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- https://ufdc.ufl.edu/UF00100814/00001
## Material Information- Title:
- Assessment of the effectiveness of quality assurance construction specifications for asphaltic concrete pavement
- Creator:
- Pathomvanich, Sutharin, 1971- (
*Dissertant*) Najafi, Fazil T. (*Thesis advisor*) - Place of Publication:
- Florida
- Publisher:
- State University System of Florida
- Publication Date:
- 2000
- Copyright Date:
- 2000
- Language:
- English
## Subjects- Subjects / Keywords:
- Arithmetic mean ( jstor )
Asphalt ( jstor ) Construction materials ( jstor ) Highways ( jstor ) Integers ( jstor ) Pavements ( jstor ) Quality assurance ( jstor ) Questionnaires ( jstor ) Sample size ( jstor ) Standard deviation ( jstor ) Civil and Coastal Engineering thesis, Ph. D ( lcsh ) Dissertations, Academic -- Civil and Coastal Engineering -- UF ( lcsh ) City of Gainesville ( local ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) government publication (state, provincial, terriorial, dependent) ( marcgt ) non-fiction ( marcgt )
## Notes- Abstract:
- A method to assess the effectiveness of highway construction specifications was developed in this research. Up to the present time, there was no truly objective method in existence that could assess the effectiveness of any state highway agency specifications. According to the proposed method, a specification is effective if the following levels of quality are the same: the quality the agency wants, the quality the agency specifies, and the quality delivered by the contractor. These three quality levels must be quantified in statistical terms (mean, standard deviation, offset from target, etc.). The developed method was tested and demonstrated on Florida Department of Transportation's (FDOT) type S asphaltic concrete specifications for pavement density and asphalt content. The identification of quality level desired by the FDOT was attempted through a literature review, supplemented with a questionnaire survey. The FDOT's specifications, specifically the acceptance plans for density and asphalt content, were analyzed to determine the quality level being ordered, with a computer program (AAD1_5) developed to assist in the analysis. The FDOT's Central Quality Reporting (CQR) database was analyzed to determine the quality level being delivered. While the research failed to clearly identify the quality level desired, sufficient information was gathered to conclude there were several inconsistencies between what FDOT wants, what FDOT specifies, and what FDOT is getting. Therefore, FDOT's current density and asphalt content specifications are ineffective. Recommendations were made to improve FDOT's specifications, increase their effectiveness, and improve the CQR database. At this time, FDOT is implementing new specifications, with features in line with the recommendations of this research. The statistical parameters determined here can be used by FDOT to evaluate how the new specifications will perform. In addition to evaluating specification effectiveness, the method documented in this research can be used by any highway agency to monitor its specifications. For FDOT, the values of the statistical parameters presented in this research can provide a baseline quality level from which one can assess whether the quality delivered to FDOT in the future is improving. The quality should be improved when new specifications or new construction procedures and developments are in use. ( ,, )
- Subject:
- KEYWORDS: quality assurance, construction, specification effectiveness, asphaltic concrete pavement
- Thesis:
- Thesis (Ph. D.)--University of Florida, 2000.
- Bibliography:
- Includes bibliographical references (p. 205-210).
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- Document formatted into pages; contains xvii, 211 p.; also contains graphics.
- General Note:
- Vita.
- Statement of Responsibility:
- by Sutharin Pathomvanich.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 47682186 ( OCLC )
002678736 ( AlephBibNum ) ANE5963 ( NOTIS )
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ASSESSMENT OF THE EFFECTIVENESS OF QUALITY ASSURANCE CONSTRUCTION SPECIFICATIONS FOR ASPHALTIC CONCRETE PAVEMENT By SUTHARIN PATHOMVANICH 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 2000 Copyright 2000 by Sutharin Pathomvanich The author dedicates this dissertation to her parents, Mana and Sukchai Pathomvanich, and her three sisters, Saluxsana, Sakara, and Anuttara. ACKNOWLEDGMENTS First, I would like to thank Dr. Fazil T. Najafi, my advisory committee chairman, for his continuing encouragement and support. Second, I am greatly indebted to Mr. Peter A. Kopac, Research Engineer for the Federal Highway Administration, who wisely advised me to contribute toward fulfilling some of the FHWA research needs and helped me in selecting a research topic based on the current needs. I would like to thank him for all of his invaluable assistance, advice, and critique throughout this research. Third, I would like to extend my sincere and heartfelt gratitude to Dr. Mang Tia, who generously gave his advice, help, kindness, and support throughout the research. Fourth, I would like to express my appreciation to Dr. Paul Y. Thompson for his kindness, concern, and encouragement. Fifth, I would like to thank Dr. Andre I. Khuri and Dr. Leon Wetherington for their interest, direction, and advice. Without their guidance, this dissertation would not have succeeded. Further, I would like to thank the FDOT personnel--Mr. Gale C. Page, Mr. Tom Malerk, Mr. Bruce T. Dietrich, Mr. Winfred S. Langley, Mr. Patrick B. Upshaw, and Mr. Glenn Mans--for their assistance. Also, I would like to thank my uncle and aunt, Mr. and Dr. Toochinda, for their love, generosity, and concern during my study in United States. This appreciation also extends to my boyfriend, Nitis Sthapitanonda, and all of my friends, especially Ratanaporn Awiphan. Finally, I would like to thank my parents and my three sisters for providing me with love and good opportunities throughout my life. TABLE OF CONTENTS page A C K N O W L E D G M E N T S ................................................................................................. iv LIST OF TABLES .................................... .. .... .... .................ix LIST OF FIGURES .......... ................... ...................... xiii A B S T R A C T .........x... .............................. ... ....................... ................ . x v i CHAPTERS 1 PROBLEM STATEMENT AND RESEARCH OBJECTIVES................. .......... 1.1 B background ....................................... 1 1.2 Problem Statem ent .................. ..................................... .. .......... .. 4 1.3 R e search O bjectiv e s.......................................................... .................................. 6 1.4 R research A approach ............................................................. ............ . ..... .... .. 8 2 LITERATURE REVIEW .................................................................. ...............13 2.1 Introduction .................... ............................... 13 2 .2 H ighw ay Specification s ........................................ ............................................ 13 2.2.1 H history ............................... .............. 14 2.2.2 Purposes of Highway Specifications ............. ..................................... 15 2.2.3 Function of the Specifications..................... ..... .......................... 16 2 .3 Q quality A assurance ............................................................. ...................... .. .. 16 2.3.1 D definitions ................................ ............................... ........ 16 2.3.1.1 Q quality A assurance ........................................... ................ .............. 16 2.3.1.2 Q quality C control .............. ... ... .. .... ................ ............ ................... 20 2.3.2 Objectives of Quality Assurance Specifications......................................... 20 2.3.3 Advantages and Disadvantages of Quality Assurance Specifications ............ 21 2.3.3.1 Advantages of Quality Assurance Specifications ................................... 21 2.3.3.2 Disadvantages of Quality Assurance Specifications............................ 22 2.3.4 Types of A acceptance Plans ........................................ .......... .............. 22 2.3.4.1 A tribute Sam pling P lan .................................................. ... ................. 23 2.3.4.2 V ariable Sam pling Plan ........................................ ......... .............. 23 2.4 Acceptance Using Lot-by-Lot M ethod ......................................... ..... ......... 24 2.5 R andom Sam pling................................ .............. .......................... .................. 25 2.5.1 Pure R andom Sam pling .............. ............................................ .............. 26 2.5.2 Stratified R andom Sam pling .................................................. ... ................. 26 2.6 Variability in Highway Construction...................................... 27 2.7 A acceptance T tolerance ......... .................................... ...................... .............. 30 2 .8 P ay F acto r ................................................................... 3 2 3 MATHEMATICAL AND STATISTICAL PRINCIPLES UNDERLYING VARIABILITY IN QUALITY ASSURANCE SPECIFICATIONS .............................35 3.1 Statistical M modeling .................. .............................................. 35 3.2 Reliability of M easurem ent........................................................ .......... .... 36 3.3 Quality and V ariability Concepts.................................... .......................... ........ 36 3.4 V ariation as a Quality Y ardstick...................................... ........................ ......... 40 3.5 D escribing Param eters and Statistics ..................................................................... 41 3.6 Specification Compliance M easures............................................... ................ 43 3.6.1 A average ................. .................................................................................... . 44 3.6.2 Quality Level A nalysis................................................. ........................... 44 3.6.3 A average A absolute D eviation.................................................. .... .. .............. 48 3.6.4 M oving Average .............. ........................................ ...... ............ .. 49 3.6.5 Range ...................................... .... ... .. ............ ........... 50 3.6.6 Pavement Density Specification Compliance Measures............................... 51 3.6.7 Asphalt Content Specification Compliance Measures............................ 51 3.7 Conformal Index Approach ............................... .................. 51 3.8 Potential Problems with Existing Quality Measures..................... .............. 53 3.9 N orm al D distribution ...................................... ............ ........................ 54 3.9.1 Skewed Distribution...................... ....... ............................. 57 3.9.2 D distribution of Group Averages.............................................. ................. 57 3.10 Correcting the Bias of Sample Standard Deviation ............................................ 59 3.11 Combining Results of Observations ....................................................... 65 3.12 Statistical Tests for A averages ...................................................... ........... ... 66 3 .13 T ests for V arian ces.......................................... ... ................ ...... ................ .. 6 7 3.14 Theory of Risk .. ................. ............................ .. .......... .. 69 4 DATA ANALYSIS ....................................... ........................71 4.1 P avem ent D density .... .............................. ................................ .............. 71 4.1.1 H historical D ata .... .................... ........................ ........ ..... .............. 7 1 4.1.2 Test M ethod ......................................... 72 4.1.3 Selection of the data ............... ............ .................... ...... .. .. .......... .. 74 4.1.4 Determination of Statistical Parameters .............. .. ............... ......... ............. 77 4.1.5 Results and Discussions .................................................... 81 4.1.5.1 Overall Pavement Density Quality Level ............................................. 85 4.1.5.2 Pavement Density Quality Level by Year............................................... 86 4.1.5.3 Summary of Typical Pavement Density Quality .................................... 86 4 .1.5.4 P ay F actor ............................................................................. ..... 93 4.1.6 Questionnaire Responses for Density Quality Level.................................... 100 4.2 A asphalt C ontent................... ................ .............. .......................... .................. 101 4.2.1 Historical Data ... ... ................................................ .............. 101 4.2.2 T est M ethod .... ............................ .... ............................ .............. 105 4.2.3 Selection of the D ata ........................ ............................... .......................... 108 4.2.4 Determination of Statistical Parameters .............. ..................... .............. 108 4.2.5 R results and D iscussion...................................................... 113 4.2.5.1 Overall Within-lot Asphalt Content Quality Level............................... 114 4.2.5.2 Within-lot Asphalt Content Characteristic by Year............................ 120 4.2.5.3 Overall Between-lot Asphalt Content Quality level............................ 125 4.2.5.4 Pay Factor ............... ............................... .. ........... .. ... .... ......... 125 4.2.6 Questionnaire Responses for Asphalt Content Quality Level ..................... 132 5 COM PUTER PROGRAM M ING ........................................ .......................... 144 5.1 Purpose of the Computer Simulation .............................. ................... 144 5.2 Computer Program Flow Chart.................................................... 145 5.3 Computer Program Development .............. ...... ....................................... 147 5.4 Softw are M annual ........................................................ .. .......... .. 150 5.5 Computer Program Output..................................................... 154 6 CONCLUSION AND RECOMMENDATIONS ................................................. 169 6.1 R research Sum m ary ........................................................................ ......... ..... 169 6.2 Research Findings and Recommendations ................................................... 172 6.3 Recommendation for Future Research............... .. ................. 175 APPENDICES A FACTORS FOR ESTIMATING UNIVERSE STANDARD DEVIATIONS ............177 B FD O T Q U E STIO N N A IR E ......... ................. .........................................................178 C CONTRACTOR QUESTIONNAIRE...................... ............................. 181 D COMPUTER SIMULATION PROGRAM (AAD1_5) SCRIPTING CODE ...........184 E EXAMPLE OF SAS PROGRAM SOURCE CODE ...............................................200 L IST O F R E FE R E N C E S ...................................................................... .....................205 B IO G R A PH ICA L SK ETCH ......... ................. ...................................... .....................211 LIST OF TABLES Table Page 2-1. D ensity Testing R equirem ents ........................................................................... ...... 28 3-1. Symbols used for Populations and Samples ....................................... ............... 43 4-1. Summary of Pooled Between-Lot Standard Deviation Density (% of Control Strip).....87 4-2. Summary of the Average Value of Density (% of Control Strip)......................... 87 4-3. Summary of Between-Lot Standard Deviation of Density by 1991-1992 (% of C o n tro l S trip ) .................................................................... . 8 8 4-4. Summary of Between-Lot Standard Deviation of Density by 1993-1994 (% of C o n tro l S trip ) .................................................................... . 8 8 4-5. Summary of Between-Lot Standard Deviation of Density by 1995-1996 (% of C o n tro l S trip ) .................................................................... . 8 9 4-6. Summary of Between-Lot Standard Deviation of Density by 1997-1999 (% of C control Strip D ensity) ................................................ .............................. 89 4-7. Summary of Average of Density by 1991-1992 (% of Control Strip) ............................90 4-8. Summary of Average of Density by 1993-1994 (% of Control Strip) ............................90 4-9. Summary of Average of Density by 1995-1996 (% of Control Strip ) ...........................90 4-10. Summary of Average of Density by 1997-1999 (% of Control Strip) ..........................91 4-11. Estimation of Typical Pavement Density Quality ...................................................91 4-12. Density Payment Schedule Specified in FDOT Standard Specifications for Road and Bridge Construction 1999. ........................................ ........................ 94 4-13. Summary of the Estimated Pavement Density Pay Factor (Percent) .............................94 4-14. Summary of Average of Pavement Density Pay Factor (Percent).............................95 4-15. Summary of the Pavement Density Pay Factor for Year 1991-1992 (Percent) ............95 4-16. Summary of the Pavement Density Pay Factor for Year 1993-1994 (Percent) ..............96 4-17. Summary of the Pavement Density Pay Factor for Year 1995-1996 (Percent) ..............96 4-18. Summary of the Pavement Density Pay Factor for Year 1997-1999 (Percent) ..............97 4-19. Summary of Percentage of Lots with Pay Reduction obtained from Database and based on FDOT's 1999 Specification ............................................................ 97 4-20. Summary of Percentage of Lots with Pay Reduction when Sample Size = 3 ...............98 4-21. Example of Estimation of Average within-lot Offset of all Lots when n = 3..............10 4-22. Example of Estimation of an Unbiased Universe within-lot Standard Deviation of all Lots w hen n = 3 .............. ........................... ........ ........ .. .. 111 4-23. Example of Estimation of a Pooled within-lot Standard Deviation of all Lots when n = 3 ...................................................................... ....... 1 1 1 4-24. Example of the Estimation of the Average of within-lot AAD when n = 3.................12 4-25. Example of Estimation of the Characteristic within-lot Conformal Index of all Lots when n = 3 ................................... .............................. ........... 112 4-26. Summary of Corrected Average within-lot Standard Deviation of Asphalt Content, Type S A sphaltic Concrete ........................................................ ............. 121 4-27. Summary of Corrected Median within-lot Standard Deviation of Asphalt Content, Type S A sphaltic Concrete ........................................................ ............. 121 4-28. Summary of Pooled within-lot Standard Deviation of Asphalt Content, Type S A sphaltic C concrete .......................................... ........................ 122 4-29. Summary of Lot Offset from JMF of Asphalt Content, Type S Asphaltic Concrete ......122 4-30. Summary of Lot Average Absolute Deviation from Job Mix Formula of Asphalt Content, Type S Asphaltic Concrete ............. ............................. .... ............. 123 4-31. Summary of Standard Deviation of lot AAD of Asphalt Content, Material Type S......123 4-32. Summary of within-lot Conformal Index of Asphalt Content, Type S Asphaltic C on create .......................................................................... 12 4 4-33. Comparison of Percentage of Observations Outside 95 percent Confident Interval of Corrected and Pooled within-lot Standard Deviation................ ........... 124 4-34. Summary of within-lot Corrected Standard Deviation of Asphalt Content, Type S Asphaltic Concrete, Year 1993-1994............... ........... ......... ..... ......... 126 4-35. Summary of within-lot Corrected Standard Deviation of Asphalt Content, Type S Asphaltic Concrete, Year 1995-1996........... ....... ........ ....... .............. 126 4-36. Summary of within-lot Corrected Standard Deviation of Asphalt Content, Type S Asphaltic Concrete, Year 1997-1999............. ............... ....... .............. 127 4-37. Summary of Lot Offset from JMF of Asphalt Content, Type S Asphaltic Concrete, Y ear 1993-1994 ....................................................................127 4-38. Summary of Lot Offset from JMF of Asphalt Content, Type S Asphaltic Concrete, Y ear 1995-1996 ....................................................................128 4-39. Summary of Lot Offset from JMF of Asphalt Content, Type S Asphaltic Concrete, Y ear 1997-1999 ................. ............................... ..... ...............128 4-40. Summary of Lot Average Absolute Deviation from JMF of Asphalt Content, Type S A sphaltic Concrete, Year 1993-1994..................................... ............... 129 4-41. Summary of Lot Average Absolute Deviation from JMF of Asphalt Content, Type S Asphaltic Concrete, Year 1995-1996............. ................ ............... 129 4-42. Summary of Lot Average Absolute Deviation from JMF of Asphalt Content, Type S Asphaltic Concrete, Year 1997-1999............. ................ ............... 130 4-43. Summary of within-lot Conformal Index of Asphalt Content, Type S Asphaltic Concrete, Y ear 1993-1994 .............................................................................130 4-44. Summary of within-lot Conformal Index of Asphalt Content, Type S Asphaltic Concrete, Year 1995-1996 ....................................... ... ..........................131 4-45. Summary of within-lot Conformal Index of Asphalt Content, Type S Asphaltic Concrete, Year 1997-1999 ................................... ......................................131 4-46. Summary of Between-Lot Statistical Parameters for Type S Asphaltic Concrete ........132 4-47. The Acceptance Schedule of Payment on Lot-by-Lot basis of the Asphalt Content Test Results by Extraction M ethod ............................................... ............... 136 4-48. Summary of the Estimated Pay Factor based on Asphalt Content Characteristic..........136 4-49. Summary of Average Asphalt Content Pay Factor, Type S Asphaltic Concrete ...........137 4-50. Summary of Average Asphalt Content Pay Factor for Year 1993-1994.......................137 4-51. Summary of Average Asphalt Content Pay Factor for Year 1995-1996 .......................138 4-52. Summary of Average Asphalt Content Pay Factor for Year 1997-1999.......................138 4-53. Summary of Percentage of Lots with Pay Reduction...................................................139 5-1. Comparison between Lot Offsets from Computer Outputs when Characteristic Offset Input = 0.15, S Input = 0.21 and Lot Offsets from Data Analysis of C Q R D atab ase .................................................................................. 155 5-2. Summary of the Results from Computer Simulation Based on 1999 FDOT Specification for Sample Size = 1, Offset = 0.15, and Standard Deviation = 0.21...... .. .................................... ........ 156 5-3. Summary of the Results from Computer Simulation Based on 1999 FDOT Specification for Sample Size = 2, Offset = 0.15, and Standard Deviation = 0.21...... .. .................................... ........ 157 5-4. Summary of the Results from Computer Simulation Based on 1999 FDOT Specification for Sample Size = 3, Offset = 0.15, and Standard Deviation = 0.21...... .. .................................... ........ 158 5-5. Summary of the Results from Computer Simulation Based on 1999 FDOT Specification for Sample Size = 4, Offset = 0.15, and Standard Deviation = 0.21...... .. .................................... ........ 159 5-6. Summary of the Results from Computer Simulation Based on 1999 FDOT Specification for Sample Size = 5, Offset = 0.15, and Standard Deviation = 0.21...... .. .................................... ........ 160 5-7. Summary of the Results from Computer Simulation Based on 1999 FDOT Specification for Sample Size = 6, Offset = 0.15, and Standard Deviation = 0.21............... ................................. ........ 161 5-8. Results of the Average of PF Distribution and Percentage of Lot with Pay Reduction of All Sample Sizes that are used as Target Values to Develop New Tolerances (Offset = 0.15, Standard Deviation = 0.21)..................................... 163 5-9. Summary of Trial and Error Results from Computer Simulation when Sample Size = 1 ............................................................................ . 1 6 5 5-10. Summary of Trial and Error Results from Computer Simulation when Sample Size = 2 ............................................................................... 1 6 6 5-11. Summary of Trial and Error Results from Computer Simulation when Sample Size = 6 ........................................................................... . 1 6 7 5-12. Comparison of Existing FDOT Specification and Recommended Asphalt Content Tolerances (when S = 0.21, Offset = 0.15) for Type S Asphaltic Concrete .........168 LIST OF FIGURES Figure Page 1-1. R research A approach Flow Chart......... ................................................. ............... 11 2-1. D degrees of Segregation ............................................................. ............... 31 3-1. Concept of Accuracy, Precision, and Bias .......................................... 37 3-2. Conformance to Specification and Quality Loss.................................. ............... 42 3-3. The Flexibility of the Percent Defective Quality Measure with Respect to [t and .....46 3-4. Percent Defective (PD) and Percent within Limit (PWL) under the Standardized N orm al D distribution Curve ...................................................... ............... 48 3-5. Comparison of Mathematical Properties of AAD and CI for Sample Size of n=2..........55 3-6. Potential Weaknesses of Common Statistical Measures of Quality .............................56 3-7. T ypes of D distribution .......................................................................... .....................58 3-8. Risks Involved in A acceptance D ecision.............................................. .....................70 4-1. Nuclear Gauge Instrument (Obtained photo from Joint AASHTO-FHWA Industry Training Com m ittee on A sphalt) .................................. .............................. ........ 74 4-2. Select a Location and Take a Count for the Normal Measurement Period (Obtained photo from Joint AASHTO-FHWA Industry Training Committee on Asphalt).....75 4 -3 B ox P lot C om ponents .......................................................................... .....................7 8 4-4. Box-plot of the Density Test Results from PROC UNIVARIATE when Sample Size = 3, Asterisks under Box-plot Column show Errors and Outliers.......................79 4-5. Example of Testing for Normality of Density Data ......................................................82 4-6. Percentage of Non-normally Distributed Groups of Same Mix Design and Project.......84 4-7. Frequency Plot of Density Pay Factor by Year when Sample Size = 3 ........................99 4-8. Questionnaire Responses from FDOT and Contractor Personnel Regarding Density M ean V alue ................................................... ................ 102 4-9. Questionnaire Responses from FDOT and Contractor Personnel Regarding Density Standard Deviation ................. .. ........... ................ ................. 103 4-10. Questionnaire Responses from FDOT and Contractor Personnel Regarding Minimum Quality Level of Density Specification................... ...............104 4-11. The Test Portion is Placed into a B ow l ................. ................................................ 106 4-12. The Extraction Equipment Extracts the Asphalt from the Paving Mixture ..................107 4-13. Percentage of Non-normally Distributed Groups of Same Project (N = Number of L ots) .............................................................. .. .... ..... ......... 115 4-14. Summary Histogram for within-lot Standard Deviations of the Difference from JM F when Sample Size = 2 .............. .... .................... ................ ..... 116 4-15. Summary Histogram for within-lot Standard Deviations of the Difference from JM F when Sample Size = 3 .............. .... .................... ................ ..... 117 4-16. Summary Histogram for within-lot Standard Deviations of the Difference from JM F when Sam ple Size = 4 ..... .............................................................1.. 18 4-17. Summary Histogram for within-lot Standard Deviations of the Difference from JM F when Sample Size = 5 .............. .... .................... ................ ..... 119 4-18. Summary Histograms of Between-Lot Offset from JMF ........................ ............133 4-19. Summary Histograms of Between-Lot Standard Deviation of the Difference from JM F ........................................................................... . 1 3 4 4-20. Summary Histograms of Between-Lot Conformal Index ....................................135 4-21. Frequency Plot of Pay Factor based on Asphalt Content Characteristic.......................140 4-22. Questionnaire Responses from FDOT and Contractor Personnel Regarding Average Offset of Asphalt Content from Job Mix Design...............................141 4-23. Questionnaire Responses from FDOT and Contractor Personnel Regarding Standard Deviation of Asphalt Content.................. ..... ................... 142 4-24. Questionnaire Responses from FDOT and Contractor Personnel Regarding Minimum Quality Level of Asphalt Content Specification..................................143 5-1. Computer Simulation Flow Chart used in Relating Offset and Standard Deviation to A A D ............... .. .......... .............. ..............................146 5-2. Com pleted Input Inform ation......................................... .... ................................ 151 5-3. Completed Input of Specification Tolerances ..................................... .................152 5-4. Display of the AAD Computer Program............. ............................ ...............153 5-5. Pay Factor Frequency Plot of Type S Asphaltic Concrete gotten from Computer Simulation when Offset = 0.15 and Standard Deviation = 0.21 ............................164 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 ASSESSMENT OF THE EFFECTIVENESS OF QUALITY ASSURANCE CONSTRUCTION SPECIFICATIONS FOR ASPHALTIC CONCRETE PAVEMENT By Sutharin Pathomvanich December 2000 Chairman: Dr. Fazil T. Najafi Major Department: Civil and Coastal Engineering A method to assess the effectiveness of highway construction specifications was developed in this research. Up to the present time, there was no truly objective method in existence that could assess the effectiveness of any state highway agency specifications. According to the proposed method, a specification is effective if the following levels of quality are the same: the quality the agency wants, the quality the agency specifies, and the quality delivered by the contractor. These three quality levels must be quantified in statistical terms (mean, standard deviation, offset from target, etc.). The developed method was tested and demonstrated on Florida Department of Transportation's (FDOT) type S asphaltic concrete specifications for pavement density and asphalt content. The identification of quality level desired by the FDOT was attempted through a literature review, supplemented with a questionnaire survey. The FDOT's specifications, specifically the acceptance plans for density and asphalt content, were analyzed to determine the quality level being ordered, with a computer program (AAD1_5) developed to assist in the analysis. The FDOT's Central Quality Reporting (CQR) database was analyzed to determine the quality level being delivered. While the research failed to clearly identify the quality level desired, sufficient information was gathered to conclude there were several inconsistencies between what FDOT wants, what FDOT specifies, and what FDOT is getting. Therefore, FDOT's current density and asphalt content specifications are ineffective. Recommendations were made to improve FDOT's specifications, increase their effectiveness, and improve the CQR database. At this time, FDOT is implementing new specifications, with features in line with the recommendations of this research. The statistical parameters determined here can be used by FDOT to evaluate how the new specifications will perform. In addition to evaluating specification effectiveness, the method documented in this research can be used by any highway agency to monitor its specifications. For FDOT, the values of the statistical parameters presented in this research can provide a baseline quality level from which one can assess whether the quality delivered to FDOT in the future is improving. The quality should be improved when new specifications or new construction procedures and developments are in use. xvii CHAPTER 1 PROBLEM STATEMENT AND RESEARCH OBJECTIVES 1.1 Background Different authors have used the term "quality assurance" in different ways. According to Willenbrock and Marcin, quality assurance, broadly interpreted, refers to the system of activities that is designed to ensure that the quality of the construction material is acceptable with respect to the specifications under which it was produced (TRB, 1979). It addresses the overall problem of obtaining the quality level of service, product, or facility in the most efficient, economical, and satisfactory manner possible. The scope of the total quality assurance system (regardless of the type of material specification used) encompasses portions of the activities of planning, design, development of plans and specifications, job advertising, awarding of contracts, construction, operation and maintenance. LaHue defined a modem quality assurance system as "the overall process whereby the joint efforts of industry, state, and Federal officials are combined to develop or establish performance related quality criteria, exercise systematic process control, establish attainable specification criteria that recognize product variability and develop unbiased sampling and testing procedures" (TRB, 1979, p.7). To put this in the most simplistic terms, modem quality assurance for highway construction is a process to assure the development of better highway facilities through effective process control, product acceptance, product sampling and testing, and systematic feedback and evaluation (TRB, 1979). According to Transportation Research Circular No.457, Glossary of Highway Quality Assurance Terms (TRB, 1996), quality assurance is defined as a process of systematic actions to provide confidence that a product or facility will perform satisfactorily in service. It addresses the overall problem of obtaining the quality of service, product, or facility in the most efficient, economical, and satisfactory manner possible. Quality assurance involves continued evaluation of the activities of planning, design, development of plans and specifications, job advertising and awarding contracts, construction, operation and maintenance, and the interactions of these activities. Quality assurance in construction includes quality control, acceptance sampling and testing, and independent assurance. The acceptance sampling and testing are done to determine whether or not the quality of produced material or construction is acceptable in terms of the specifications. The independent assurance is a management tool that requires a third party to provide an independent assessment of the product and/or the reliability of test results obtained from process control and acceptance testing. The results of the independent assurance are not used for product acceptance (TRB, 1996). Highway construction specifications that are generally used can be classified as either "recipe or method specifications" or "end-result specifications." Recipe or method specifications. These two terms are used interchangeably to mean those specifications that not only state what is wanted but also the manner by which it is to be attained. Limitation might also be placed on the hauling and lay down equipment and the types of rollers and patterns of rolling. This type of approach is traditional for many highway operations. End-result specifications. An end-result specification implies that the state or the consumer organization will define the product wanted and will examine only the final product to decide if it is acceptable or not. As yet, no state has adopted a true end-result specification under which a total project is to be built by the contractor and the final product in place is to be accepted or rejected by the state. Generally, advocates of end- result specifications for highway construction believe that detailed "how to" instructions should be eliminated as much as possible and that units of construction should be accepted or rejected on a lot-by-lot basis by measuring significant characteristics of the complete lot. Such an end-result specification places the entire responsibility for quality control on the contractor and is commonly referred to as a "quality assurance specification." It relies on statistical acceptance plans based on random sampling both to define the product wanted and to determine the acceptability of the lot. Before 1970, a recipe system was frequently used. In more recent years, end- result quality assurance specifications have been emphasized. The advantage of quality assurance specifications to state agencies is the actual placing of responsibility for materials and construction quality on the contractor or producer. The contractors and producers can choose their own materials and equipment and design the most economical mixtures meeting the specified requirements (Dobrowolski and Bressette, 1998; Rilett, 1998; Schexnayder and Ohm, 1997; TRB, 1979). Although it is generally agreed that quality assurance specifications are an improvement over recipe specifications, no one has actually quantified the effectiveness of either type of specification, i.e., in terms of how well the specification serves its function. Since the primary function of a specification is to describe the quality level of the product desired, an effective specification is one for which the contractors correctly interpret the desired quality level and consistently provide that level. There are many possible reasons why contractors might provide a consistently lower, or higher, quality level than that desired by the state agency. Additionally, either a lower quality level or an unnecessarily higher quality level than that desired can be a detriment to society and the travelling public. The lower quality level results in a highway that will exhibit premature distresses (potholes, roughness, cracking, etc.) and will need added maintenance or early rehabilitation, often increasing highway user delay costs and accident potential. The unnecessary higher quality level invariably results in higher initial construction costs. 1.2 Problem Statement Specifications are the communication means that tell the contractor what level of construction quality is desired. However, it is not clear what quality level is being asked for in most highway construction specifications. In order to develop quality assurance specifications, the state agency needs to answer the following four questions: 1. What do we want? 2. How do we order it? 3. How do we evaluate the product? 4. What do we do if we did not get what we ordered? For statistical specifications, the answers provided by the agency are couched in statistical terms and may be found in the acceptance plan portions of the developed specifications. To submit an informed bid, the prospective contractor must examine the acceptance plan and decide what his target quality level will be. The contractor's target quality level may or may not be the same as the quality level that the agency wants and/or believes it has ordered. In this current time period with much national emphasis on continuous quality improvement, it would make sense for agencies to monitor how well their acceptance plans are working. Were the acceptance plans developed properly? Is there consistency between what the agency wants and what it is actually ordering? Are the specifications working properly? Are contractors providing the quality level the agency wants? Should the agency be specifying a higher, lower, or the same quality level? These and other similar questions can be answered by investigating the effectiveness of specifications. When a specification is not effective, a good understanding of the problem (and the underlying reasons for the problem) is critical as a first step toward improving the specifications. (The word "specification" here is used to refer to a single property, for example, a density specification or a smoothness specification. The word "specifications" is used to refer to more than one property.) Up to now, no truly objective method existed that could assess the effectiveness of any state highway agency's specifications. This research created a method to assess the effectiveness of highway construction specifications. According to the method, a specification is effective if the following levels of quality are the same: the quality the highway agency wants, the quality the agency specifies, and the quality delivered to the agency. These three quality levels must be quantified in statistical terms (mean, standard deviation, offset from target, etc.). The Florida Department of Transportation (FDOT) began using quality assurance specifications many years ago, and the effectiveness ofFDOT's specifications has never been specifically investigated. Some specifications may be effective, but others may not be; all can probably be improved. Therefore, a statistical evaluation is necessary to do this investigation. In this research, the method to assess the effectiveness of specifications was tested and demonstrated on FDOT's asphaltic concrete pavement construction specifications. The scope was limited to type S asphaltic concrete material and two quality characteristics--pavement density and asphalt content. Data were collected and analyzed to determine the specifications' effectiveness in providing appropriate quality levels. It is anticipated that the analyses would directly help FDOT make improvements to its asphaltic concrete pavement construction specifications. The approach taken in this research can also be used by FDOT or other highway agencies to improve other specifications (e.g., portland cement concrete) and other quality characteristics (e.g., gradation and thickness). Such specification improvements should result in sound, unambiguous, and realistic requirements that clearly communicate exactly what quality level the contractor is to provide. Highway agencies, contractors, and the traveling public all stand to benefit from the improved specifications. 1.3 Research Objectives The objective of this research is to develop a method to assess the effectiveness of highway construction specifications. The method was tested and demonstrated on the existing FDOT asphaltic concrete pavement construction specifications. With the time limit and data availability, only two quality characteristics--density and asphalt content-- for type S asphalt mix were examined in this research. The data were analyzed to determine if the present test result variations are consistent with what FDOT wants and has ordered through its specifications. A computer program was developed to convert the statistical parameters that were used in data analysis to average absolute deviation (AAD), which is used as FDOT's measure of quality for asphalt content. Guidelines and recommendations are presented to improve the existing specifications for asphaltic concrete (Type S) pavement construction. Specific objectives for this study are summarized as follows: 1. To demonstrate how the construction quality assurance database can be analyzed to monitor the quality of construction and determine when changes are needed to specifications and/or to procedures. 2. To determine what quality levels FDOT wants the contractor to provide in terms of population parameters. 3. To determine what quality levels FDOT is specifying in highway construction specifications in terms of population parameters. 4. To evaluate and determine what quality levels the contractors are providing in terms of population parameters. 5. To develop a computer program that helps FDOT assess its AAD specifications. This computer program was used as a tool to convert the quality levels that the contractors are providing in terms of mean and standard deviation to the quality levels in terms of average absolute deviation that are specified in FDOT construction specifications for the asphalt content quality characteristic. 6. To investigate and evaluate the effectiveness of presently used FDOT construction specifications and to make some recommendations to improve their effectiveness. Even though this research was specifically aimed towards implementation by the FDOT, other highway agencies will find it beneficial because the objectives are common to many highway agencies. Moreover, the same approach can be used to develop a similar technique which fits other kinds of materials, such as Superpave, Friction Course, Portland Cement Concrete, etc. 1.4 Research Approach In order to achieve the research objectives, the development of the research methodology was organized into six tasks. Task 1--Literature search. Find and review the following: 1. Previous research reports. 2. Past and current Florida asphaltic construction specifications, including existing Florida Superpave construction specifications. 3. Other asphaltic construction specifications (e.g. AASHTO, other states, etc.) Task 2--Data collection. 1. Collect the results of any experimental research projects that may have been conducted by FDOT that could be used to answer the following question: What quality level (in terms of mean, standard deviation, offset from target, etc.) existed prior to implementation of specifications? 2. Interview selected FDOT officials and Florida contractors to obtain information that can be used to supplement data collection in Subtask 2-1, above, to answer the following question: What quality level does FDOT want? 3. Collect quality control/acceptance data from FDOT projects after implementation of current FDOT quality assurance specifications. Because of the availability of information, the data that were observed started from year 1991 to the present. These data were used to answer the following question: What quality level are contractors actually providing under the current specifications? Task 3--Data analysis. 1. Analyze collected data in Subtasks 2-1 and 2-2 to provide answers to each question posed in those subtasks. 2. Analyze the current FDOT specifications to answer the following question: What quality level is actually being ordered? 3. Analyze collected data collected in Subtask 2-3 to provide an answer to the question posed in that subtask. Note: Data analysis primarily consisted of determining statistical parameters from data based on small sample sizes (n = 1 through 7). In addition, data analysis included several instances of hypothesis testing (e.g., test hypothesis that the mean and/or standard deviation of two or more data sets are equal) and testing to determine whether data are normally distributed. Task 4--Computer program development. 1. Develop a computer program to help evaluate the effectiveness of the existing FDOT construction specifications. This software was used as a tool to relate the quality levels in terms of mean and standard deviation to the average absolute deviation in order to compare the contractors' provided quality levels with those being specified. The results in subtask 3-3 were used as inputs. The computer program simulates the test results and generates the value of average absolute deviation, which is used to determine the pay factor that the contractors will get. Task 5--Interpretation. 1. Determine effectiveness of FDOT specifications. For example, is the FDOT actually ordering the quality level it wants, and are contractors providing that quality level? 2. Depending on findings from Subtask 5-1, present reasons for the effectiveness (or lack of effectiveness) of FDOT's current specifications. 3. Make any recommendations for improvement of FDOT's current specifications. Task 6--Final dissertation. 1. Write draft and final dissertation. 2. Make a presentation. Task 1--Literature search. Find and review the following: 1. Previous research reports. 2. Past and current Florida asphaltic construction specifications 3. Other asphaltic construction specifications (e.g., AASHTO, other states, etc.) Task 2--Data collection. 1. Collect the results of any experimental research projects that may have been conducted by FDOT prior to implementation of current FDOT asphaltic concrete pavement construction specifications. 2. Interview selected FDOT officials and Florida contractors to obtain information that can be used to supplement data collection in Subtask 2-1. 3. Collect quality control/ acceptance data from FDOT projects after implementation of current FDOT quality assurance specifications. Task 3--Data analysis. 1. Analyze collected data in Subtasks 2-1 and 2-2 to provide answers to each question posed in the subtasks (see pp.8-9). 2. Analyze the current FDOT specifications. 3. Analyze collected data collected in Subtask 2-3 to provide an answer to the question posed in that subtask. Task 4--Computer program development. 1. Develop a computer program to use as a tool to evaluate the effectiveness of the existing FDOT construction specifications. Figure 1-1. Research Approach Flow Chart Figure 1-1--continue Task 5--Interpretation. 1. Determine effectiveness of FDOT specifications. 2. Depending on findings from Subtask 5-1, present reasons for the effectiveness (or lack of effectiveness) of FDOT's current specifications. 3. Make any recommendations for improvement ofFDOT's current specifications. Task 6--Final dissertation. 1. Write draft and final dissertation. 2. Make a presentation. CHAPTER 2 LITERATURE REVIEW 2.1 Introduction There are several reasons for ensuring the quality of a product; however, the main reason is money. In highway quality assurance, the contractors earn more money when producing a good quality product while the highway agencies save more money in future maintenance costs if the quality is built into the pavement. There are two main steps in ensuring good quality of the pavement. The first step is preparation of good specifications for the project. The second step is ensuring the specifications are met during mix design and construction. 2.2 Highway Specifications Specifications are one of the most important tools to be concerned with in producing a good quality pavement. Specifications are used to describe the materials, workmanship, and other general requirements for the project that the highway agencies expect from the contractors. Good specifications should be easy to understand for both the contractors and the highway agencies in describing what quality is expected from the contractors. Unclear specifications often result in increased cost to the contractor, resulting in claims that have to be evaluated by the owner and that, in many cases, end up in court (Roberts et al., 1996). According to a survey conducted by the American Society of Civil Engineers, the contractors estimated that owners could save about 7.8% on construction costs if specification quality were upgraded. Assuming the annual cost of new construction (excluding homebuilding) to be $100 billion, $7.8 billion could be saved (Engineering News Record, 1979). 2.2.1 History Before the 1970s, recipe or method specifications were used in most highway projects to define the quality that the highway agencies expected from contractors. When using recipe specifications, the highway agency spells out in detail what is to be built and how it is to be done. As was mentioned in the AASHO Road Test, the use of recipe specifications does not insure that the pavement would perform and last as expected (TRB, 1976; Rilett, 1998b). Moreover, the acceptance procedure is based on engineering judgement. Engineering judgement is strongly based on past experience, and if variables unknown to the specification writer change under new conditions, the end result may not be satisfactory (Miller-Warden Associates, 1965; Rilett, 1998a). It is difficult to define quality in legal or contractual terms when engineering judgement is used. The degree of acceptable variation will differ from engineer to engineer and from job to job. In more recent years, quality assurance specifications have been emphasized. The advantage of quality assurance specifications to state agencies is the actual placing of responsibility for materials and construction quality on the contractor or producer. The specifications place few restrictions on the materials and methods to be used in order to obtain a completed product. The contractors and producers can generally choose their own materials and equipment and design the most economical mixtures meeting the specified requirements. Quality assurance specifications rely on statistical acceptance plans based on random sampling both to define the product wanted and to determine its acceptability (McMahon and Halstead, 1969; Miller-Warden Associates, 1965; TRB, 1976; Rilett, 1998b). The Florida Department of Transportation began to develop the groundwork for the quality assurance specifications in 1965. By 1971, the preliminary specifications for asphalt pavement construction were developed. In 1976, FDOT made a decision to adopt the quality assurance specifications with pay adjustment for all asphalt concrete construction effective with contracts awarded after January 1, 1977. The acceptance plans contained in the specifications have undergone some changes. For example, the minimum limit of pavement density for type S asphaltic concrete was initially defined as 98 percent of control strip, and the control strip density had to be at least 95 percent of Laboratory Density (Office of Materials and Research, 1977). In 1991, the minimum limit of the control strip density was changed to 96 percent of Laboratory Density (FDOT, 1991). In 1977, the allowable tolerance of the asphalt content was +/-0.5 percent from the job mix formula (Office of Materials and Research, 1977). From 1982 to 1991, the deviation of the arithmetic average of the lot acceptance test from the job mix formula was used to define limits of asphalt content for type S asphaltic concrete (FDOT, 1982). In 1991, the specifications were changed to an average of accumulated absolute deviations of the acceptance tests from the job mix formula (FDOT, 1991). The limits instituted in 1991 are still in use today (FDOT, 1999). 2.2.2 Purposes of Highway Specifications Highway specifications are used as follows: 1. To provide contractor a definite basis for preparing bid. 2. To inform all buyer representatives as to what the contractor is obligated to do. 3. To describe procedures that are required by the highway agencies. 4. To state the basis for sampling and testing methods, including acceptance or rejection of the completed work (Miller-Warden Associates, 1965). 2.2.3 Function of the Specifications Practical and realistic specifications are an important consideration in any quality system. A practical specification is designed to ensure the highest overall value of the resulting construction. A realistic specification acknowledges the cost associated with specification limits and the presence of variability in all products, processes, and construction. The quality level of any product should be associated with the degree of variability. Statistically developed specifications are both practical and realistic because they provide a rational means for achieving the highest overall quality of the material or construction, while recognizing and providing for the variability of the process and product (Willenbrock, 1975). 2.3 Quality Assurance 2.3.1 Definitions 2.3.1.1 Quality Assurance According to the Transportation Research Board's Glossary of Highway Quality Assurance Terms (TRB, 1996), quality assurance is defined as a process of planned and systematic actions to provide confidence that a product or facility will perform satisfactorily in service. It addresses the overall problem of obtaining the quality of service, product, or facility in the most efficient, economical, and satisfactory manner possible. Quality assurance involves continued evaluation of the activities of planning, design, development of plans and specifications, advertising and awarding contracts, construction, maintenance, and the interactions of these activities. Quality assurance in construction includes quality control, acceptance sampling and testing process, and independent assurance. The acceptance sampling and testing is done to determine whether or not the quality of produced material or construction is acceptable in terms of the specifications. The independent assurance is a management tool that requires a third party to provide an independent assessment of the product and/or the reliability of test results obtained from process control and acceptance testing. The results of the independent assurance are not used for product acceptance (TRB, 1996). The current regulations on sampling and testing of materials and construction appear in the Federal Register (FHWA, 1995). According to these regulations, contractor testing results may be used in an acceptance program. An acceptance program is defined as the process of determining whether the materials and workmanship are in reasonably close conformity with the requirements of the approved plans and specifications. The rule provides flexibility to the states in designing their acceptance programs. Acceptance of materials and construction is not necessarily based solely on any one set of information; i.e. it may or may not include the contractor's test results. The quality of the product will be insured by each state's verification sampling and testing. In addition, the data from the contractors' quality control sampling are allowed to be used if the results from the states' verification sampling and testing programs confirm the quality of the material. The samples used for the verification sampling and testing must be obtained independently by the states or a designated agent. A dispute resolution system must be established to resolve discrepancies between results from a state's verification sampling and testing program and those of the contractor (FHWA, 1995). Quality assurance of highway construction requires proper answers to the following four questions (McMahon and Halstead, 1969; TRB, 1979): 1. What do we want? 2. How do we order it? 3. Did we get what we ordered? 4. What do we do if we do not get what we ordered? What do we want? (planning and design stage). Answers to this question encompass research, development, engineering technology, and experience. When the proper materials are specified, the design is correct, good construction practices are followed, and gross deficiencies are eliminated from the beginning. The quality level of the finished project is judged by how well it serves society--physically, functionally, emotionally, environmentally, and economically. How do we order it? (plans and specifications). The second question relates to how the details are spelled out in specifications. One factor that affects the attained quality is how well the requirements of the plan and specifications define the needed characteristics of the finished project. Did we get what we ordered? (inspection, etlinlg. and acceptance procedures). In order to answer this question, the inspection, testing, and acceptance procedures need to be done. The accuracy of the answer depends on both the skills of the engineer or inspector and on the results of a system of sampling and testing. How the samples are taken and how the results are interpreted depend on the type of specifications. Under the recipe approach, the highway agency's inspector observes the procedures and makes necessary tests as construction proceeds. Thus, acceptance depends on the ability of the inspector to detect improper procedures or inferior materials. For the statistical quality assurance technique approach, a specific number of samples need to be taken on a random basis. The following are a number of problems regarding sampling and testing that affect the efficacy of quality assurance system: 1. The total of materials use in construction cannot be tested. The sample test results are only the characteristic estimation. 2. There is some testing variability. Different answers may be obtained even when the materials are the same. 3. It may take a long period of time to get the test results. 4. Often acceptance is based on indirect or empirical measurements to estimate the characteristic desired. Although there are some problems with testing time and performance-related results, as mentioned above, these aspects are beyond the scope of this research. What do we do when we do not get what we ordered? It is legally possible to insist that the failing material be replaced; however, the replacement uses more time and costs more money. Therefore, the principle of reasonable conformity and partial payments has been established. When using statistical probabilities, a system of preset partial payments for different percentages of materials within definite ranges of characteristics is provided. The payment system appears in the contract; therefore, the contractor knows in advance what the reduction or increase in payment will be for specific levels of test results and variability. There is no guarantee that the variability always will be exact as estimated by statistical probabilities; however, if sampling and testing have been properly done, a high level of confidence can be assumed. 2.3.1.2 Quality Control Quality control is defined as the process that the contractor or producer performs to assure that the materials or construction conforms to the specifications. This concept of quality control includes sampling and testing to monitor the process; however, it does not include acceptance sampling and testing (TRB, 1996). 2.3.2 Objectives of Quality Assurance Specifications The following objectives need to be considered for a successful quality assurance plan (Weed, 1996a): 1. Communicate to the contractor in a clear and unambiguous manner exactly what is wanted. Various statistical measures are used to describe the desired end result. 2. Sufficient incentive should be provided for the contractor to produce the desired quality or better. This can be accomplished by means of adjusted pay schedules. Pay reduction will be imposed on the contractor for deficient quality. A bonus will be given for superior quality when appropriate. 3. The specification should specify 100 percent payment for acceptable work, and it should be fair and equitable in assigning pay factors for work that differs from the desired quality level. 4. The specification should define an acceptable quality level (AQL) and rejectable quality level (RQL) realistically for each quality characteristic. The AQL should be set high enough to satisfy design requirements; however, it should not be so high that extraordinary methods or materials will be required. The RQL should be set low enough that the option to require removal and replacement is truly justified when it occurs. 5. The appropriate target level of quality for obtaining 100 percent payment should be clear to the contractor. 2.3.3 Advantages and Disadvantages of Quality Assurance Specifications 2.3.3.1 Advantages of Quality Assurance Specifications The biggest advantage to the state highway agencies is by placing the responsibility for materials and construction quality on the contractor or producer. The benefit to contractors and producers is the freedom to choose their own materials and equipment and to design the most economical mixtures meeting the specified requirements. The benefits of quality assurance specifications are primarily due to the lot-by-lot acceptance procedures. When lots are immediately accepted, conditionally accepted with a reduction in payment, or rejected, contractors or producers know their position. A price reduction motivates the contractor to take corrective action before large quantities of non-specification material or construction are produced. Moreover, it avoids tie-up of capital when payment is held up due to failing tests (Hughes, 1996; TRB, 1976, 1979). The quality assurance specifications are easier to write and to interpret what is expected from a highway agency by describing the desired end result in statistical terms rather than in a vague term like "reasonably close conformance." The acceptance criteria and random sampling procedures are clearly defined. The risks to both the contractor and the highway agency can be controlled and known in advance. Quality assurance specifications are easier to enforce because of a clear separation of responsibilities for control and acceptance. Moreover, they are easier to apply because pay adjustment for defective work is predetermined; thus, no negotiations are required. Under the earlier method-type specifications, a contractor's bid was often influenced by the reputation of the engineer who was in charge of the project acceptance. An additional benefit of quality assurance specifications is the produced data. Whereas historical data collected in conjunction with method specifications have been notoriously unreliable, the quality assurance specifications produce useful data obtained with valid random sampling procedures. These data can be analyzed at a later date to develop better specifications (Weed, 1996a). 2.3.3.2 Disadvantages of Quality Assurance Specifications Agencies performing the contractor quality control activities as well as their own quality assurance sampling and testing may experience an increase in workload because the number of tests may increase. Small contractors may not be able to hire a full-time quality control technician when the prospect of successful bidding contracts was uncertain. These organizations would have to arrange with a testing laboratory to do the work (TRB, 1976). 2.3.4 Types of Acceptance Plans There are two general types of acceptance plans in quality assurance. One is an attribute sampling plan, and the other is the variable sampling plan. 2.3.4.1 Attribute Sampling Plan An attribute sampling plan is used when the samples are inspected with a go/no go gauge. When attribute sampling is used, each lot is assumed to consist of a collection of N units. A random sample containing n units is chosen from the lot, and each of them is checked. The attribute sampling plan is useful when it is not practical to measure the characteristic, but each unit can be classified as acceptable or defective by visual inspection (Chang and Hsie, 1995; Vaughn, 1990; Wadsworth et al., 1986). An attribute sampling plan does not require complicated computation. Generally, the inspection process is to subject each item in the sample to a rapid visual examination or to use a simple gage to determine whether or not a certain dimension meets specifications. Elaborate testing or measuring equipment is not needed. The time that is required for inspecting a large number of items is minimal. The great disadvantage of attribute sampling is that not much information is obtained. The purpose of attribute sampling is to classify an item as accepted or rejected; the inspection does not provide the average level and the variability of a characteristic. Therefore, there is no clue in regard to the type of corrective action that should be taken (Hudson, 1971; Wadsworth et al., 1986; Vardeman and Jobe, 1999). 2.3.4.2 Variable Sampling Plan Sampling by variables makes use of all the relevant information (number of tests, means, standard deviation, etc.) computed from the sample to estimate the quality. Sampling by variables provides greater discriminating power for any given sample size. Moreover, this type of sampling produces a continuous result which is more suitable for developing adjusted pay schedules to deal with the intermediate levels of quality that are often encountered. The continuous measure of percent defective is a more appropriate parameter upon which to base a system of adjusted payments (Chang and Hsie, 1995; Hudson, 1971; Wadsworth et al., 1986; Vardeman and Jobe, 1999). In general, attribute sampling is much less efficient than variable sampling. To obtain a certain buyer's risk or seller's risk, the number of samples needed for sampling by attribute may be 30 percent greater than the number needed for the 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. In most highway construction situations, the true standard deviation, o, is not known. However, the standard deviation can be estimated from random measurements taken from the population. There are three forms of specification limits in any type of variable acceptance plan. The limits of the measured characteristic may be an upper limit, a lower limit, or both an upper and a lower limit. The acceptance plan may be designed in several ways. It may specify a minimum percentage of material or construction having a value of the measured characteristic within the limitss, or a maximum or minimum value of the measured characteristic may be specified (TRB, 1976). For density and asphalt content, variable sampling plans are used in current Florida standard specifications for road construction. The minimum value of the lot mean is defined for density, while the average absolute deviation from the job mix formula is used for asphalt content (FDOT, 1999). 2.4 Acceptance Using Lot-by-Lot Method In lot-by-lot acceptance plan, one or more samples are chosen at random from the lot. The decision of acceptance or rejection is based on the test results of the samples. The lot-by-lot sampling inspection improves quality in at least two ways. First, inspection by lots lowers the number of defective items per accepted lot when compared with the number of detectives in the lots taken as a whole. Second, because a large number of rejected lots is costly to the supplier, the supplier will try very hard to submit better quality lots in the future (Bowker and Goode, 1952). A lot in highway quality control can be applied to a very large group of units, to a large quantity of material, or to an infinite number of locations. However, a lot is generally a definite amount of similar material (Chang and Hsie, 1995; Hudson, 1971a). Different lots of the same kind of material can differ in quality, as indicated by variations in the measured values of some characteristic of material. The lot size needs to be defined for sampling and testing purposes. Only after establishing the size of the lot can the sampling locations and frequencies for quality control and assurance be determined. Under lot-by-lot testing for acceptance, the process of constructing a highway may be thought of as the production of a succession of lots. These lots are individually considered by highway agencies for acceptance or rejection. When estimating the size of lots and sublots, the subject of risk is raised. The acceptance plan becomes burdened with an excessive amount of costly testing when the lot size is too small. When the lot size is large, it is a disadvantage for the contractor because of the large quantity of material that can be rejected when the quality is not acceptable (Anglade, 1998). 2.5 Random Sampling If a sample is to provide us with useful information about the population, it must be representative, i.e., the sample must be made up of typical members. A representative sample for quality assurance is generally obtained by random sampling. Random sampling is often defined as a manner of sampling which allows every member of the population (lot) to have an equal opportunity of being selected as a sample. Most state highway agencies use stratified random sampling, where the lot is divided into equal sublots and the sample is obtained by random sampling from each sublot (Drain, 1996; Hughes, 1996). The more fundamental method of random sampling, which can be called pure random sampling, allows the samples to be selected with an unbiased manner, based entirely on chance. However, this method has some practical drawbacks that will be discussed shortly. 2.5.1 Pure Random Sampling 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, neither the highway agency nor the contractor would feel that it adequately represents the lot. Sampling locations that tend to be spread more uniformly throughout the work are believed to represent the lot better. Therefore, most highway agencies use stratified random sampling for acceptance. 2.5.2 Stratified Random Sampling The stratified sampling method for highway material and construction items is designed to eliminate the clustering problem and tend to be quite similar. (Weed, 1989) Each lot is considered to be made up of sublots. Sublots are defined as an equal size subdivision of lot. Random sampling is done within the boundaries of each sublot. Stratified random sampling is used in the current Florida road specifications for type S asphaltic concrete material. For the density quality characteristic, the standard size of a lot is 1500m of any pass made by the paving train regardless of the width of the pass or the thickness of the course. A sublot is 300m or less. At the end of a production day, when the completion of the lot is less than 1500m, it is considered as a partial lot. If the partial lot length is 600m or less, and a full-size lot from the same day is available, then the previous full-size lot is redefined to include this partial lot. The number of tests required is shown in Table 2-1. For asphalt content, a standard size lot for acceptance at the asphalt plant consists of 3600 metric tons with four equal sublots of 900 metric tons each. If the partial lot contains one or two sublots, this partial lot is included to the previous full-size lot from the same day (if available), and the evaluation is based on either five or six sublot determinations. When the total quantity of the mix is less than 2700 metric tons, the engineer will evaluate the partial lot for the appropriate number of sublots from n=l to n=3 (FDOT, 1999). 2.6 Variability in Highway Construction The quality of highways has always been a concern of highway engineers and contractors. The variability of materials and construction processes is used as one of the measures to assess quality in the American Association of State Highway and Transportation Officials (AASHTO) Guide for Highway Construction (AASHTO, 1996). In connection with the inspection of highway materials or construction, various kinds of measurements are made. For example, it is necessary to measure the density of pavement to ensure its quality. It is time consuming and costly to measure every small portion of pavement. Therefore, decisions must be based on measured density in a few Table 2-1. Density Testing Requirements Lot Size Number of Tests Less than 900 m 3 901 to 1200 m 4 1201 to 1500 m 5 1501 to 1800 m 6 1801 to 2100 m 7 Greater than 2100 m Two lots Source: FDOT Standard Specifications for Road and Bridge Construction 1999 (FDOT, 1999). suitable locations. The samples and locations should be so chosen that the measured values can be considered as representative of the density of the entire pavement. For these reasons, statistics need to be used to determine the variability with respect to each material or construction characteristic. No matter what kinds of measurements are made, it is unlikely that all measured values will be exactly the same. Relatively small variations in the measured values of a property of a material may be caused by the fact that the measurements cannot be made exactly enough. However, fairly large variations usually occur because of the nature of the materials and the fact that no two samples of the material will be alike. Therefore, increasing the precision of a test method, or the care with which the measurements are made, beyond a certain limit would not make the measured values more reliable. Factors that greatly affect the variation are called "Assignable Causes". The assignable causes are actual errors and usually produce much larger variations than random causes. An example of assignable causes is the intentional departure from specified proportions or methods or a malfunction of equipment. Assignable causes can be detected and eliminated by thorough inspection. Assuming no assignable causes are operating, there are three sources of variations involved in highway construction (Hudson, 1971; Hughes, 1996): The actual variation. The actual variation is the unavoidable variation in material or a combination of materials that are tested. The sampling variation. The variation due to differences in the samples selected for testing such as segregation, etc. Segregation is a major source of variation in most property measure values of a sample used in highway construction. Segregation separates a material into unlike parts. Most of the highway materials tend to segregate to some degree. If we could get perfectly mixed material in which the particles are arranged in the manner indicated in Figure 2-la, the accuracy of the measured values made on samples taken from any part of the area would depend only on the precision with which the measurements were made. In contrast, if the material is completely segregated as indicated in Figure 2-lb, samples taken from different areas would be widely different. The actual construction materials are neither mixed with complete uniformity nor completely segregated. They are most likely as indicated in Figure 2-1c. As a result of segregation, the density test results at two locations may differ greatly (Miller-Warden Associates, 1965; Hudson, 1971). Random sampling is mostly used in highway quality assurance to reduce the effect of segregation. The locations or units from which the samples are obtained must be entirely random, which means that the locations of the samples are determined without bias, such as by using a table of random numbers. The testing variation. The testing variation is the variation due to the lack of uniformity in the testing procedure and includes the effect of differences in the preparation of portions of a sample for testing. The testing variation would be measurable if the test did not destroy the material. The same sample could be used to repeat the test. The relation between the total standard deviation and its three components is usually represented by the following equation: ST = S 2 + S (2.1) ST = Total standard deviation Sa = Actual variation Ss = Sampling variation (also called sampling error) St = Testing variation (also called testing error) 2.7 Acceptance Tolerance Under most current practices, one periodic sample is taken by stratified random sampling. This sample is tested, and the testing results are used to determine if the material is accepted or rejected. If the measured test results are within the tolerance specified in the specification book, the material or construction lot is accepted. If the test results are not within the tolerance stated in the specifications, the material or construction lot is rejected. M Completely random arrangement of types of particles produced by perfect mixing. Complete segregation of types of particles. InILSWWTLY EISa T Arrangement of particles intermediate between completely random and completely segregated. The type of mixture commonly found in practice. rrW mCuamo Figure 2-1. Degrees of Segregation Reasonable specification limits should allow for normal testing variability and process variability. According to a FHWA report, a considerable gap exists in highway work between the quality of work specified and the quality of work received (Quality here refers to quality of compliance to specifications limits and not quality of performance) (FHWA, 1977). Although the AASHTO Guide Specifications are a noteworthy milestone toward standardization, they are not necessarily the best engineering or the most economic specifications for some states (Miller-Warden Associates, 1965). Willenbrock (1975) suggested that every highway agency should have their own specifications to describe realistic standards, which more accurately reflect the inherent variability of a given material type or construction characteristic. The realistic specifications would enable a contractor who is normally applying good control processes to run a minimum risk of having acceptable material rejected. Hughes (1996) stated that the state highway agencies use their experience, engineering judgement, tolerances from other agencies, and standard precision statements more often than they use variability data from studies and projects. Moreover, many specification limits are still being set the same way as the ones used in the AASHO Road Test almost 40 years ago. 2.8 Pay Factor A common feature of most statistical end-result specifications is the pay adjustment. When a construction item falls just short of the specified level, it may not warrant replacement or removal but neither does it deserve 100 percent payment. Therefore, the pay factor in the specifications is used to adjust the contractor's pay according to the level of quality actually achieved. The pavement has more chance to fail prematurely if the construction is deficient. It may not be capable of withstanding the design loading. The necessity of repairing this pavement early results in an additional expense to the highway agency. The highway agency is normally responsible for this expense because such repairs typically occur long after any contractual obligations have expired. A main objective of the pay adjustment is to withhold sufficient payment at the time of construction to cover the extra cost anticipated in the future repair that was caused by the deficient quality work. The FHWA initially supported the incentive pay concept as an experimental feature. After several years of satisfactory experience, it is now used as a standard feature in many highway construction specifications (Weed, 1996b). Under the incentive pay concept, a contractor receives a bonus as a reward for providing superior quality product. That means the quality levels exceed the specification in areas where additional value is provided in terms of performance of the finished product. The incentive not only tends to soften the punitive perception the construction industry originally had of statistical end-result specifications, it provides an increased incentive to produce high- quality work believed to be in the best interest of all concerned. A specification with incentive pay adjustment is intended to give conscientious contractors with good quality control a bidding advantage over contractors with poor quality control. In a competitive environment, incentives provided in the contract documents will normally result in very little if any additional project costs. A good contractor will be confident of achieving the incentives and will bid accordingly in order to increase his chances of getting the work. Absolutely, this assumption relies on the premise that it does not cost any more to do quality work. The good quality-conscious contractors have proven this premise over and over (Wegman, 1996). Pay adjustment with maximum pay factor of 100 percent is used in current Florida Road Construction Specifications. For density property, partial payment is given when the lot has an average density less than 98 percent of the control strip density. For asphalt content, the limits depend on the sample size of each lot (FDOT, 1999). There are factors that must be taken into account in pay adjustment for deficient quality pavement: 1. The cost of earlier repair because the poor quality pavement was constructed, 2. The administrative costs involved in preparing for the premature pavement repair, 3. The motoring public costs for the earlier disruption of traffic to make the necessary repairs, and 4. For practical reasons, a small area of poor quality pavement may make it necessary to overlay a larger area of pavement (Weed, 1989). CHAPTER 3 MATHEMATICAL AND STATISTICAL PRINCIPLES UNDERLYING VARIABILITY IN QUALITY ASSURANCE SPECIFICATIONS The purpose of this chapter is to present an overview of the mathematical and statistical concepts related to an acceptance plan of quality assurance specifications. 3.1 Statistical Modeling Shapiro and Gross (1981) stated that a statistical model is a mathematical formulation that expresses in terms of probabilities the various outputs of a system. A statistical model is mostly useful in situations where the output cannot be expressed as a fixed function of the input variables. For example, consider the measurement of the pavement density. Assuming several measurements are taken, it will not be surprising to find a different reading for each measurement. These measurements can be considered as the output of the system. It can be further assumed that the actual pavement density is fixed and that this variability in the reading is due to errors in measurement. Thus, a model is selected to represent this variability. y, = + (3.1) y = The output (i.e. the ith measurement) y = The true mean of the population , = Measurement error for the ith trial Equation 3.1 can be considered as a statistical model when a probability distribution is selected to represent the variability e,, which is sometimes positive and sometimes negative. When taking a large number of observations, the average of e, will be zero; therefore, the net result is [t. However, in a real problem there is only a limited number of data points, and because of this fact, only an approximation of [t is obtained. Therefore, an estimate of the variability of the measuring error is required. In statistics, this estimate of the variability is called a standard deviation and is represented by the symbol c. 3.2 Reliability of Measurement The terms precision, accuracy, and bias are often used when comparing the reliability of estimated values that are based on tests of samples. If the measurement values are spaced closely together near one spot, these values provide good precision. If the mean of the measurement values tend to coincide with the true mean of the population, these values provide good accuracy. Bias is a measure of inaccuracy and is the degree to which the mean of a distribution of measurements tends to be displaced from the true population value. A common way to explain these terms is by imagining a marksman shooting at a target, as shown in Figure 3-1 (Hudson, 1972; Hughes, 1996; Weed, 1996a). 3.3 Quality and Variability Concepts Quality in this dissertation refers to the quality of conformance with the specifications. The greater the compliance is, the more effective the specifications are. STATISTICAL DESCRIPTION ACCURATE AND PRECISE WHAT THIS MEANS DECISIONS ARE USUALLY CORRECT AND RESOURCES ARE USED EFFECTIVELY ACCURATE BUT NOT PRECISE a a DECISIONS TEND TO BE CORRECT BUT RESOURCES ARE WSTED PRECISE BUT NOT ACCURATE DECISIONS ARE OFTEN INCORRECT BIAS Figure 3-1. Concept of Accuracy, Precision, and Bias The concept of variability comes from the fact that all materials and construction are not exactly the same and subject to some variations. The variations could be natural and occur randomly, which most specifications allow. However, variations resulting from errors (design, equipment, materials, or construction errors) will penalize the producer by deducting a percentage of his payment depending on the amount of variation. The variability can be defined by using the sampling data to compute two important properties. The first one is the central tendency of all the measurements, known as the average value or mean. The other is a measure of variation from the mean that is known as the standard deviation (Adam and Shah, 1966). The central tendency is the central position on a scale of measurement, the value about which the observations have a tendency to center. The most common measure of the central tendency is the average value. The average can be determined by adding all the measurements or values in the data set and dividing the sum obtained by the number of measurements that make up the data set. The equation is as follows: x =- (3.2) n This characteristic is not enough to describe the distribution adequately. Even though the central tendencies of two sets of data are the same, the distributions may be different. Therefore, at least a second characteristic called the dispersion is required. The dispersion or a measure of variation describes the degree of scatter shown by the observations. There is not much variability if the measurements are closely clustered about the mean. The variability is greater when the measurements spread far from the mean on both sides. The dispersion can be measured by the use of statistical parameters such as the range (R) or the standard deviation (c). The range is the difference between the largest (Xma,) and the smallest (Xmn) values in a set of data as shown in the following equation: R = max xmn (3.3) The major drawback of the range is that it uses only two extreme values in the calculation. It shows that the other values lie between the extremes; however, the range does not provide any measure of the dispersion of the other values. The standard deviation is the most satisfactory and most commonly used parameter to measure the variation. Since the standard deviation is the square root of the average of the squares of the numerical differences of each observation (x) from the arithmetic mean (.i), it takes into account the effect of all of the individual observations (n) (Willenbrock, 1975). The population standard deviation (c) can be determined by the following equation: o-=Z -- (3.4) The sample standard deviation (S) can be estimated from the following equation: S = - (3.5) where x Sample average When the value of the standard deviation is known for a particular measurement, under given conditions, statistical principles can be used to estimate the percentage of measurements that will fall within selected limits under similar conditions. Therefore, the realistic deviations will help in providing realistic tolerances for specifications that will ensure that future similar construction will be as good as or better than the quality that is currently produced. In most cases in highway construction, the difference between most values in a group and the calculated average for the group will not exceed 2 times the value of C (Hudson, 1971). 3.4 Variation as a Quality Yardstick Taguchi (1986) viewed variation as a lack of consistency in the product that will give rise to poor quality. Therefore, Taguchi developed methodologies aimed at reducing two elements of variation: (a) deviation from the target and (b) variation with respect to others in the group. A typical quality measure of a product is compared to the desired state as shown in Figure 3-2. Taguchi believed that even though the product mean value is within upper and lower acceptance limits, the cost of quality goes up if it is off the target and the variation around the mean is large. The more the deviation, the higher is the expected life-cycle cost (Taguchi, 1986). Life-cycle cost is defined as the total economic worth of a usable project segment that was determined by analyzing initial costs and discounted future costs, such as maintenance, user, reconstruction, rehabilitation, restoring, and surfacing costs, over the life of the project segment (Walls III and Smith, 1998). Taguchi (1986) used a simple model of the loss imparted to the seller, the buyer, and society. This model serves its purpose in highlighting the fact that a product is cheaper and better if it is consistently produced close to its target value. A distribution of more frequent achievement of the target value and smaller variation around the target value is preferred. The bottom picture in Figure 3-2 shows the loss function model, which is L(y)= k(y-TV)2 (3.6) where k = Constant (y-TV) = The deviation form the target value TV is the target value of a variable at which the product is expected to perform best. The horizontal axis shows values of the variable, while the vertical axis shows the loss associated with each value of the variable. The assumption of this model is that the loss at the target value is zero, and the buyer dissatisfaction is proportional only to the deviation from the target. The buyer is satisfied if the quality of the product is at the target value (Raheja, 1991). 3.5 Describing Parameters and Statistics One difference between a population and a sample is the way the summary measures are calculated for each. Summary measures of a population are called parameters, while summary measures of a sample are called statistics. For example, if the data set is a population of values, the average is a parameter, which is called the population mean. If the data set is a sample of values, the average is a statistic, which is called the sample average (Schlotzhauer and Littell, 1997). To prevent confusion, the TARGET Figure 3-2. Conformance to Specification and Quality Loss PROCESS A PROCESS B QUALITY LOSS = COST LOSS rest of this research uses mean to indicate the population mean and average to indicate the sample average. The Greek alphabet is used to denote the population parameters. The differences in notation between the sample and the population measures that are used in this research are shown in Table 3-1. Table 3-1. Symbols used for Populations and Samples Data Set Average Variance Standard Deviation Population [t (2 C Sample x S2 S 3.6 Specification Compliance Measures Most states, including Florida, are using plant-produced mix properties, density, and smoothness tests to determine overall quality and acceptance of asphaltic concrete construction work. The mix properties of the asphaltic concrete describe overall material quality. The density shows the capacity of the pavement to withstand repetitive loads from traffic, while the smoothness is used to evaluate the ride quality experienced by the traveling public. These measures describe the quality level achieved during construction whether viewed independently or collectively (FDOT, 1999; Schmitt et al., 1998). There are five different measures that are used to determine specification compliance by state highway agencies: average, quality level analysis, average absolute deviation, moving average, and range (Schmitt et al., 1998). 3.6.1 Average When the average is used as a compliance measure, an assumption has been made by the developers of the acceptance plan that the variation must be known because it determines how accurately the average can be estimated from a given sample size. A confidence interval should be constructed to describe the interval of the mean that can be found at a specified probability level. The confidence interval of mean can be estimated by using the following equation: Confidence Interval of mean = x z -, (3.7) -Vn 2 where x = Sample mean z = Standardized statistic; c = Confidence coefficient; Y2 = Known variance; and n = Number of tests. Acceptance plan developers can make the assumption that the standard deviation is known if they have data showing that the standard deviation does not change significantly from contractor to contractor or from project to project. The FDOT uses the average method as a compliance measure for pavement density acceptance. 3.6.2 Quality Level Analysis When the quality level analysis method is used for the specification compliance measure, the percent defective or the percent within limits need to be estimated. The percent defective in quality assurance specifications is the portion of the measured characteristic that falls outside a single lower or upper specification limit or outside both lower and upper limits. The smaller the percentage defective in the lot, the better the quality is. The good-quality lots will get full payment. Penalty or payment deduction will be applied to lots that have some defects. The amount of deduction will depend on the amount and the seriousness of the defects. For asphalt content and pavement density characteristics, the potential economy of using percent defective could serve as an incentive to maintain a good quality control process. When the contractor maintains a high level of quality control, the variability of the production process will be reduced. As a result, the contractor can aim for a lower characteristic mean and still meet the specifications. The contractor with a loose quality control program will have high variability in the production process that will create difficulty in meeting the specification requirement; therefore, the contractor must aim for a higher mean. The higher the production mean is, the more expensive the cost is (Al- Azzam, 1993). Figure 3-3 shows several sets of the average and variance value combinations that give the same percent defective result. In order to estimate the lot percent defective (PD) or percent within limit (PWL), it is first necessary to determine either one or two quality index values (Q). One value is needed for a quality characteristic having a single specification limit. Two values are used for a quality characteristic having a double specification limit. Since the variability is estimated by the standard deviation calculated from the sample, it is a "variability- unknown" percent defective. The equations used to compute the quality index are as 46 (A Constant Percent Defective OC ;A g 1C L Figure 3-3. The Flexibility of the Percent Defective Quality Measure with Respect to [t and y. follows. x-L --- L Q L = (3.8) S U -x Qu -- (3.9) where QL = Lower quality index Qu = Upper quality index x = Sample mean S = Sample standard deviation L = Lower specification limit U = Upper specification limit After obtaining the value of Q, PD/PWL can be estimated from acceptance plan tables that have values of PD/PWL associated with any specific value of Q and sample size. The individual estimates of PD are added to obtain PD for a double specification limits. Percent defective and percent within limit are shown in Figure 3-4. The total PWL can be found by the following equation: Total PWL = (Pu + PL) 100 (3.10) where PWL = Percent within limit Pu = Upper percent within limit PL = Lower percent within limit There are four cases to measure percent defective (Willenbrock and Kopac, 1976): 1. Population mean ([t) and population standard deviation (c) are both known. 2. Population mean ([t) is known, but population standard deviation (C) is not known. 3. Population mean ([t) is not known, but population standard deviation (C) is known. 4. Population mean ([t) and population standard deviation (c) are both unknown. Case 4 is the most encountered case in construction situations and it is the one, which is assumed when a PD/PWL acceptance plan is developed. PDu = Upper percent defective PDL = Lower percent defective L = Lower limit U = Upper limit TV = Target value PWL t = Mean TV PDL PDu L U Figure 3-4. Percent Defective (PD) and Percent within Limit (PWL) under the Standardized Normal Distribution Curve. 3.6.3 Average Absolute Deviation The asphalt content characteristic has been controlled to achieve average values approximating target values. Highway agencies often use the average of absolute deviations from target values instead of the average of arithmetic deviations to control process manipulation (Parker et al., 1993). However, the quality level analysis is the most frequently used (Schmitt et al., 1998). The average of the absolute deviations (AAD) from target values is used in Florida construction specification for asphalt content quality acceptance. Specifications are currently structured to allow greater deviations from the target for smaller sample sizes. The equation that is used to determine the average absolute deviation is as follows: (Zx, TI) A= (3.11) n where A = Average absolute deviation; x = Individual test result; TV = Target value; and n = Number of tests. Parker et al. (1993) states that the average absolute deviation is a simple but statistically correct method that maintains consistent levels of control for both central tendency and variability of absolute deviations from the job mix formula (JMF). Weed (1999) believes that there are some problems with AAD. The AAD should be a function of both population spread and population shift, but sometimes it is determined entirely either by the population spread or by the population shift. Moreover, two materials may yield the same value of AAD although they have different distributions. Another problem is that it is based on a target value, which normally is the midpoint between lower and upper specification limits; therefore, it is not suitable for one-sided specifications for which a single, specific target value cannot be defined. Some examples of the problems mentioned above are presented later in this chapter. 3.6.4 Moving Average The moving average can be computed by finding the average of the test results. When a new test result is obtained, it is included in the calculation, but the oldest test result is dropped out of that set (Hudson, 1971). For a better understanding, see the following example. Test No. 1 2 3 4 5 6 7 Xn 3.55 3.70 3.65 3.60 3.60 3.63 3.57 3.62 3.64 3.61 Assume above that the sample size is 5. The value of x, for test No.5 is the average of the values ofx for the first five tests. For test No.6, the result is equal to the sum of the test results of test No.2 to 6 divided by 5. The first test result in the original set is dropped out, while the new test result is added. The other values are computed in a similar way. 3.6.5 Range The range method is a specification compliance measure that does not use the distribution of values. Only the maximum and minimum values are used in the calculation. The range of values is compared to the specification limits. The range of the test results can be computed by the following equation: Range = (Max Min) (3.12) where Max = Maximum test value; and Min = Minimum test value. 3.6.6 Pavement Density Specification Compliance Measures According to research done by Schmitt et al. (1998), from the information obtained from 38 states, quality level analysis is the most common compliance measure for pavement density (20 states). The next common method is the average (8 states), followed by range (4 states), absolute deviation (3 states), and moving average (3 states). Florida is among the few states that use the average method in density pavement acceptance for type S asphaltic concrete material (FDOT, 1999). 3.6.7 Asphalt Content Specification Compliance Measures Quality level analysis is the most frequently used compliance measure for the asphalt content property (14 states out of 38 states). Average absolute deviation is next (8 states), followed closely by moving average (7 states), and average (6 states). Range (3 states) is less commonly used (Schmitt et al., 1998). Average absolute deviation is currently used as a compliance measure for asphalt content acceptance in Florida. The acceptance range of average absolute deviation is wider when the sample size is smaller (FDOT, 1999). 3.7 Conformal Index Approach An alternative approach to the use of the standard deviation is a statistic referred to as the conformal index (CI). The Material Research and Development Inc., first used this approach. The conformal index can be used to estimate accurately the size and incidence of variations from a quality level target such as the target job mix formula (JMF). The CI is similar to the standard deviation; however, the standard deviation is used to measure the deviation from the arithmetic average value, while the CI measures the deviation from the target value such as the JMF value. In other words, the standard deviation is a measurement of precision, whereas the CI is a measurement of exactness (accuracy) or degree of conformance with the target value. The CI is as useful as the standard deviation. Both can be used with both percent within limits/percent defective and the loss function approach. Nevertheless, the attractiveness of CI is that it focuses on the target value, and it is this target value that is defining the quality level (Cominsky et al., 1998; Hudson et al., 1972; Kandhal et al., 1993). The standard deviation (S) and conformal index (CI) can be written in equation form as follows: S1= (3.13) S(X- TV)2 CI =-- (3.14) V n where TV = Target Value n = Sample Size The following equation shows the relationship between the standard deviation and the conformal index (Hudson, 1972): (n -1)S2 + nd2 (3.15) n CI (3.15) where d = The average bias or offset of the average of group of measurements from the target value, i.e., d = TV = x 3.8 Potential Problems with Existing Quality Measures The following examples will be considered to explore the mathematical properties of the different quality measures. In Figure 3-5, the average absolute deviation (AAD) and the conformal index (CI) are computed for a sample size of n = 2 and for two different cases. In the first case, one test result value falls on either side of the target value. In the other case, both values fall on the same side of the target value. From this example, it is seen that AAD = 6 in the former case and AAD = A in the latter case, while CI seems to be the same for both cases. The AAD is determined entirely by the population spread in the former case and entirely by the population shift in the latter case. This effect may be less pronounced when sample sizes get larger. Nonetheless, there is some doubt concerning the consistency of AAD as a quality measurement (unless this unique property happens to characterize performance accurately). There is nothing to suggest a problem with CI as a measure of quality in Figure 3-5 because the performance is logically expected to be a function of both population location (shift) and population spread. The three basic quality measures--AAD, CI, and PD/PWL--are explored in order to see if widely different distributions could be found that would produce the same levels of the quality measures identically as shown in Figure 3-6. Both the narrow and wide distributions have AAD = 1.59 in the top figure. Both distributions have CI = 2.00 in the middle figure. Both distributions have PD = PWL = 50 in the bottom figure. The problem with these three quality measures is that they could not distinguish between distributions that might reasonably be expected to produce markedly different levels of performance. From the previous examples, it is seen that there are inherent mathematical inconsistencies in AAD that weaken its usefulness as a quality measure. The AAD is variably sensitive to both the shift of the mean away from the target value and the variability of the population itself. CI is somewhat more consistent than AAD; however, its weakness is that it can give the same CI value even though the combinations of mean and standard deviation are different. The PD/PWL was also found to have inconsistencies because it is insensitive to changes in variability around PD = PWL = 50, while performance may be sensitive to variability in that region (Weed, 1999). 3.9 Normal Distribution As mentioned previously in this dissertation, test results of most highway quality characteristics are normally distributed. That is to say, if all the items in the lot were to be tested, the test results would be distributed among the possible values similar to the bell-shaped curve. The main features of the normal distribution are a symmetrical distribution of readings on each side of the average. The relative height of the normal curve at its center depends on the value of o. The curve is relatively tall and narrow if the C is small. The curve becomes flatter and wider when the cy gets larger. The pattern of the frequency Represents population spread within itself Represents shift of population away from target Case 1 Case 2 X 6 6 X X TARGET TARGET AAD = [(6 A) + (5 + A)] 2 = AAD = [( 8) ( + 6) / 2 = A ct = V[(0-A f +(6 + ) /2 = V62 + A2 CI= \/[(A 6 + (A+ )2]2 =\^+A62 Figure 3-5. Comparison of Mathematical Properties of AAD and CI for Sample Size of n=2. p = 7.59 o = 0.50 BOTH DISTRIBUTIONS HAVE AAD = 159 (L= 3, U = 9, TARGET = 6) p = 6.00 a = 2.00 5 10 15 S= 7.94 a" = 0.50 BOTH DISTRIBUTIONS HAVE CI = 2.00 (L = 3, U =9. TARGET = 6) 2 =6.00 a = 2.00 5 10 15 p = 9.00 = 0.50 p = 9.00 ao 2.00 5 10 15 Figure 3-6. Potential Weaknesses of Common Statistical Measures of Quality BOTH DISTRIBUTIONS HAVE PD= PWL = 60 (L 3, U 9) rates, as deviating from the average, should be noted in particular. The rate of decrease is slight when the values are near the average, and the rate of decrease is sharper when the values are farther from the average. Finally, the frequencies approach zero. The equation that can be used to calculate the height of this curve is: (x p)2 1 y= 2e 2 (3.15) It is assumed that the curve encloses all of the measured test results and the probability is 100 percent. With this assumption, a certain percentage of the area under the normal curve to each distance on the o scale between the center of the curve and any selected point can be assigned. These percentages can be used to predict the future measured values that can be expected to fall between the two points. 3.9.1 Skewed Distribution In some cases, the distribution of some kinds of measurements is not symmetrical, meaning it does not have the same shape on both sides of the mean of the values. The unsymmetrical characteristic of the distribution is called skewness. If the distribution curve has a long tail on the right, then the distribution is positively skewed. On the other hand, if the long tail is on the left, the distribution is negatively skewed. Positive and negative skewed distributions are shown in Figure 3-7. 3.9.2 Distribution of Group Averages An important theorem in statistics is the central limit theorem. The central limit theorem states that if a population has a finite variance o2 and a mean [t, then the distribution of the sample mean approaches the normal distribution with variance 2/n a.) Positively Skewed Distribution Neuativelv Skewed Distribution Figure 3-7. Types of Distribution and mean [t, as the sample size increases. If the measured values are divided into groups in a random manner, the averages of these groups will form a histogram having nearly the same pattern as the normal curve. According to the central limit theorem, when the number of measured values in each group becomes larger, the shape of the histogram gets closer to that of the normal curve. The preceding statement is true even though the pattern of the individual measured values is skewed, rectangular shaped, triangle shaped, or shaped some other way. For this reason, the averages of small groups of measured values are sometimes used when basing inferences on the normal curve. The size of the standard deviation is affected when using the averages of groups of measured values. The deviation for the distribution of the averages will be smaller than the deviation of individual measured values. The standard deviation of the averages of groups of measured values can be calculated from the deviation of the individual measured values divided by the square root of the number of values in each group as shown in the following equation: S S- = (3.16) 3.10 Correcting the Bias of Sample Standard Deviation Dr. Walter A. Shewhart, father of statistical quality control, simulated theoretical models by marking normal distribution numbers on chips, placing them in a bowl, and mixing them thoroughly. Each set of chips as different sized samples was drawn at random. In the long run, the standard deviations of samples of any size from a normal universe will follow a chance pattern that can be predicted by mathematics. These predicted numbers are used to correct the bias of sample standard deviation. The Shewhart's normal bowl played a vital role in the development of ideas and formulation of methods culminating in the Shewhart control charts (Grant and Leavenworth, 1980; Burr, 1976; American Society for Quality, 2000; National Institute of Standards and Technology, 2000). When values of (x x)2 from samples are used to estimate universe dispersion, a source of difficulty is that the mean of the universe ([t) is unknown. Thus, the deviations that are squared must be measured from the sample average (x) of each sample. S(x, )2 will be less than (x, )2 except in the occasional case where the x i i happens to be identical with the unknown [t. Some compensation for this bias is, therefore, needed in any statistic based on -(x, )2 if the statistic is to be used to estimate the universe standard deviation (o) or the universe variance ("2). An unbiased 02 may be estimated from the sample variance (S2) defined as follows: Z (x )2 S2= (3.17) n-l The use of n 1 rather than n in the denominator tends to compensate for the bias created by measuring deviations from the sample average (x) rather than from the unknown universe average (t). Although S2 gives an unbiased estimate of universe variance, S gives a biased estimate of universe standard deviation. The bias involved in the use of S may be fairly substantial where n is small (the usual condition in highway acceptance plans) (Duncan, 1974; Burr, 1976; Grant and Leavenworth, 1980; Vardeman and Jobe, 1999; Wadsworth et al., 1986). In order to eliminate the biased estimate of universe standard deviation, S will be divided by a correction factor, which is equal to c4 (The value of c4 for subgroup sizes from 2 to 30 are given in Table A-i, Appendix A.). The corrected S value will give us an unbiased estimation of o. Without this correction, the inherent bias in the use of S tends to give too low an estimate of o (Duncan, 1974; Burr, 1976; Grant and Leavenworth, 1980; Vardeman and Jobe, 1999; Wadsworth et al., 1986). When the number of observations is more than 30, the correction factor is assumed equal to 1. If samples are drawn randomly and independently from a normal population, then it can readily be proved that (n 1)S2 2 (3.18) = X (3.18) -2 follows the / distribution with n-1 degree of freedom. A proof may be found in any mathematical statistics book. The density function for this X2 variable is (X2)[(n l)/2]-1 '/2 f 2) = 2F[( 1)] 0< < 2(n-1) / 2 171(n 1) / 2] The gamma function in the denominator is used here to make the integral of f(y2) from 0 to co equal to 1. By definition, the value of F(k)= j 'e L dw k>0 (3.19) 0 depends upon the exponent k. In particular F(1) edw c i = -e- s 1 0 A convenient recursion relation F(k + 1)= k(k) is obtained by integration by parts: F(k +l1)= 'e dw 0 u =i ,dv= ewdw du = kwldw, = - F(k + 1)= e- ] + Jkwk le-wdw o 0 = 0 + kF(k) From the two relations mentioned above, taking k as any positive integer n (n) = (n 1)! (3.22) Therefore, the gamma function takes factorial values for positive integers and may be regarded as an interpolation formula between them. In the X2 distribution, F(1/2) is proved to be V-. A sketch of the proof is as follows: F(1/2)= w 1/2ewdw >0 0 (3.20) (3.21) k>0 Let w = x2, dw = 2xdx F(1 / 2) = 2e dx 0 Since this cannot be evaluated directly, its square is estimated. [F(1/2)]2 = 2e x2dx 2e Ldy o o 0 0 =4e-(x +y2 )dxdy 00 Then, transforming to polar coordinates by let X = r sin 0, y = r cos 0, dxdy = r dr dO, x2+y2 r2 The integral over the first quadrant becomes oo -/2 [F(1/2)]2 =4j re ^drdO 0 0 = er 2rdr dO 0 0 = 2[-e-r ]o (/2)= r Since F(1/2)> 0 F(l / 2) = (3.23) For the moments of S using (3.18), the density function X2 is as follows: -1)S)2 /n-1)S2 [ ]n,1)/21e 2" d (n - f(X2 )dZ2 02 C.2 2(n-1)/2F[(n -1)2] Then, distributing the 2(n-1)/2 as needed, the expectation of Si is 64 0 S'[(n 1)S2 (n-1)/2- E(S')= 2a2 SF[(n - S(ni)S2 (n-1)S2 e dg d 202 1)/2] Now let w (n 1)S2 202 2w S = \n-I S0'w(n-1+z)/2 121/2e w E(S')1)/2](n f1)' 0i F[(n 1)/2](n 1)y/2 and using (3.19) 2 /2 F[(n + i)/2] E(S'(nn /2] (n 1)'/2 F[(n -1)/2] Taking i = 1, yields E(S) 2 F(n / 2) n -1 F[(n 1)/2] Therefore, 2 F(n / 2) n -1 F[(n 1)/2] For example, if n 5, using (3.21)-(3.23) 2 F(5/2) C4 = (2) 5 -1 F(2) (3.24) c40- (3.25) (3/2)(1/2) 0.9400 -,2 The objections for using s instead of s2 in determining quality level that the contractors are providing are that a single large s2 will have more effect on s2 than will the same sample s on s. Moreover, the distribution of s2 is far more unsymmetrical than that for s (Burr, 1976). 3.11 Combining Results of Observations When pooling data, measured values should be separated into rational subgroups, and the average and the variance of each subgroup are calculated separately. When standard deviations for two or more subgroups are pooled, it is assumed that they are estimates of a common true standard deviation. If the averages of subgroups are different, the standard deviation computed directly for an entire group of measured values will be larger than those computed separately for each group and then pooled. The weighted averages and the weighted variances may be combined to obtain pooled values x and S2 if the measured values in similar subgroups are homogeneous. Since an average of a large subgroup of measured values is presumably more significant than the average of a small subgroup, it is usual practice to weigh each average x before the values are pooled. A weighted average of the averages can be obtained by multiplying each average by the number of measured values it represents. After that, sum these products and divide by the total number of measured values. The equation is n, x, + 7X2 +... 2 nkx, x,-2 =2+. (3.26) n, +n2 +...+ k nk = The number of measured values represented by xk The pooled value of the standard deviations can be computed from the standard deviations of a numb er of independent samples. Each of the variances can be obtained by squaring the standard deviations. Next, each variance is multiplied by the corresponding number of degrees of freedom (n-1), where n is the number of measured values for which the standard deviation was computed. Finally, the summation of these products needs to be found and is to be divided by the total number of degrees of freedom to obtain a pooled value of the variance. The equation is P (3.27) (n, 1) + (n2 ) +... + (nk 1) The pooled standard deviation Sp is the square root of the pooled variance (Hudson, 1971a). 3.12 Statistical Tests for Averages A significant difference between the averages of two groups of values obtained by measurements on random samples can be determined by the t test. If the variance of the population is unknown, and we assume the population is normally distributed, then the sample variance S2 is used to estimate o2. To compare the average (x) of a small group measured with the grand average (po) of a very much larger group (Ho: y = g0), the t test for a significant difference between the average is applied by using the equation (Hudson, 1972) to =-- (3.19) S where n = number of measured values in the small group S = standard deviation for the very large group of measured values If hypotheses are Ho : =Po H, :P Po the null hypothesis (Ho) would be rejected when to > t/2,n-_, where ta/2,-1 denotes the upper a/2 percentage point of the t distribution with oo degrees of freedom. If the null hypothesis is rejected, the averages of the very large group of measurements (wo) and the average of the small group of measurements (x) are considered to be significantly different at the level a (Montgomery, 1997). 3.13 Tests for Variances The F test is used to compare the variability of the data. The ratio of the two computed variances, S2 and S is used in this test. If the ratio is near one, it is assumed that the true variances are equal. In practice, the computed ratio of the variances is compared with a tabular value ofF. The size of this tabular value depends on the number of degrees of freedom in the numerator, the number of degrees of freedom in the denominator, and the probability of occurrence of a ratio not greater than the tabular value. In an F table, the number at the head of a column is the number of degrees of freedom in the numerator, while the numbers identifying the rows are the numbers of degrees of freedom in the denominator (Hudson, 1972). If independent random samples of size nl and n2 are taken from populations 1 and 2 respectively, then the test statistic for H0: 02j = 20 H,: O 7 2 is the ratio of the sample variances FO$= (3.25) $2 The reference distribution for Fo is the F distribution with nl-1 numerator degrees of freedom and n2-1 denominator degrees of freedom. If Fo > F/ 2,n -1, or if Fo F -(/ 2),n-1,n- 1 denote the upper a/2 and lower 1-(a/2) percentage points of the F distribution with nl-1 and n2-1 degrees of freedom. The upper and lower tail are related by (Montgomery, 1996) F, -v 1V (3.26) Fa,v2,v, where v = Degrees of freedom 3.14 Theory of Risk Since a highway agency cannot test the entire lot of material or construction, the acceptance decision must be based on a small number of tests made on samples or made at selected locations. Whenever a decision is made to accept or reject a material or item of construction on the basis of a sample, there is a possibility of making an error. The computed average of test results (x) from the small number of test samples will seldom or never be the same as the true mean (u) of the results of all possible tests that could have been made on an entire lot of material or construction. Since some variability always occurs in the test results, there is always a chance that a lot of good material will be rejected or a lot of poor material will be accepted. There are two types of risks: seller's risk and buyer's risk. 1. Seller's risk or a Type I error is made when the engineer rejects acceptable material or construction. The risk associated with such an error is called the alpha (ca) risk. 2. Buyer's risk or a Type II error is made when the engineer accepts rejectable material or construction. The risk associated with such an error is called beta (3) risk. These two risks can never be entirely avoided; however, increasing the number of measurements can reduce them. Figure 3-8 shows the relationship between the type of error and its related risk (Duncan, 1974; Barker, 1994). Quality of the Lot Acceptance Decision Good Poor t C Type II Error Buyer's Accept Correct Risk Rejt Type I Error Seller's Reject RCorrect Risk Figure 3-8. Risks Involved in Acceptance Decision CHAPTER 4 DATA ANALYSIS Data analysis was done in order to determine whether the FDOT's specifications were effective. The plan was to determine (1) what quality level the FDOT wanted, (2) what quality level it was specifying, and (3) what quality level it was getting. Only two quality characteristics of asphaltic concrete material were investigated--asphalt content and pavement density in terms of percent of the control strip density. The definition of the specification effectiveness in this dissertation is that what FDOT wants = what FDOT is specifying = what FDOT is getting. The lot average, lot offset, lot average absolute deviation, within-lot and between- lot standard deviation and conformal index were all calculated and used to represent the quality the FDOT is getting. 4.1 Pavement Density 4.1.1 Historical Data The historical data allowed the identity of the variation and the average capabilities by gathering a large number of samples from a variety of projects. In this dissertation, the statistic parameters were derived based on the data that were available in FDOT's Central Quality Recording (CQR) database, which began in 1991. The CQR database is a SAS (Statistical Analysis System) file. The average pavement density test result of each lot was recorded in the CQR database. However, there was no individual density test result or information about sample size. The sample size that was used in density data analysis was estimated based on the assumption that the number of obtained samples per lot was equal to the required sample size in the FDOT construction specifications. The number of the sample size depends on the length of the pavement. The sample size increases when the pavement length increases. As was noted in Chapter 2, the current density quality characteristic of the Florida road specifications for type S asphaltic concrete material specifies that the standard size of a lot is 1500m of any pass made by the paving train regardless of the width of the pass or the thickness of the course. A sublot is 300m or less. At the end of a production day when the completion of the lot is less than 1500m, it is considered a partial lot. If the partial lot length is 600m or less and a full-size lot from the same day is available, then the previous full-size lot is redefined to include this partial lot. The number of tests required is shown in Chapter 2, Table 2-1. 4.1.2 Test Method The in-place pavement density test results of each course of asphalt mix construction in this study were determined by the nuclear gauge method. This test method is useful as a rapid nondestructive technique for determining the in-place density of compacted asphaltic concrete (Brown, 1990). With proper calibration and confirmation testing, this test method is suitable for quality control and acceptance (ASTM, 1993b). The nuclear gauge instrument uses the effects of Compton scattering and photoelectric absorption of gamma photons to measure the density of the pavement being tested. Both the source and the detectors are on the surface. A portion of the gamma photons passing into the pavement is scattered back to the detectors. Based on a count ratio between the number of counts detected in the pavement and the number of counts detected in a standard block of known density, the number of gamma photons detected by the gauge can be converted to density in kilograms per cubic meter. The brief procedures of this test method are as follow (ASTM, 1993b; FDOT, 1997): 1. Turn the instrument (Figure 4-1) on prior to use to allow it to stabilize and leave the power on during the testing day in order to provide more stable and consistent results. 2. Nuclear test devices are subject to long-term aging of the radioactive source, detectors, and electronic systems, which may alter the relationship between count rate and material density. Therefore, the apparatus may be standardized as the ratio of the measured count rate to a count rate made on a reference standard in order to offset this aging. The reference count rate should be of the same order of magnitude as the measured count rate over the useful density range of the apparatus. At the start of each day's work, the equipment should be standardized and a permanent record of these data retained. 3. Select a test location according to the specifications (Figure 4-2). 4. It is critical to maximize contact between the base of the instrument and the surface of the material under test. 5. Take a count for the normal measurement period (typically 4 minutes). 6. Determine the ratio of the reading to the standard count or the air-gap count. From this ratio and the calibration and adjustment data, determine the in-place density. 4.1.3 Selection of the data The test results of type S asphaltic concrete material that were obtained by the nuclear gauge method were investigated in this dissertation. The data were further categorized into different sample sizes from 3 to 7. Figure 4-1. Nuclear Gauge Instrument (Obtained photo from Joint AASHTO-FHWA Industry Training Committee on Asphalt) Figure 4-2. Select a Location and Take a Count for the Normal Measurement Period (Obtained photo from Joint AASHTO-FHWA Industry Training Committee on Asphalt) Some of the data recorded in the CQR database were found to be in error. For example, the test results were less than 1 or more than 150 percent of the control strip. By engineering judgement, these numbers were considered as errors. Thus, some criteria need to be set to eliminate the errors and outliers of the test results in the database. The PROC UNIVARIATE command in SAS software was used to check the errors and outliers in each group of different sample size of the pavement density data. Box plot was one of the outputs from this command that was used to eliminate errors and outliers. A box plot is a graphical display of the measurements in a sample. The box plot attempts to highlight the sample's location and dispersion characteristics. Its purpose is to display the main distributional characteristics of a data set. Three key components of a box plot are as follows (see Figure 4-3): 1. Box--The box contains 50 percent of the sample value which starts at the first sample quartile and ends at the third sample quartile. 2. Whisker--The two whiskers extend above and below the box up to the locations of the largest and smallest sample values that are within a distance of 1.5 times the interquartile range. 3. Outlier--The outliers are the sample values located outside the whiskers. The box, which is represented by a rectangle in Figure 4-3, shows the relative location of the middle 50 percent of the values. An outlier is the value outside the whiskers because such a value occurs with a very small probability in random samples from normally distributed populations. The relative location of the median and the relative lengths of the whiskers are the indicators of the sample value symmetry. For ideal symmetrical data, a median is located at the center of the box, and the length of the two whiskers is equal. The difference between the upper and lower whisker lengths provides information about the difference between the lengths of the left and right tails of the sample frequency distribution. Each whisker extends up to 1.5 interquartile ranges from the end of the box. Values that are marked with 0 are the values between 1.5 and 3 interquartile ranges of the box. The values that are farther away are called outliers. The outliers indicate either that some values are not consistent with the rest of the data or that the sample has been selected from a population containing measurements with extreme values (relatively large or small values) (Cody and Smith, 1997; Schlotzhauer and Littell, 1997; Rao, 1998). Figure 4-3 shows the box plot where the median is close to the center of the box but with unequal whisker lengths. The upper whisker is longer than the lower one, which indicates a higher concentration of data at the lower end. The two outliers are below the median, and none of them is above the median. Figure 4-4 shows the box plot of density test result data for lots having a sample size = 3. The asterisk (*) in the box plot represents errors and outliers. Figure 4-4 shows that the highest test result is extreme, which is a value of 102500 and; therefore, should be eliminated. After all of the outliers and errors were deleted from the database that was separated into groups of different size (n= 3 to 7), the statistic parameters were calculated. 4.1.4 Determination of Statistical Parameters The standard deviation of within-lot for pavement density characteristics could not be calculated because the individual test results were not recorded in the database. Since the calculation of between-lot standard deviation is based on the average test value of each lot, the assumption was that there was no difference in between-lot and within-lot test variation. First, the data were separated into years 1991-1992, 1993-1994, 1995-1996, and 1997-1999. Next, the data in each period of time were further separated into different mix designs and projects. Second, the average and the standard deviation of the average values of lot density test results from the same mix design and project were calculated by using equations 4.1 and 4.2, respectively. __ Upper whisker S Median Lower whisker Outliers Figure 4-3. Box Plot Components 79 UNIVARIATE Procedure Variable = Density (% of Control Strip) Histogram 102500+* 92500+ 62500+ 42500+ 32500+ 22500+ 12500+* 3 2500+.*..t... ******mt.****fltik*ktt*4tfrft,* j*4**a*4** 1776B my ----* ..rep----+----+res. ..+..p to 31 co.. *ay represent up to 371 counts Figure 4-4. Box-plot of the Density Test Results from PROC UNIVARIATE when Sample Size = 3, Asterisks under Box-plot Column show Errors and Outliers Boxplot * * t. -0-* + ZXt x-= (4.1) n S = (4.2) (n- 1) Next, the pooled estimate of average and standard deviations by equations 4.3 and 4.4, respectively, were calculated. 7nx, +n2 x2 +...+ k (4n x = ~ (4.3) n, +n2 +... + k S2 1 -1)S12 2 1)S2 ... k -1)S (4.4) (n, -1) + (n, 1)+... + (n, 1) Finally, the pooled standard deviation at each sample size (n) was converted to the pooled standard deviation of the individual test result by multiplying by square root of the sample size (n). S = S- -n (4.5) Data analysis in this research assumes that the values in a data set are a sample from a normal distribution. In order to decide if this assumption is reasonable or not, the testing of normality was done. The procedure for testing of normality produces a test statistic for the null hypothesis that the input data values are a random sample from a normal distribution. The test statistic compares the shape of the sample distribution with the shape of a normal distribution. It is necessary to examine the probability (called P- value) associated with the test statistic to determine whether to reject the null hypothesis of normality. This probability is labeled PROB PROB>D for the Kolmogorov test. If the sample size is less than or equal to 2000, the Shapiro-Wilk statistic is computed. The P-value can range from 0 to 1. A P-value close to 0 means the idea is very doubtful and provides evidence against the idea. In this study, if the P-value is less than 0.10, then the null hypothesis is rejected, and it is concluded that the data do not come from a normal distribution (Cody and Smith, 1997; Delwiche and Slaughter, 1995; SAS Institute Inc., 1990; Schlotzhauer and Little, 1997). The formal test for normality is obtained by specifying the NORMAL option in PROC UNIVARIATE in SAS software. This program shows one page of output. Figure 4-5 shows a portion of this page. After the density test results were separated into groups of the same mix design and project, the normality test was done to verify the assumption that the average pavement density test results are normally distributed. If the P-value is less than 0.10, it is believed that the data do not come from a normal distribution and the null hypothesis is rejected. 4.1.5 Results and Discussions From the test of normality, it was indicated that the average lot density test results of the same mix design and project were most likely normally distributed. As expected, the likelihood of normal distribution is greater for small groups (small number of lots) than for large groups extending over several days. From a total of 1662 same design and project groups containing a maximum of 10 lots, only 217 groups (13.06 percent) were not normally distributed. For groups containing more than 10 lots per group, 87 out of UNIVARIATE Procedure Variable = Density (% of Control Strip) *Quantileg [LCf-5) 9 899.6 $. 37;0278 -0.1139 2.962222 .202 B35 9 0.01039 0.0039 0,9915 Lowest 99( 99,3( 99,6( 99.8( 100( 101 100.3 IOU 99.6 99 Range C3-C1 Mode tzesmea Obs Highest 31 100( 1] 100.31 5) 1)3j.4t 9) 1011 Figure 4-5. Example of Testing for Normality of Density Data Moments ean Std Dev Skewness UBSS CV T:WMan"O Nua *- 0 N(Sign) Sl Rank W:Normal 9 99.95556 0.608505 0. O56887 B9922.9 B 0.60P775 492.7928 9 4.5 22.5 0.9 6B197 Sum EWats Sum Variance Kurtosis CSS Std Mean Pr>iTI HuM > 0 Pr>NIMI Pz>-|H| Pr 244 groups (35.66 percent) were not normally distributed (Figure 4-6). The between-lot test results were mostly normally distributed. It was believed that the within-lot test results were normally distributed. Florida construction specification for pavement density requires that the lot average value must be equal to or greater than 98 percent of control strip density to get full payment. There is no variation requirement. Although FDOT's specification does not explicitly specify density variability, in one sense it encourages low variability. A contractor who can achieve low variability in density does not need to have a high mean density. On the other hand, however, because of variability not being explicitly specified, the specification can encourage higher variability. A contractor can increase mean density during compaction operations so that the sample average will be acceptable. One of the test results may be extremely low, while the other may be extremely high. If this is the case, the density specification is not working effectively (according to anybody's definition) and should be thoroughly revised. Both high and low density can cause premature failure to the pavement. High variability in density should be prevented. Every test result should be in the acceptable range and yield a suitable average value. Thus, the variability should be an important consideration in specifying the quality level for pavement density (e.g., adopt a PWL specification as recommended in AASHTO). Typically, when developing quality assurance specifications, the highway agency wants that same quality level or just slightly higher be achieved that led to good performance in the past. Such a quality level specified is reasonable and results in satisfactory performance without increasing the cost of construction. Old records prior |