines used for each AQC. The survey participants were then asked to assess the change in costs for improvements in strength, thickness, and smoothness quality levels so the relationship between quality and cost could be determined. Both questionnaires were structured so that only one design AQC was changed at a time. For example, one of the scenarios was to increase the concrete pavement strength by an additional 1,000 pounds per square inch (psi) (7 megapascal (Mpa)) from the specified strength that was the state standard for JPCP construction. The subgrade and type of materials (e.g., soil, aggregate, etc.) used were not considered in this research. This research dealt only with the quality characteristics of the concrete pavement slab. If the respondents had no experience or if a question did not apply to them, they were asked to answer "Don't know" or "Not applicable." This was also useful information because it shed light on which party knows more about the cost associated with AQCs. It also showed which AQCs were relatively easier to relate to cost. Although the questionnaires were separate surveys, the questions that pertained to concrete pavement quality and cost were identical. A copy of the questionnaires along with detailed answers from both the concrete contractors and SHAs can be found in Appendices B and C. 3.2.1 Concrete Contractor Respondents A total often responses, 25%, were received from the participating PCC paving contractors. Despite an effort to increase the response rate, this is a low, but not unexpected, number of concrete contractor respondents. All the responses (SHAs and concrete contractors) will be taken as a whole. Out of the respondents, 70% participated and 30% did not want to participate or do not have enough data to complete the questionnaire. PCC paving contractors providing responses to the questionnaire surveys included contractors from the following states: Colorado, Indiana, Iowa, Kansas, Louisiana, Ohio, and Oklahoma. 3.2.2 State Highway Agency Respondents Out of the 50 SHAs, only 52% responded, and out of the respondents 77% participated and 23% said that they did not have enough data to complete the questionnaire or they do not construct any PCC pavements. The SHAs that provided data for to the questionnaire survey included: California, Delaware, Florida, Idaho, Illinois, Indiana, Iowa, Kansas, Louisiana, Maryland, Missouri, Nebraska, Nevada, Oklahoma, South Carolina, South Dakota, Virginia, Washington, West Virginia, and Wisconsin. 3.2.3 Desired Number of Acceptance Quality Characteristics Cost Responses A statistical evaluation was performed to determine the desired number of questionnaire responses required to have a reasonable estimate of the change in cost for each AQC increase. In determining the desired sample size, it is assumed that the total population has a normal distribution. The purpose of the questionnaires is to estimate the average of the population, or more specifically, the average incremental change in cost of an AQC given incremental changes in the AQC quality level. The following equation is often used to determine sample size (i.e., number of respondents needed in a questionnaire survey) (Kopac, 1991). n = (31) Where y = population standard deviation za/2 = number of standard error units (based on the desired confidence level and obtained from a normal probability table) T= required precision or tolerance In this evaluation, the standard deviation is estimated from the original data. Furthermore, three desired confidence levels and four desired precision levels are selected. By running a range of values with an initially assumed, reasonable average, the effect these inputs have on the resulting number of samples can be determined. For the purposes of estimating the number of samples, the analyses for the cost taken from the questionnaires are broken out separately. The change in incremental cost considered the three basic questions: 1. What would be the estimated cost ($/yd2) for the paving if the average thickness requirement is 1 in (25.4 mm) more than was initially assumed? 2. What would be the estimated cost ($/yd2) for the paving if the average strength requirement is 1,000 psi compressive strength (or 237 psi flexural strength) more than was initially assumed? 3. What would be the estimated cost ($/yd2) for the paving if the average smoothness requirement is 2 in/mile (PI0.2in) (IRI = 80.8 in/mile, PI = 31.75 mm/km. IRI= 84.5 mm/km) better than was initially assumed? Table 31 shows that for greater precision, and/or higher confidence levels, more cost responses (n) are needed. As indicated above, each standard deviation was estimated from the raw data to make a determination of whether the number of respondents resulted in sufficient precision and confidence levels. The desired number of respondents believed to be sufficient is indicated in bold text. This research uses a 95% confidence level and a precision level of $0.5/yd2 ($0.6/m2) for thickness. A lower precision was used for thickness because it is a more costly AQC due to more materials (e.g., cement, aggregate, sand, fly ash, etc.) used to achieve a higher thickness. Therefore, assuming these, a minimum of 14 respondents is desirable for the thickness cost portion, Table 31. This was met, having 20 responding to the change in thickness cost. A 95% confidence level and a precision level of $0.3/yd2 ($0.36/m2) were used for strength. A higher precision than thickness was used for strength. This is because increasing strength is less costly than increasing thickness. Less material is used to increase strength than to increase thickness. For example, one way to increase compressive strength by 500 psi (201 psi flexural strength) is by adding 47 pounds of cement at $0.04 per pound, which would only cost $1.88 per cubic yard (Smith, 2005). Therefore, assuming 95% confidence level and a precision level of $0.3/yd2 ($0.6/m2), a minimum of 13 respondents is desirable for the strength cost portion, Table 31. There were only 10 respondents that gave a change in increase compressive strength cost. This was short by three respondents. The costs associated to each increase in AQC were compared with another report. Even though a sufficient number of responses was obtained at the 90%ile confidence level for the strength portion, there was not good agreement with the IPRF study (Hoerner et al., 2004). For smoothness, a 95% confidence level and a precision level of $0.2/yd2 ($0.24/m2) was used for surface smoothness. A higher precision was used for smoothness because it is the least costly of the three AQCs as there is no need to add material to make a pavement smoother. Therefore, assuming these, a minimum of 11 surveys is desirable for the smoothness cost portion, Table 31. This was met, having 12 responding to the change in thickness cost. This simply means that the standard deviation of the means of 12 data points are lower than certain specified levels. 3.3 Contractor's Bidding Decision Making This survey concentrated only on concrete contracting firms that produced from as low as $5 to $20 million per year to as high as $100 to $500 million per year of PCC work. Contractors' bidding behaviors are affected by numerous factors related to specific features of the project and dynamically changed situations. These can make decision problems highly unstructured. There are also many risks involved in bidding decisions. Most of the findings of this survey on bidding decisions are not unexpected, but some of them are important and need to be emphasized. In order to obtain more information on contractor's bidding decisions, the questionnaire focused on questions pertaining to risk and competition. Many contractors use certain methods or techniques to assist them in winning the bid. Through the questionnaire, it was found that 43% of the contractors use a formal method to assist them in submitting a winning bid. One of the methods mentioned that was used was Oman Systems. Oman Systems is an estimating software that also includes Bid Tabs Professional and Pro Estimate. These software programs provide accurate and detailed project information, analyze projects to make better decisions and limit the risk of miscalculating or leaving an item out (Oman Systems, 2005). The majority of the contractors (57%) stated that they do not have a formal method to assist them in winning a bid, Figure 33. All of the contractors that responded use a unit price contract for PCC pavement work. In this contract, the price is charged per unit for the major elements of the project. This consists of a breakdown of the work and estimated quantities for each of the items (Gould, 2002). To consider how concrete contractors consider uncertainty or risk in pricing concrete pavement elements, the following two questions were asked: * How would you handle the uncertainty of pricing quality for JPC pavements while working on the bid? * How do you consider job related contingency? The questionnaire revealed that 42% considered uncertainty by adjusting a markup and 29% considered uncertainty by applying a correction factor on a certain quality factor, Figure 34. The remaining 29% stated that the money would be figured into the bid for quality and escrowed for the duration of the warranty or that they will not bid if uncertain about anything. 60% 50% 40% 30% 20% 10% 0% Yes No Figure 33. Percent of Contractors that Use a Formal Technique to Win a Bid Table 31. Summary of the Required Number of Samples for Relative Incremental Cost for Each AQC Calculated a change in cost ($/yd2) Number of Required Samples 90% Confidence 95% Confidence 99% Confidence (z = 1.645) (z = 1.96) (z = 2.58) Precision of Average Cost Precision of Average Cost Precision of Average Cost Estimate (T) ($/yd2) Estimate (T) ($/yd2) Estimate (T) ($/yd2) within within within within within within within within within within within within 0.5 0.4 0.3 0.2 0.5 0.4 0.3 0.2 0.5 0.4 0.3 0.2 Slab 150.65 slab 0.95 9.80 15.31 27.22 61.24 13.91 21.74 38.64 86.94 24.10 37.66 66.96 Thickness Compressive Compressive 0.53 3.07 4.80 8.53 19.19 4.36 6.81 12.11 27.24 7.55 11.80 20.98 47.21 Strength Surface 0.34 1.22 1.90 3.38 7.60 1.73 2.70 4.79 10.79 2.99 4.67 8.31 18.69 Smoothness In addition, the majority of the contractors (57%) stated that they would charge contingency an additional cost item, Figure 35. All these are methods that take uncertainty and risk into consideration. Since risk is a major factor in pricing quality, it was added into the computer program as a percentile since there are different levels of risks (e.g., high risk taker, neutral, low risk taker). Other Correction Factor 29% 29% Markup 42% Figure 34. Method used to Handle Uncertainty in Pricing Quality in JPC Pavement Both (depending on project) 14% Included in the Markup 29% Charged as a Cost Item 57% Figure 35. Method used for Job Related Contingency 3.4 State Highway Agency's Cost Estimating Procedures SHAs use different methods to calculate cost estimates for a project. It was found through the questionnaire that the majority of the SHAs (61%) use a statewide database to calculate the estimated cost for a concrete pavement project. Figure 36 shows the methods used by SHAs to calculate costs for JPC pavement projects. Only 13% stated that they use a district wide database. The remainders 26% use the following methods: * Complete Analysis Method: This method calculates production rates, labor costs, and material costs. It may be used individually or in combination with the Statewide and Districtwide database method. * Worksheet: A normal worksheet that calculates local labor costs, local material costs, and etc. * Historical Prices * Phone surveys: Estimates based on actual costs from phone surveys with suppliers. 70% 60% 50% 40% 30% 20% 10%  0% Statewide Database Districtwide Database Other Figure 36. Method Used to Calculate Cost for Jointed Plain Concrete Cement Projects It was found, through the questionnaire, that the majority of SHA's (95%) cost estimation procedures are independent of the quality requirements. Figure 37 shows the percent of the cost estimating procedures used by SHAs that are independent or dependent of quality. Only 5% of the SHAs responded that the cost estimating procedure allows the estimator to differentiate costs with respect to quality. This indicates that SHAs are not sufficiently aware of the cost of quality. Higher cost does not necessarily mean higher quality. 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Independent Dependent Figure 37. Cost Estimation Procedures that is Independent/Dependent of Quality 3.5 Concrete Pavement Acceptance Quality Characteristics Change in Cost This research used both concrete contractor and SHA questionnaire responses to calculate the average cost associated with AQCs in PCC pavement. The questionnaire responses showed that concrete contractors have a better understanding of the cost of quality than do SHAs, see Figure 38. They also showed that SHAs have a better understanding of pricing thickness and smoothness than strength. An initial review of the data indicated that an inch (0.0254 m) increase in thickness could increase the cost of paving by 5%. The questionnaire shows that an increase of 1,000psi compressive strength (284 psi flexural strength or 7 MPa) can increase the cost of paving by 3%. 100%C. 90%/c. 80'/c. 70'/c. U 60/6% 50 0c. (D 40% 00 ( 30%/c. 20% 100/% SHAs Concrete Contractors Thickness U Strength U Smoothness Figure 38. Understanding of Cost Associated with Incremental Change of AQC An improvement in smoothness (i.e., a decrease in PI or IRI) does not require a major increase in total paving costs. The questionnaire responses showed that a one in/mi (16 millimeter/kilometer (mm/km)) improvement in smoothness can increase total paving costs by 1%. Table 32 shows the average incremental AQCs that were analyzed from the questionnaire with the original incremental change in cost for each AQC. The AQCs that are located in the center of the first, third, and fifth columns (eg., 10.9 in, 3,825 psi, and 5.71 in/mi) are considered the average design values from the questionnaire responses. Each design value equals a change in cost of zero percent. As the design value increases or decreases, the percent change of cost also increases or decreases. For example, a thickness of 9.90 inches (a difference of one inch less from the design value) yields a percent change in cost of 6.16%. As mentioned before, the number of respondents to estimate strength cost data was not as high as desired. Since the change in cost for compressive strength was questionable (due to obvious misinterpretation of the strength questions by several respondents), cost data from the IPRF study (Hoerner et al., 2004) were used. Table 33 shows the final average incremental AQC values and costs that were used in this dissertation. The summarized cost data served as the "default" database for use in evaluating the relative cost of each concrete pavement design AQC. They can be considered as typical within the United States. A summary of the raw relative cost data collection from SHAs and Concrete Contractors is provided in Appendix D of this dissertation. Table 32. Average AQCs and Incremental Change in Cost from Respondents Compressive Surface Thickness A Cost Compressive A Cost Surface A Cost (in) (%) Strength () Smoothness (psi) (in/mi) 8.90 12.34 2,825 7.27 3.79 2.51 9.90 6.16 3,325 3.55 4.71 0.81 10.90 0 3,825 0 5.71 0.00 11.90 6.16 4,325 3.55 6.71 0.81 12.90 12.34 4,825 7.27 7.71 2.51 Table 33. Average AQCs and Revised Incremental Change in Cost (in SCompressive Surface ( Thickness A Cost Compressive A Cost Surface A Cost SStrength Smoothness (in) (%) .S (%) (%) (psi) (in/mi) 8.90 12 2,825 2 3.79 2 9.90 6 3,325 1 4.71 1 10.90 0 3,825 0 5.71 0 11.90 6 4,325 1 6.71 1 12.90 12 4,825 2 7.71 2 CHAPTER 4 STATISTICAL AND MATHEMATICAL METHODS UNDERLYING TARGET QUALITY IN HIGHWAY CONCRETE CONSTRUCTION 4.1 Introduction At the start of the AASHTO Road Test, concrete thickness, strength, surface smoothness, and many other construction measures were found to vary widely about their target values. Construction data was illustrated in the form of the bellshaped normal distribution curve. The Road Test was the Impetus for highway engineers to learn to understand the statistical principles associated with construction process. Today, construction specifications developed are based on statistical concepts. The purpose of this chapter is to present an overview of the mathematical and statistical concepts related to acceptance plans for quality assurance specifications. 4.2 Variability Measures in PCC Pavements All materials and construction are not exactly the same because they are subjected to a different variability. The variations could be natural and occur randomly, which most specifications allow. However, variations resulting from poor process control (e.g., equipment, materials, or construction errors) are undesirable and will penalize the contractor by deducting a percentage of his/her payment depending on the amount of variation. In order to use variability data properly in specifications, it is important to understand the ways variability is measured (Hughes, 1996). Extensive research has concluded that numerous measurements that occur in highway construction distribute themselves about some average value with the majority of the measurements grouped near the mean and with progressively fewer results recorded as one proceeds away from the mean. This describes the normal distribution (bellshaped curve), which is the most important probability distribution for highway construction and materials. The normal distribution is useful in the analysis of acquired data and in providing inferences about the population from sample data. It is defined by two parameters, the mean value and the standard deviation. Samples are intended to represent the population Samples can also range from very large to very small. The closer the sample size gets to the population size, the more likely the sample statistics will be representative of the population statistics (Chiang, 2003; Ott, 1993). The population mean (.i) is the average value that determines the xaxis location of the normal distribution. The population mean can be obtained by summing all the values (xl+x2+... x ) in a data set and dividing it by the number of values (N) as follows (Ott, 1988): N /P=1 (41) N The population mean is usually unknown and can be estimated by the sample mean (7). It is calculated from the following equation, where n is the number of values in the sample. n x = (42) n The other useful parameter is the population variance (c2). It measures the variability or the spread of a data set. For example, a small variance indicates a tight data set with little variability, and vice versa. The population variance is calculated using the following equation (Walpole and Myers, 1985): N (x, )2 o_2 = z=1 (43) Nl When the variance is computed in a sample, it is calculated using Equation 44. N Z(x~ )2 S2 z= 1 (44) nl Typically, it is the square root of the variance that is calculated. The square root of the population variance is the population standard deviation (o). The standard deviation determines the height and width of the normal distribution. It measures the variability of data in a population. It is usually and unknown constant and is calculated as follows: n (x, )2 s 7= = _ (45) nl The sample standard deviation (s) measures the variability of data in a sample and is calculated using Equation 45 (Chiang, 2003). N N1 V=1  (46) 4.3 Quality Measures There are several quality measures that can be used. In past acceptance plans, the average deviation from a target value was often used as the quality measure. However, the use of the average alone provides no measure of variability. Several quality measures that have been preferred in recent years because they simultaneously measures both the 49 average level and the variability of AQCs are refereed as percent within limits (PWL), also called percent conforming, and percent defective (PD) (Burati et al., 1995). 4.3.1 Percent Within Limits The PWL is the percentage of the lot falling above the lower specified limit (LSL), below the upper specified limit (USL), or between the specified limits, as seen in Figure 41. PWL may refer to either the population value or the sample estimate of the population value. The PWL quality measure uses the mean and standard deviation in a normally distributed curve to estimate the percentage of population in each lot that is within the specified limit (TRB, 2005). LSL ,. r V PWL I J a USL I I I I I II SPD Figure 41. Percent Within Limits. LSL = Lower Specified Limit, USL = Upper Specified Limit, PD = Percent Defected, PWL = Percent Within Limits In practice, it has been found that statistical estimates of quality are reasonably accurate provided the sampled population is at least approximately normal (i.e., bell shaped and not bimodal or highly skewed). The PWL is calculated using the following equation: PWL, =100PD 1 B(a,f ) 0.5 QL, (2(N x1100 (47) F(2(N 1)) Where PD = percent defected B(a, ) = beta distribution with parameters a and P (a,f) = shape parameters of the distribution QL, = lower quality index for an AQC N = number of samples per lot Unlike the normal distribution, which is a single distribution that uses the zstatistic parameter to calculate areas below the distribution, the beta distribution is a family of distributions with four parameters alpha (c) and beta (3). The PWL calculation uses the symmetrical beta distribution. For symmetric distributions, the alpha and beta are the same. Figure 42 shows three examples of a symmetric beta distribution. As a and 3 values increase the distributions become more peaked. The uniform distribution has alpha and beta both equal to one. This does not have a welldefined mode because every point has the same probability. Distributions with alpha and beta less than one are bathtub shaped curves and generally not useful for statistical modeling (Ramanathan, 1993). 4.3.2 Quality Index The Qstatistic, also referred to as the quality index (QI) performs identically the same function as the zstatistic of the normal distribution except that the reference point is the mean of an individual sample instead of the population mean. In addition, the points of interest with regard to areas under the curve are the specification limits: LSL and the USL (Burati et al., 1995). 51 .Or k 0 1 ':/ ; "," Uniform I .  S L / 4 Q \ Q^   IIt  0 I I I I I ! 0 0 Q 0 0 0 O 0 Figure 42. Three Examples of Symmetric Beta Distributions The USL and LSL are the limiting value or values placed on an AQC for evaluating material or construction within the specification requirements. In this research only one limiting value was needed. The reason is that the AQCs used in this research are single sided and not double sided. Singlesided AQCs consist of a maximum or a minimum value and not both. The only specification limit specifically identified in the AASHTO QA guide specifications is the LSL for the slab thickness. It suggests the following equation (AASHTO, 1996b): LSLDesign Thickness = DV 0.2 inches (48) The AASHTO QA guide specifications do not suggest a LSL equation for concrete strength. It is up to the contractor and SHA to choose the lower specified level for strength. For surface smoothness the guide specifications do not use the PWL to calculate the payadjusted factor. Instead, the individual smoothness measurement (an average between two wheel paths) is used to determine pay adjusted factor values that are specified by AASHTO (AASHTO, 1993). For doublesided AQCs (such as asphalt content or air voids), the quality index consists of an upper (Qu) and lower (QL) quality limit. (USL (4)9) QU (49) s (X LSL) QL (Y LSL) (410) s As discussed above, this research addresses only onesided AQCs but it can be extended without too much difficulty to the twosided AQCs that are more prevalent in asphalt concrete pavement. A table relating quality index values with the appropriate PWL estimate is shown in a table for various sample sizes from N = 3 to N = 30, see Appendix A (AASHTO, 1996b). 4.4 Pay Adjustments In highway pavement construction, an AQC may fall just short of the specified quality level. It may not be acceptable but neither does it deserve 100% payment. This provides the DOT with a decision point at which to exercise its option to require removal and replacement, corrective action, or the assignment of a minimum pay factor for the lot. Therefore, a pay adjustment factor (PF) in the specifications is used to adjust the contractor's pay according to the level of quality achieved. A pay adjustment factor is the percentage of the bid price that the contractor is paid for the construction of a concrete pavement lot. A PF is calculated for each AQC (Darter et al., 2003; Hughes, 1996). 4.4.1 Pay Factor A PF is a multiplication factor expressed as a percentage used to determine the contractor's payment for a unit of work. It is based on the estimated quality of work and applies to only one quality characteristic (TRC, 2005). Slab thickness and strength have the same quality measure (i.e., the PWL). These two AQCs also use the same equations below (Equation 411 and 412) to calculate their PF. If the PWL is over 60%, which is most often the case, then Equation 412 must be used. A PWL of 60%, however, may be the cause for rejection. In this case, AASHTO specifies that the agency's engineers make a special evaluation of the material to determine whether it is to be rejected or whether to accept it at considerably reduced pay (AASHTO, 1996b). In this research, Equation 412 was used for an AQC with a PWL less of 60%. The assumption was made that concrete pavement is rejected 25% of the time when the PWL is less than 60%, and the other 75% of the time it is accepted at a reduced PF in accordance with Equation 411. The following pay adjustment equations were used in this research: IfPWL > 60 Then PF = 55 + (0.5 xPWL) (411) IfPWL < 60 Then PF=0.75[55+(0.5xPWL)] (412) As seen from Equation 411, if the percent of test results within the specification limits is equal to 90% for a lot, then the contractor's PF is 100%. Therefore the contractor receives 100% payment for that concrete AQC for that lot. If the percent of test results within the specification limits is greater than 90%, then the contractor's PF is greater than 100% and the contractor receives greater than 100% payment for that concrete AQC for that lot. The contractor receives a bonus when the PWL is greater than 90%. The maximum PF that can be achieved for 100% of test results within the specification limits is 105% (i.e. a 5% bonus in payment). Mathematically, the pay factor equation would generate a pay factor of 55% if there were zero percent of test results within the specification limits. However, the state highway agency's specifications have clauses that deal with low pay factor material. If the PWL is between 60% and 90%, then the contractor receives a penalty. It is up to the agency to reject or further reduce pay when the PWL is lower than 60% (AASHTO, 1996b). For smoothness, on the other hand, the PF results are based on a California profilograph (0.2 inch BB) traversing at a speed no greater than three miles per hour. The price adjustment for smoothness is shown in Table 41. Table 41. AASHTO Price Adjustment Factors for Smoothness Index Profile x P Price Adjustment (PIO.2inch) r Me p Percent of Pavement Unit Inches per Mile per Bid Price 0.1Mile Section ( (%) 3 or less 105 Over 3 to 4 104 Over 4 to 5 102 Over 5 to 7 100 Over 7 to 8 98 Over 8 to 9 96 Over 9 to 10 94 Over 10 to 11 92 Over 11 to 12 90 Over 12 Corrective work required AASHTO states that when the PIo.2inch is greater than 5 inches per mile but does not exceed 7 inches per mile per 0.1mile section, payment will be made at the contract unit price for the completed pavement. When the PIo.2inch is greater than 7 inches per mile but does not exceed 12 inches per mile per 0.1mile section, the Contractor may accept a contract unit adjusted price in lieu of correcting the surface to reduce the PI0.2inch. When the PIo.2inch is less than or equal to 5 inches per mile, the contractor is entitled to an increase in payment or profit (AASHTO, 1993). 4.4.2 Composite Pay Factor The ultimate performance of most construction items is dependant upon several characteristics. Statistical construction specifications based on multiple AQCs use payment equations that include a separate term for each of the AQCs so that the resultant payment adjustment is a function of the combined effect of all quality measures. A composite factor (CPF) considers two or more quality characteristics and is used to determine the contractor's final payment for a unit of work (TRB, 2005; Burati et al., 1995). There are four different methods to calculate the composite pay factor pay factor: Weighted Average (CPFwAve), Averaging Method (CPFAve), Summation Method (CPFsum), and the Product Method (CPFProd): Z(PI xWt,) CPFA =' x100 (413) (Wt ) 1=1 n PF, CPFAe = ' x 100 (414) n CPFs, = [f(P 1)+ x1100 (415) CPFProd = (PF x PF2 x...PF) x 100 (416) The CPFwAve method is different than the rest of the CPF equations because it considers a respective weight (Wtn) for each PF. The value of each weight is determined through empirical observation or other engineering considerations. None of these methods is considered more correct than the other. There are many perspectives with regard to the actual value added for various quality attributes and their interrelationships are not completely understood (AASHTO, 1996a). A cap is placed in order to put a limit on the highest CPF percentage a contractor can achieve. A CPF equation often includes a cap to define the minimum and/or maximum CPF allowed. The default cap that was used in this research was a cap of 108%. Therefore, when the calculated CPF exceeds the cap, the contractor receives only 108% payment. 4.5 Methods for Selecting Target Quality Contractors are responsible for concrete pavement projects. Therefore, it is up to the contractors to establish a target quality level, target value, for each design (D) AQC value specified. According to Transportation Research Circular EC074 (TRC, 2005): "A target value is a number established as a goal for operating a given process. Once it is established, adjustments should be made in the process as necessary to maintain a central tendency about the target value. The target value for a quality characteristic is established by the contractor based on economic considerations. It may not be the same as the agencyestablished design value (obtained from structural or mixture design, or both) or the specified AQC value." It is necessary for contractors to maintain a central tendency about the target value. There are two types of approaches in selecting target values: deterministic and probabilistic. 4.5.1 Deterministic Method The most common method employed by contractors to establish target quality levels under QA specifications will be referred to as the deterministic method. The deterministic method is more of a mathematical thought process than a formal recognized method. Deterministic methods have predictable and repeatable inputoutput relationships. They contain no random variables. Contractors who use the deterministic method often rely greatly on engineering judgment, intuition, and their past experience with the specifications to set target quality levels for specific projects. The deterministic method is based on an assumption that the sample statistics are equal to the population (e.g., lot) parameters. For example, if a contractor submits a lot having a compressive strength of PWL of 90, the assumption is that the acceptance sample taken from that lot will result in a compressive strength lot PWL estimate of 90%. Figure 43 shows a decision tree of the deterministic structure that is used in this research. The deterministic method can be used by the contractor to assist in establishing a bid. The questionnaire survey, however, indicated most contractors use it prior to construction, as that is when they set target values. At any rate, before the bidding takes place, the contractor already knows the three design AQCs (e.g., thickness, strength, and smoothness) that are specified. Depending on the increment used, each design AQC has potential target AQC that is associated with different pay percentages. Each AQC pay is then combined to form one composite pay that calculates a certain profit. The contractor evaluates them and chooses the best AQC target value combination that will maximize profit before the bid phase (or, if so inclined, prior to construction). To better understand the deterministic approach, the AQC values that were used for this example can be seen in Table 42. In addition, it will be assumed that the contractor's process capabilities reflect the standard deviations, which include sampling and testing error. Table 43 shows 15 different potential target quality levels with five target means (kT) for each of the three AQCs mentioned in Table 42. The default change in cost was used. The deterministic approach uses the standard normal curve. The z value is calculated by using the following equation: z value (= LSL) (417) Table 42. AQC Values and their Measures for Deterministic Example Problem Thickness Compressive Surface Strength Smoothness Measure core 28day core PI0.2inch D 11 in 4,000 psi 7 in/mile a 0.3 in 600 psi 1 inch/mile LSL 10.8 in 3,200 psi NA one per 0.1 mile n 4/lot 4/lot section PF Equations (411) and (412) Use Table 41 CPF CPFprd < 108% The PWL is the area under the normal curve and is determined by looking up the z value in the standard normal curve table, see Appendix A. The PF is calculated using the PWL. The percent pay increase/decrease and profit is calculated using the following two equations: Percent pay increase/decrease = PF 100 (418) Profit =percent pay increase/decrease Cost (419) As seen in Table 43, if the contractor were to target (and achieve) a compressive strength of 4,500 psi with a standard deviation of 600 psi, the submitted lot will have an actual PWL of 98.46%, and the acceptance sample taken from the lot will yield a lot PWL estimate of 98.46%. That PWL estimate corresponds to a PF of 104.23%, or a pay increase of 4.23%. Since the relative cost to produce a compressive strength mean of 4,500 psi and a standard deviation of 600 psi is 1%, the contractor's extra profit is 3.23% for that individual AQC. According to Table 43, the most profitable target quality levels for the contractor is a thickness of 11.5 in, a compressive strength of 4,500 psi, and a smoothness profile index of 3 in/mi. In this case, the profit calculations are made independently for each AQC and do not consider the effect of the CPF equation on profit. If the CPF equation is taken into effect, the most profitable target values may actually be other than those identified in Table 43. For example, considering the effect of the CPF equation, the contractor will have to do a trial and error approach with the AQCs to find the combination that is most profitable. Considering the CPFprod equation with a cap of 108% for the target values identified as most profitable in Table 43, the calculated composite pay is 114.37%. This composite pay goes over the cap of 108%. Therefore, the contractor can only receive 108%, a profit of 2% as the cost to achieve that particular target value combination is 6%. This is an indication that the overall target quality might be higher than necessary. In this case, the contractor needs to explore different scenarios with one or more lowerquality, lowercost AQC target values that will result in a calculated composite pay closer to 108%. Decreasing the target thickness from 11.5 inches to 11 inches and keeping the strength and smoothness the same may not yield the maximum profit. Such a decrease in thickness will yield a calculated composite pay of 100.98% and a profit of2.02%. However, increasing the target thickness from 11 inches to 11.25 inches, after interpolation, (having the same strength and smoothness) will equal a composite pay of 108%, which will yield a profit of 3.5%. Another possibility is to change the compressive strength from 4,500 psi to 4,000 psi and keeping a thickness of 11.5 inches with a smoothness of 3 in/mi. This will yield a profit of 3%. Further, keeping the change in mix design to 4,000psi concrete strength with a simultaneous increase in smoothness PIo.2inch from 3 in/mi to 4 in/mi, and a thickness of 11.25 inches the calculated CPF will equal 108 with a profit of 3.16%. Similarly, an increase in strength from 4,000 psi to 4,500 psi with a thickness of 11.25 inches and a smoothness of 4 in/mi, will yield a profit of 4%. Similarly, a thickness of 11.5 in, strength of 4,500 psi, and a smoothness of 7 in/mile will also equal a profit of 4%. Each combination of target values changes the contractor's profit. Using the deterministic approach, the two target AQC combinations that achieved the highest profit of 4% is the following: * A thickness of 11.25 in, strength of 4,500 psi, and a smoothness of 4 in/mi * A thickness of 11.5 in, strength of 4,500 psi, and a smoothness of 7 in/mi Clearly, the maximum payment cap on the composite pay factor, along with the incremental cost of higher quality levels, have the effect of discouraging contractors from targeting especially high levels of quality. In addition, in some cases like this, the inclusion of a cap makes it more profitable for a contractor to target a decreased quality level for one or more individual quality characteristics and still be assured of obtaining a higher profit. 4.5.2 Probabilistic Method The probabilistic approach, unlike the deterministic, evaluates different construction scenarios by eliminating the assumption regarding sample statistics. Probabilistic models account for system uncertainties and can be considered only as estimates of the true characteristics of a model. In determining price adjustments, the probabilistic approach takes the risks associated in concrete cement pavement construction variability into consideration. Moreover, the statistic could either be favorable or unfavorable to the contractor. Figure 44 shows a decision tree of the probabilistic structure that is used in this research. It starts off in a similar manner as the deterministic method, but the probabilistic has four different types or risks associates with each AQC, which also calculate to four different costs for each risk. Each AQC pay, for each risk, is then combined to form one composite pay that calculates to a certain profit. The contractor evaluates them and chooses the best AQC combination that will maximize profit. Figure 44 only shows two targets for each AQC. The more target quality, more increments, and more AQCs, the more difficult it may become. In this case, the trial by error can get complex and take too long. Figure 44 only shows a few AQC combinations. The combinations that make up each CPF are the numbers that are shown in subscript. The statistical calculations and the trial and error aspects of the problem, lend themselves to a computerbased approach. This led the development of a spreadsheet program that uses Macros and Visual Basic called Probabilistic Optimization for Profit (Prob.O.Prof). A simulation technique, known as Monte Carlo simulation, draws values from the probability distributions for each target AQC input variable, and uses these values to compute single economic output values (e.g., single pay, profit, and composite pay). This sampling process is repeated thousands of times to generate a probability distribution for four types of risk probabilities. A more detailed description of this process is provided in Chapter 5. 4.6 Evaluating Probabilities of Risks in Concrete Pavement Construction Prob.O.Prof draws on Monte Carlo computer simulation to arrive at four quality level percentiles from any desired thickness, strength, or smoothness population: upper 25th percentile (25% risk taker), 50th percentile (50% risk taker), lower 25th percentile (75% risk taker), and lower 5th percentile (95% risk taker). In this dissertation, the word "risk" simply means "the probability of an outcome". A contractor trying to achieve a certain target acceptance quality characteristic cannot be sure what the test values will turn out to be, due to the variability of the test data. The test data may come out with low or high values, resulting in penalties or bonuses for the contractor. For example, a very optimistic contractor is said to be a 25% risk taker. This means that the AQC PF will be expected to come out at the upper 25th percentile of the population. The 50% risk taker is said to be neutral in respect to risks and therefore expected to come out at the median of the population. The pessimistic contractor is not sure if he/she will achieve the target AQC. A contractor that is uncertain in this situation is said to be a 75% risk taker or a 95% risk taker, depending on the percent of uncertainty. The 75% risk taker (moderately averse in taking a risk) means that the AQC PF will be expected to come out at the lower 25th percentile of the population. The 95% risk (highly risk averse) taker means that the AQC PF will be expected to come out at the lower 5th percentile of the population. There may be some reasons why a user would want to make a decision based strictly on one specific risk probability, particularly when a project consists of only one or two lots. One such scenario is the case of a contractor who has obtained information just prior to or during construction to indicate that acceptance test results will be favorable. It may be due to a change in testing personnel or testing equipment, anticipation of ideal weather conditions or other conditions conducive to highquality construction, etc. This contractor might then select the 25th percentile knowing that it allows him/her to decrease the target quality level, thereby decreasing his/her costs and leading to a greater profit (if indeed the test results are favorable as is assumed by this risk taking contractor). However, it is recommended for the majority of applications that the user first examine Prob.O.Profs output target value recommendations before committing to a specific risk probability. The user can in this manner gain information that could be helpful in the decision process. In examining the totality of the profit information obtained from Prob.O.Profs output, one must be careful to interpret correctly. For any target value, the 25th percentile profit can be expected to be exceeded 25% of the time; the 50th percentile profit can be expected to be exceeded 50% of the time; the 75th percentile profit can be expected to be exceeded 75% of the time; and the 95th percentile profit can be expected to be exceeded 95% of the time. A helpful way to view the risk probabilities is to look at the 25th and 75th percentile profits associated with a given target value as the higher and lower limits of a confidence interval centered at the 50th percentile profit. Thus for any given target quality level, the user can expect 50% of the time (75% minus 25%) to receive a profit between the profits indicated at the 25th and 75th percentiles, 70% of the time (95% minus 25%) to receive a profit between the profits indicated at the 25th and 95th percentiles, etc. Figure 43. Deterministic Model. TT = Target Thickness, Ts = Target Strength, Tsm = Target Smoothness, PT = Thickness Pay (%), Ps = Strength Pay (%), Psm = Smoothness Pay (%), CPF = Composite Pay Factor, Pr = Profit (%) Table 43. Deterministic Method for Selecting Target Quality Levels Potential Max STargt z e PL PF Pay Cost Profit Profit AQC Target zvalue PWL AQC (%) +/(%) (%) (%) AQC [1T = XTA Target 10.0 2.67 0.39 41.40 58.6 6 52.6 10.5 1.00 15.87 47.20 52.8 3 49.8 Thickness in) 11.0 0.67 74.54 92.27 7.73 0 7.73 (in) 11.5 2.33 99.01 104.51 4.51 3 1.51 4 12.0 4.00 100.00 105.00 5.00 6 1.00 3,000 0.33 37.07 55.15 44.85 2 42.85 Compressive 3,500 0.50 68.79 89.40 10.6 1 9.60 Strength 4,000 1.33 90.82 100.41 0.41 0 0.41 (psi) 4,500 2.17 98.46 104.23 4.23 1 3.23 5,000 3.00 99.87 104.93 4.93 2 2.93 3.0 NA NA 105 5 2 3 4 Surface 5.0 NA NA 102 2 1 1 Smoothness 7.0 NA NA 100 0 0 0 (in/mi) 9.0 NA NA 96 4 1 3 11 NA NA 92 8 2 6 Figure 44. Probabilistic Model. TT = Target Thickness, Ts = Target Strength, Tsm = Target Smoothness, R = Risk Probability (%), PT = Thickness Pay (%), Ps = Strength Pay (%), Psm = Smoothness Pay (%), CPF = Composite Pay Factor, Pr = Profit (%) CHAPTER 5 COMPUTER PROGRAMMING AND ANALYSIS 5.1 Introduction Under statistical quality assurance specifications, contractors are responsible for the quality of concrete pavements. Their acceptance of the quality is based on the end result that is achieved. In the past, acceptance was written on a passfail basis with little consideration given to variability. Today, a development of adjustable payment plans set payment levels that accurately reflect diminished or enhanced value of the completed work (Chamberlin, 1995). 5.2 Purpose of Computer Program The purpose of developing a computer program is to address the optimization of target quality levels for an associated risk probability. This will allow the contractor to target the levels of quality during the preconstruction phase or construction phase that will obtain high quality and maximize profit cost. In addition, it will help SHAs in validating their quality assurance specifications and pay adjustment provisions. In order to achieve this, a simulation technique known as Monte Carlo simulation was used. 5.2.1 Computer Program Development The most common frequency distribution in nature is the normal distribution. The vast majority of highway construction measurements use normal random numbers. In order to evaluate the quality factors used in highway concrete pavement construction, it is necessary to have a method to generate random data that is essentially identical to the normally distributed data produced at a highway construction site. This is accomplished by developing a computer subroutine to generate random numbers from a standard normal distribution (NORM) having a mean and standard deviation with any desired quality level in terms of PWL. The simulated construction variable (X) is as follows: X = X + o x NORM (51) There are a variety of algorithms available for generating normal random numbers. They all require several lines of coding and are computationally intensive that they tend to slow the execution of any program using thousands or replications. Computer simulation is one of the most powerful analysis methods available for solving a wide variety of complex problems. Most simulations require only the following steps: * Generate random data simulating the real process * Apply the procedure that is to be tested * Store the results in memory This sequence of steps is then repeated many times to provide a large database to use to perform an analysis. In this manner, it is possible to accurately assess the performance of the procedure under evaluation. Computer simulation is particularly useful for problems for which direct, closedform solutions do not exist or for which very complex mathematics would be required. They are able to provide users with practical feedback when designing real world systems. Highway acceptance procedures based on PD or PWL fall into this category and, in many cases, computer simulation is the only practical means of analysis (Weed, 1996b). A different number of lots were simulated (e.g., 20, 100, 500, 1,000, 1,500, 2,000, and 2,500) for each individual AQC to determine the number of random values to generate. Each simulation was performed five times (five trials) for each risk probability (e.g., upper 25h percentile, median, lower 25th percentile, and lower 5th percentile). In addition, an average of each simulated trial was then calculated for each risk probability. The variation of concrete pavement thickness pay adjustment, depending on the number of lots used, was simulated using a mean of 12 inches and a standard deviation of 0.5 inches. It simulated five thickness samples per lot and then calculated the average thickness and standard deviation per lot, then the quality index, PWL Figure 51 shows the convergence of pay decrease starts to take place at 1,500 simulated lots used. 95% 75% 50% 1500  1400 1300  1200 1100 1000 ' 900 J 800 700 z 600 500 400 300 200  100 0o Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Average 95% Average 75% Average 50% 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 Pay Increase/Decrease (%) Figure 51. Variation of Average Thickness Depending on Number of Lots Used The variation of average concrete pavement strength depending on the number of lots used was simulated using a mean of 3,200 psi, and a standard deviation of 500 psi. It simulated five strength samples per lot and then taken the average strength per lot. Figure 52 shows that convergence of pay decrease takes place at 2,000 simulated lots used. The variation of average concrete pavement surface smoothness depending on the number of lots used was simulated using a mean of 3 in/mile, and a standard deviation of 1 in/mile. A simulation of the smoothness for each lot was calculated and then computed an average of inside and outside wheel paths for each lot. Figure 53 shows that convergence of pay increase takes place at 2,000 simulated lots used. Each AQC figure is also separated into three risk probabilities (e.g., ., upper 25th percentile, median, lower 25th percentile, and lower 5th percentile). 95% 75% 50% 2500 2400 2300 2200 2100 2000 1900  1800 1700 1600 Trial 1 1500 d Trial 2 c 1400 I_ l ii Trial 3 b 1300 Trial 4 w 1200 Trial 5 1100 IIIAverage 95% z 1000 Average 75% 900 Average 50% 800 700 600 500 400 300 200 100 0 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 Pay IncreaselDecrease (/%) Figure 52. Variation of Strength Pay Adjustment Depending on Number of Lots It was found through this analysis that as the number of lots increased, the spread of the data (e.g., variations of thickness, strength, and smoothness) converged. It was concluded to use a simulation of 2,000 lotrepetitions for the computer program to obtain the pay and profit for each incremental change of cost for each AQC. It was pointed out to the author that the Figure 53 sinusoidal pattern with all trial points behaving together is likely more than simply coincidental. The author agrees and adds that the same patterns are also recognizable in Figures 51 and 52 (although to a lesser degree because of the different xaxis scales). The problem certainly needs to be investigated further, and the author is doing so. With respect to its effect on current Prob.O.Prof output, the pay increase/decrease values in Figures 51 through 53 are seen to converge by increasing the number of runs as should be expected, although perhaps not as quickly as could be expected. This and other performed checks on the Prob.O.Prof outputs used to draw conclusions in this thesis indicate that the risk probability profits are nonetheless reasonable and fairly accurate. 5.2.2 Monte Carlo Method The Monte Carlo Method encompasses the technique of statistical sampling to approximate solutions to quantitative problems. This method can solve probability dependent problems where physical experiments are impracticale and the creation of an exact formula is impossible. It involves determining the probability distribution of the variables under consideration and then sampling from this distribution by means of random numbers to obtain data. In effect, a generation of a large number (e.g., 100  1,000) of synthetic data sets generates a set of values that have the same distributional characteristics as the real population. (Manno, 1999; Thierauf, 1978). The Monte Carlo Simulation method was used in the computer program to simulate the AQC samples per lot as if their samples were taken from the field. This method draws values from the probability distributions for each design AQC input variable, and uses these values to compute single economic output values (e.g., single pay, profit, and composite pay). This sampling process is repeated thousands of times to generate a probability distribution for four types of risk probabilities, which were described in Chapter 4. 95% 75% 50% 2500  2400  2300 2200  2100  2000 1900  1800  1700 Trial 1 1600  Trial 2 0 1500  1400 Trial 3 1400 o 1300 Trial 4 M 1200 Trial 5 E 1100 Averag z 1000 Averag 900 800Averag 700 600 500 400  300  200  100  e95% e 75% e 50% 0 "U2Fl US r f,. 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Pay Increase/Decrease (%) Figure 53. Variation of Smoothness Pay Adjustment Depending on Number of Lots 5.3 Program Structure As mentioned before, this program uses Macros/Visual Basic. It is designed to generate pay factors for each AQC that will result in a combined target AQC that will maximize profit. As mentioned in Chapter 4, the default cost of change in quality used in the computer program was attained by a questionnaire and by IPRF (Hoerner and Bruinsma, 2004). The default cost for each incremental change of AQC can be changed so that the user can input other cost values. This program is limited for use of three to nine samples per lot for thickness and strength. In addition, the program is limited for use of 0.1 to seven miles of total sub lots for smoothness. However, the program can easily be modified to enable more PWLs of more than nine samples per lot for thickness and strength. This program only uses the English unit system. This can also be easily modified to include the Metric system in later use. The flowchart of the program is shown in Figure 54. The first step is to input the number of concrete pavement AQCs (thickness, strength, and smoothness) that will be analyzed. The user should input "one" for one AQC, "two" for two AQCs, or "three" for all three AQCs. If the thickness is chosen to be analyzed, the following should be inputted: * The thickness design value that is specified in the construction specifications. * The LSL for thickness. * The standard deviation for thickness. * The thickness target value increment to be analyzed. * The number of samples per lot. * The percent cost values of the bid price. A default cost will automatically be used if there are no input values. If the strength is chosen to be analyzed, the following should be inputted: * The type of concrete strength test used (e.g., compressive strength or flexural strength). * The strength design value that is specified in the construction specifications. * The LSL for strength. * The standard deviation for strength. * The number of samples per lot. * The strength target value increment to be analyzed. * The percent cost values of the bid price. A default cost will automatically be used if there are no input values. If the smoothness is chosen to be analyzed, the following should be inputted: * The type of index used for smoothness (e.g., PIo.2inch, or IRI). * The smoothness design value that is specified in the construction specifications. * The standard deviation for smoothness, for simulation purposes. * The smoothness target value increment to be analyzed. * The percent cost values of the bid price. A default cost will automatically be used if there are no input values. Once all the AQC parameters are inputted, the program runs the Monte Carlo simulation. Random numbers are picked for each QI from a normal distribution. The QI is then calculated for each average thickness and strength for each lot. Each AQC is then placed in descending order to identify the QI for the upper 25th percentile, median, lower 25th percentile, and lower 5th percentile. Depending on the number of samples taken per lot, the QI is looked up in a matrix table to find the PWL for the associated thickness and strength. The PF is then calculated using the PWL. However, the Monte Carlo simulation for smoothness is different. Smoothness does not use the PWL to measure the quality. The randomly generated test results for smoothness are directly entered into the AASHTO pay factor table to look up the PF for each smoothness result. The PF values are then placed in descending order to identify the corresponding PF for each risk probability. Knowing the pay and the cost, the profit is then calculated for each AQC at each risk probability. The user should input a percent cap before selecting the composite pay method to calculate the CPF for each AQC combination. The default cap that the program uses is 108%. There are four composite pay methods to choose from: weighted average, average, summation, and product. There is no composite pay method considered more correct than the other because there are many perspectives with regard to the actual value added for various quality attributed. In addition, the quality interrelationships are not completely understood (AASHTO, 1996a). Once the user selects the composite pay method to use, a list of 27 combinations of AQCs for each risk probability is ranked from one to 27 (rank number one being the one with the highest profit). The best three ranked combinations that give the highest profit are highlighted so the user can easily see and choose the combined target quality. The user can choose another CPF method. This will automatically change the combined target AQCs and profit. It is also easy for the user to go back and make any changes and rerun the program. 5.4 Computer Program Output Variability The variability between the number of runs performed and the composite pay method used was analyzed. The input values that were used for this analysis are shown in Table 51. Cost plays a major role in selecting the target quality. Depending on the incremental cost used for an AQC, the analysis can change dramatically. For the example used to find variance, the default incremental change in AQC cost was used and the AQC target combinations with the three highest profits were analyzed. Table 51. AQC Properties Used Weight AQC ( p LSL a n ncrement Thickness 3 11 in 10.8 in 0.3 in 4 0.5 inch Strength 3 4,000 psi 3,200 psi 600 psi 4 500 psi Smoothness 5 7 in/mile 1 in/mile 10 2 in/mile The average, standard deviation, and variance were calculated for the overall 10 trials that were executed from the program. These trials have been analyzed and the AQC variability output is shown in Table 52. Input parameters for thickness, strength, and smoothness AQCs Generate normal random numbers (Simulate 2000 normally distributed values for each AQC increment) Figure 54. Computer Program Flow Chart. The user should be cautioned that Prob.O.Prof had not fully been beta tested. Figure 54. Computer Program Flow Chart (Continued). The user should be cautioned that Prob.O.Prof had not fully been beta tested. The table is arranged to show where there was variability (marked in an "x") for every composite method and three top combined AQC ranks used. For example, using the summation method and the number one ranked combination, variability occurred only at the 95th percent risk probability for profit. This means that the profit at the 95th percent risk probability may vary while the rest stay consistent on every run. The overall table shows that the majority of the variability takes place in the 95th percent risk probability. The contractor who is highly averse in taking a risk under the circumstances will have to account that the 95th risk probability in AQCs and profit may vary. Table 52. Variability in AQC Combinations Composite Variability in Target AQC Pay Rank Thickness Strength Smoothness Profit Method 95% 75% 50% 25% 95% 75% 50 25% 95% 75% 50% 25% 95% 75% 50% 25% 1 X X X Weighted 2 X X X X X X Average 3 X X X X X X 1 X X X Average 2 X X X X X X 3 X X X X X X X X 1 X Summation 2 X X X X 3 X X X X X X X 1 X X Product 2 X X X X 3 X X X X X X It was also found that the type of composite method used can play a role in the outcome of the profit achieved. Figures 55 through 57 shows the profit versus the percent risk probability for each composite pay method for only the three topranked combined target AQCs. As seen in Figures 55, the Summation and Product methods compute the same profit outputs for the number one rank. The other ranks (e.g., number 2 and 3) can vary less than a percent difference but still compute very close to the same profit. In this example, the Summation and Product methods will always compute the highest profit because of the use of multiplication. The Weighted Average and Average methods obtain lower profits but the Weighted Average computes the lowest compared to the rest of the composite pay methods. This is because it depends on the percent weight used for each AQC. All of these composite pay methods give an increase in profit as the risk probability increases (e.g., upper 25th percentile). However, it should be noted that the profits shown in Figure 55 and in Table 53 cannot be compared for different risk probabilities of a given AQC in order to arrive at the best target value. The 25th risk probability will always contain the highest relative profit no matter what composite method is used. This is because the 25th risk probability uses the computer program in anticipation of getting favorable sample statistics. As the anticipation is to receive higher pay, the risk taker's expected profit is always greater than those at the 50t, 75th, or 95th percentiles. There is a risk/return tradeoff. That is, the greater risk accepted, the greater must be the potential return as reward for an uncertain outcome. Generally, this may only happen if the contractor obtains extremely good test results. 5.5 Probabilistic Optimization for Profit Prob.O.Prob allows the user to input the AQC parameters and analyze the output results. In order for the user to understand how Prob.O.Prof can be beneficial, an illustrative exercise will be worked through. The executed results for the exercise can be seen in Table 53. This table was developed using Prob.O.Prof. The table establishes the contractor's profit for the same 15 quality levels that were evaluated using the deterministic method in Chapter 4. The same AQC parameters from the deterministic approach example were used for this example. In addition, the default incremental change in cost for each AQC is used and a cap of 108%. 80 9.00 8.00 7.00 6.00 5.00 4.00 S3.00 2.00 0000 00*  2.00 1.00 0.00  1.00 950 75% 2.00 3.00 4.00 5.00 Risk Probability(%) [4 Weighted Average 1Average A Summation Product Figure 55. Profit versus Risk Probability for Number One Rank 8.00 7.00 6.00 5.00 4.00 3.00 S2.00 1.00 0.00 1.00 / 75% 0 25% 2.00 3.00 4.00 5.00 Risk Probability (%) ..Weighted Average 4 Average  Summation IEProduct Figure 56. Profit versus Risk Probability for Number Two Rank 8.00 7.00 6.00 5.00 4.00 3.00 S2.00 2 1.00 0.00 2.00 3.00 4.00 5.00 Risk Probability (%) 4 Weighted Average Average A Summation * Product Figure 57. Profit versus Risk Probability for Number Three Rank Table 53 is thus analogous to Table 43, for the deterministic approach. A major difference in Table 53 is that four AQC maximumprofit target values are identified for each of the four percent risk probabilities. Once the parameters of each AQC are inputed, the program can be executed. The highest individual AQC profit achieved for each risk probability is indicated in bold. The individual target values identified as most profitable are as follows: * Lower 5th percentile (95%): 12 in, 5,000 psi, and 3 in/mile (PWL = 108%, profit =  2%) * Lower 25th percentile (75%): 11.5 in, 4,500 psi, and 3 in/mile (PWL = 108%, profit = 2%) * Median (50%): 11.5 in, 4,500 psi, and 3 in/mile (PWL = 108%, profit = 2%) * Upper 25th percentile (25%): 11.5 in, 4,000 psi, and 3 in/mile (PWL = 108%, profit = 3%) These profit calculations are made independently for each AQC. They do not consider the effect of the composite pay equation on profit. As mentioned before, upon considering each composite pay, the target AQCs mentioned above may not be profitable. The optimum target value combinations for the each risk probability, using the Weighted Average method are shown in Table 53. The contractor does not have to target an overall quality level that yields the maximum 108% pay. In this example, there are no profitable target value combinations. In this case, if the SHA chooses to use the Weighted Average method, an increase in profit margin to compensate the losses should be applied. As mentioned before, the Weighted Average method depends on the percent weight given for each AQC. In other words, a higher weight may be given to a higher quality AQC and a lower weight may be given to a lower quality AQC. If this is the case, then the CPF will be larger. The optimum target value combinations for the each risk probability, using the Average method are shown in Table 55. Similar with the Weighted Average method, the contractor does not have to target an overall quality level that yields the maximum 108% pay. In this example, like the Weighted Average method, there are no profitable target value combinations. The same concept that was used in the Weighted Average method should be used in the Average method compensate for the loss in profit. In Table 55, the second rank profit target values at the 95th risk probability are a twoway tie between 11.5 in thickness, 5,000 psi compressive strength, 3 in/mi smoothness PI and 11.5 in thickness, 5,000 psi compressive strength, 5 in/mi smoothness PI. This can happen when the change in cost values are whole numbers or closely related to each other symmetrically. The optimum target value combinations for the each risk probability, using the Summation method are shown in Table 56. In this method, the contractor targets an overall quality level that exceeds the maximum cap of 108% pay, which the contractor can only receive 108% pay. This method gives the contractor more profitable target value combinations than the Weighted Average and Average methods. Table 56 shows more twoway ties between some combined target AQCs in the 75th, 50th, and 25th risk probability. In addition, it shows a threeway tie in the number three rank of the 75th risk probability. Although these target values are considered as the optimum target values, the contractor might want to further use Prob.O.Prof to zeroin on more precise optimal target values that lie in between the AQC level intervals analyzed (similar to what was done in the deterministic exercise to arrive at 11.25 in, 4,500 psi, and 4 in/mi). The optimum target value combinations for the each risk probability, using the Product method are shown in Table 57. Similarly, like the Summation method, the contractor targets an overall quality level that exceeds the maximum cap of 108% pay, which the contractor can only receive 108% pay. In addition, there are twoway ties between some combined target AQCs in the 75th, 50th, and 25th risk probabilities. Unlike the abovementioned methods, the Product method was the only method that had a two way tie between twocombined target AQCs in the number one rank (median). As seen from the other composite pay methods, since the change in incremental cost for the strength and smoothness were similar, a tie between combined target AQCs can easily happen. 5.5 Deterministic vs. Probabilistic Approach As seen from the previous chapter, the most profitable combinations in the deterministic approach were a thickness of 11.25 in, strength of 4,500 psi, a surface smoothness of 4 in/mile and a thickness of 11.5 in, strength of 4,500 psi, and strength of 7 in/mi. These two AQC combinations gave a profit of 4%. Using the Product method and the 50th percent risk probability, Prob.O.Prof also calculated two target AQC combinations that gave a profit of 4%, as seen in Table 57. The deterministic method and Prob.O.Prof both agree on one of the twocombined target AQCs (thickness of 11.5 in, 4,500 psi, and 7 in/mi). This is because the two approaches both happen to exceed the cap on that target AQC combination. The contractor, in this case, might want zeroin on more precise optimal target values that lie in between quality level intervals analyzed using Prob.O.Prof. The contractor can do this by inputting a smaller change of increment for the individual AQC. It is clear that the two approaches will yield different profits. It happened for this example that one of the two approaches equaled the same profit. This may be in some cases. Both approaches have different single quality characteristics. The deterministic approach is based on an assumption that the sample statistics are equal to the population parameters and Prob.O.Prof (probabilistic approach) evaluates different construction scenarios and eliminates the assumption regarding sample statistics. In addition, the deterministic approach uses the average value of the statistic, while Prob.O.Prof uses the median value of the statistic. There is a great difference among the topranked profit percentages between different risk probabilities using the probabilistic approach. For example, looking at the 50th and 75th percent risk probability (Product Method), achieving a four percent profit in 