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 personnelMr. Gale C. Page, Mr. Tom
Malerk, Mr. Bruce T. Dietrich, Mr. Winfred S. Langley, Mr. Patrick B. Upshaw, and Mr.
Glenn Mansfor 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 LotbyLot 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 Withinlot Asphalt Content Quality Level............................... 114
4.2.5.2 Withinlot Asphalt Content Characteristic by Year............................ 120
4.2.5.3 Overall Betweenlot 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
21. D ensity Testing R equirem ents ........................................................................... ...... 28
31. Symbols used for Populations and Samples ....................................... ............... 43
41. Summary of Pooled BetweenLot Standard Deviation Density (% of Control Strip).....87
42. Summary of the Average Value of Density (% of Control Strip)......................... 87
43. Summary of BetweenLot Standard Deviation of Density by 19911992 (% of
C o n tro l S trip ) .................................................................... . 8 8
44. Summary of BetweenLot Standard Deviation of Density by 19931994 (% of
C o n tro l S trip ) .................................................................... . 8 8
45. Summary of BetweenLot Standard Deviation of Density by 19951996 (% of
C o n tro l S trip ) .................................................................... . 8 9
46. Summary of BetweenLot Standard Deviation of Density by 19971999 (% of
C control Strip D ensity) ................................................ .............................. 89
47. Summary of Average of Density by 19911992 (% of Control Strip) ............................90
48. Summary of Average of Density by 19931994 (% of Control Strip) ............................90
49. Summary of Average of Density by 19951996 (% of Control Strip ) ...........................90
410. Summary of Average of Density by 19971999 (% of Control Strip) ..........................91
411. Estimation of Typical Pavement Density Quality ...................................................91
412. Density Payment Schedule Specified in FDOT Standard Specifications for Road
and Bridge Construction 1999. ........................................ ........................ 94
413. Summary of the Estimated Pavement Density Pay Factor (Percent) .............................94
414. Summary of Average of Pavement Density Pay Factor (Percent).............................95
415. Summary of the Pavement Density Pay Factor for Year 19911992 (Percent) ............95
416. Summary of the Pavement Density Pay Factor for Year 19931994 (Percent) ..............96
417. Summary of the Pavement Density Pay Factor for Year 19951996 (Percent) ..............96
418. Summary of the Pavement Density Pay Factor for Year 19971999 (Percent) ..............97
419. Summary of Percentage of Lots with Pay Reduction obtained from Database and
based on FDOT's 1999 Specification ............................................................ 97
420. Summary of Percentage of Lots with Pay Reduction when Sample Size = 3 ...............98
421. Example of Estimation of Average withinlot Offset of all Lots when n = 3..............10
422. Example of Estimation of an Unbiased Universe withinlot Standard Deviation of
all Lots w hen n = 3 .............. ........................... ........ ........ .. .. 111
423. Example of Estimation of a Pooled withinlot Standard Deviation of all Lots when
n = 3 ...................................................................... ....... 1 1 1
424. Example of the Estimation of the Average of withinlot AAD when n = 3.................12
425. Example of Estimation of the Characteristic withinlot Conformal Index of all Lots
when n = 3 ................................... .............................. ........... 112
426. Summary of Corrected Average withinlot Standard Deviation of Asphalt Content,
Type S A sphaltic Concrete ........................................................ ............. 121
427. Summary of Corrected Median withinlot Standard Deviation of Asphalt Content,
Type S A sphaltic Concrete ........................................................ ............. 121
428. Summary of Pooled withinlot Standard Deviation of Asphalt Content, Type S
A sphaltic C concrete .......................................... ........................ 122
429. Summary of Lot Offset from JMF of Asphalt Content, Type S Asphaltic Concrete ......122
430. Summary of Lot Average Absolute Deviation from Job Mix Formula of Asphalt
Content, Type S Asphaltic Concrete ............. ............................. .... ............. 123
431. Summary of Standard Deviation of lot AAD of Asphalt Content, Material Type S......123
432. Summary of withinlot Conformal Index of Asphalt Content, Type S Asphaltic
C on create .......................................................................... 12 4
433. Comparison of Percentage of Observations Outside 95 percent Confident Interval
of Corrected and Pooled withinlot Standard Deviation................ ........... 124
434. Summary of withinlot Corrected Standard Deviation of Asphalt Content, Type S
Asphaltic Concrete, Year 19931994............... ........... ......... ..... ......... 126
435. Summary of withinlot Corrected Standard Deviation of Asphalt Content, Type S
Asphaltic Concrete, Year 19951996........... ....... ........ ....... .............. 126
436. Summary of withinlot Corrected Standard Deviation of Asphalt Content, Type S
Asphaltic Concrete, Year 19971999............. ............... ....... .............. 127
437. Summary of Lot Offset from JMF of Asphalt Content, Type S Asphaltic Concrete,
Y ear 19931994 ....................................................................127
438. Summary of Lot Offset from JMF of Asphalt Content, Type S Asphaltic Concrete,
Y ear 19951996 ....................................................................128
439. Summary of Lot Offset from JMF of Asphalt Content, Type S Asphaltic Concrete,
Y ear 19971999 ................. ............................... ..... ...............128
440. Summary of Lot Average Absolute Deviation from JMF of Asphalt Content, Type
S A sphaltic Concrete, Year 19931994..................................... ............... 129
441. Summary of Lot Average Absolute Deviation from JMF of Asphalt Content, Type
S Asphaltic Concrete, Year 19951996............. ................ ............... 129
442. Summary of Lot Average Absolute Deviation from JMF of Asphalt Content, Type
S Asphaltic Concrete, Year 19971999............. ................ ............... 130
443. Summary of withinlot Conformal Index of Asphalt Content, Type S Asphaltic
Concrete, Y ear 19931994 .............................................................................130
444. Summary of withinlot Conformal Index of Asphalt Content, Type S Asphaltic
Concrete, Year 19951996 ....................................... ... ..........................131
445. Summary of withinlot Conformal Index of Asphalt Content, Type S Asphaltic
Concrete, Year 19971999 ................................... ......................................131
446. Summary of BetweenLot Statistical Parameters for Type S Asphaltic Concrete ........132
447. The Acceptance Schedule of Payment on LotbyLot basis of the Asphalt Content
Test Results by Extraction M ethod ............................................... ............... 136
448. Summary of the Estimated Pay Factor based on Asphalt Content Characteristic..........136
449. Summary of Average Asphalt Content Pay Factor, Type S Asphaltic Concrete ...........137
450. Summary of Average Asphalt Content Pay Factor for Year 19931994.......................137
451. Summary of Average Asphalt Content Pay Factor for Year 19951996 .......................138
452. Summary of Average Asphalt Content Pay Factor for Year 19971999.......................138
453. Summary of Percentage of Lots with Pay Reduction...................................................139
51. 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
52. 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
53. 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
54. 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
55. 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
56. 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
57. 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
58. 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
59. Summary of Trial and Error Results from Computer Simulation when Sample Size
= 1 ............................................................................ . 1 6 5
510. Summary of Trial and Error Results from Computer Simulation when Sample Size
= 2 ............................................................................... 1 6 6
511. Summary of Trial and Error Results from Computer Simulation when Sample Size
= 6 ........................................................................... . 1 6 7
512. 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
11. R research A approach Flow Chart......... ................................................. ............... 11
21. D degrees of Segregation ............................................................. ............... 31
31. Concept of Accuracy, Precision, and Bias .......................................... 37
32. Conformance to Specification and Quality Loss.................................. ............... 42
33. The Flexibility of the Percent Defective Quality Measure with Respect to [t and .....46
34. Percent Defective (PD) and Percent within Limit (PWL) under the Standardized
N orm al D distribution Curve ...................................................... ............... 48
35. Comparison of Mathematical Properties of AAD and CI for Sample Size of n=2..........55
36. Potential Weaknesses of Common Statistical Measures of Quality .............................56
37. T ypes of D distribution .......................................................................... .....................58
38. Risks Involved in A acceptance D ecision.............................................. .....................70
41. Nuclear Gauge Instrument (Obtained photo from Joint AASHTOFHWA Industry
Training Com m ittee on A sphalt) .................................. .............................. ........ 74
42. Select a Location and Take a Count for the Normal Measurement Period (Obtained
photo from Joint AASHTOFHWA Industry Training Committee on Asphalt).....75
4 3 B ox P lot C om ponents .......................................................................... .....................7 8
44. Boxplot of the Density Test Results from PROC UNIVARIATE when Sample Size
= 3, Asterisks under Boxplot Column show Errors and Outliers.......................79
45. Example of Testing for Normality of Density Data ......................................................82
46. Percentage of Nonnormally Distributed Groups of Same Mix Design and Project.......84
47. Frequency Plot of Density Pay Factor by Year when Sample Size = 3 ........................99
48. Questionnaire Responses from FDOT and Contractor Personnel Regarding Density
M ean V alue ................................................... ................ 102
49. Questionnaire Responses from FDOT and Contractor Personnel Regarding Density
Standard Deviation ................. .. ........... ................ ................. 103
410. Questionnaire Responses from FDOT and Contractor Personnel Regarding
Minimum Quality Level of Density Specification................... ...............104
411. The Test Portion is Placed into a B ow l ................. ................................................ 106
412. The Extraction Equipment Extracts the Asphalt from the Paving Mixture ..................107
413. Percentage of Nonnormally Distributed Groups of Same Project (N = Number of
L ots) .............................................................. .. .... ..... ......... 115
414. Summary Histogram for withinlot Standard Deviations of the Difference from
JM F when Sample Size = 2 .............. .... .................... ................ ..... 116
415. Summary Histogram for withinlot Standard Deviations of the Difference from
JM F when Sample Size = 3 .............. .... .................... ................ ..... 117
416. Summary Histogram for withinlot Standard Deviations of the Difference from
JM F when Sam ple Size = 4 ..... .............................................................1.. 18
417. Summary Histogram for withinlot Standard Deviations of the Difference from
JM F when Sample Size = 5 .............. .... .................... ................ ..... 119
418. Summary Histograms of BetweenLot Offset from JMF ........................ ............133
419. Summary Histograms of BetweenLot Standard Deviation of the Difference from
JM F ........................................................................... . 1 3 4
420. Summary Histograms of BetweenLot Conformal Index ....................................135
421. Frequency Plot of Pay Factor based on Asphalt Content Characteristic.......................140
422. Questionnaire Responses from FDOT and Contractor Personnel Regarding
Average Offset of Asphalt Content from Job Mix Design...............................141
423. Questionnaire Responses from FDOT and Contractor Personnel Regarding
Standard Deviation of Asphalt Content.................. ..... ................... 142
424. Questionnaire Responses from FDOT and Contractor Personnel Regarding
Minimum Quality Level of Asphalt Content Specification..................................143
51. Computer Simulation Flow Chart used in Relating Offset and Standard Deviation to
A A D ............... .. .......... .............. ..............................146
52. Com pleted Input Inform ation......................................... .... ................................ 151
53. Completed Input of Specification Tolerances ..................................... .................152
54. Display of the AAD Computer Program............. ............................ ...............153
55. 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 "endresult 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.
Endresult specifications. An endresult 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 endresult
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 lotbylot basis by measuring significant characteristics of the
complete lot. Such an endresult 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
characteristicspavement 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 characteristicsdensity 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 1Literature 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 2Data 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 21, 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 3Data analysis.
1. Analyze collected data in Subtasks 21 and 22 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 23 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 4Computer 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 33 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 5Interpretation.
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 51, 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 6Final dissertation.
1. Write draft and final dissertation.
2. Make a presentation.
Task 1Literature 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 2Data 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 21.
3. Collect quality control/ acceptance data from FDOT projects after implementation
of current FDOT quality assurance specifications.
Task 3Data analysis.
1. Analyze collected data in Subtasks 21 and 22 to provide answers to each question
posed in the subtasks (see pp.89).
2. Analyze the current FDOT specifications.
3. Analyze collected data collected in Subtask 23 to provide an answer to the
question posed in that subtask.
Task 4Computer program development.
1. Develop a computer program to use as a tool to evaluate the effectiveness of the
existing FDOT construction specifications.
Figure 11. Research Approach Flow Chart
Figure 11continue
Task 5Interpretation.
1. Determine effectiveness of FDOT specifications.
2. Depending on findings from Subtask 51, 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 6Final 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 (MillerWarden 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; MillerWarden 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 (MillerWarden 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 societyphysically, 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 performancerelated
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
lotbylot 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 nonspecification material or construction are produced. Moreover, it
avoids tieup 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
methodtype 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 fulltime
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 samplingone 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 LotbyLot Method
In lotbylot 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 lotbylot 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 lotbylot 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 fullsize lot from the same day is available,
then the previous fullsize lot is redefined to include this partial lot. The number of tests
required is shown in Table 21.
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 fullsize 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 21. 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 2la, 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 2lb, 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 21c. As a result of
segregation, the density test results at two locations may differ greatly (MillerWarden
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 21. 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 (MillerWarden 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 endresult 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 endresult 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 qualityconscious 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 31 (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 31. 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 32. 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
lifecycle cost (Taguchi, 1986). Lifecycle 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 32 shows the loss function model, which is
L(y)= k(yTV)2 (3.6)
where
k = Constant
(yTV) = 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 32. 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 31.
Table 31. 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 plantproduced 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 goodquality 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 33 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 33. The Flexibility of the Percent Defective Quality Measure with Respect to [t
and y.
follows.
xL
 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 34. 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 34. 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
onesided 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 35, 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 35 because the performance
is logically expected to be a function of both population location (shift) and population
spread.
The three basic quality measuresAAD, CI, and PD/PWLare 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 36. 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
bellshaped 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[(0A f +(6 + ) /2
= V62 + A2
CI= \/[(A 6 + (A+ )2]2
=\^+A62
Figure 35. 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 36. 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 37.
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 37. 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)
nl
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 Ai, 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 n1 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(n1) / 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 lewdw
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[er ]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 /n1)S2
[ ]n,1)/21e 2" d (n 
f(X2 )dZ2 02 C.2
2(n1)/2F[(n 1)2]
Then, distributing the 2(n1)/2 as needed, the expectation of Si is
64
0 S'[(n 1)S2 (n1)/2
E(S')= 2a2
SF[(n 
S(ni)S2 (n1)S2
e dg d
202
1)/2]
Now let w
(n 1)S2
202
2w
S =
\nI
S0'w(n1+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 (n1), 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 nl1 numerator degrees
of freedom and n21 denominator degrees of freedom. If Fo > F/ 2,n 1, or if
Fo
F (/ 2),n1,n 1 denote the upper a/2 and lower 1(a/2) percentage points of the F
distribution with nl1 and n21 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 38 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 38. 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 investigatedasphalt 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, withinlot 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 fullsize lot from the same day is available, then
the previous fullsize lot is redefined to include this partial lot. The number of tests
required is shown in Chapter 2, Table 21.
4.1.2 Test Method
The inplace 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 inplace 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 41) 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 longterm 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 42).
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 airgap count.
From this ratio and the calibration and adjustment data, determine the inplace
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 41. Nuclear Gauge Instrument (Obtained photo from Joint AASHTOFHWA
Industry Training Committee on Asphalt)
Figure 42. Select a Location and Take a Count for the Normal Measurement Period
(Obtained photo from Joint AASHTOFHWA 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 43):
1. BoxThe box contains 50 percent of the sample value which starts at the first
sample quartile and ends at the third sample quartile.
2. WhiskerThe 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. OutlierThe outliers are the sample values located outside the whiskers.
The box, which is represented by a rectangle in Figure 43, 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 43 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 44 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 44 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 withinlot for pavement density characteristics could
not be calculated because the individual test results were not recorded in the database.
Since the calculation of betweenlot standard deviation is based on the average test value
of each lot, the assumption was that there was no difference in betweenlot and withinlot
test variation.
First, the data were separated into years 19911992, 19931994, 19951996, and
19971999. 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 43. 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 44. Boxplot of the Density Test Results from PROC UNIVARIATE when
Sample Size = 3, Asterisks under Boxplot 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
ShapiroWilk statistic is computed. The Pvalue can range from 0 to 1. A Pvalue close
to 0 means the idea is very doubtful and provides evidence against the idea. In this study,
if the Pvalue 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
45 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 Pvalue 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 [LCf5)
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
C3C1
Mode
tzesmea
Obs Highest
31 100(
1] 100.31
5) 1)3j.4t
9) 1011
Figure 45. 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 46). The betweenlot
test results were mostly normally distributed. It was believed that the withinlot 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
