EVALUATION OF PROCEDURES FOR QUALITY ASSURANCE SPECIFICATIONS

October 2004
FHWA-HRT-04-046
PDF version (3.20 MB)

Foreword

Much has been written to guide highway agencies in the development, implementation, and use of quality assurance specifications. Unfortunately, the guidance is scattered and piecemeal. In some cases, it is out-of-date, inconsistent, or even contradicts statistical principles. Further, agencies' negative experiences with quality assurance specifications have often not been recorded, and common mistakes are repeated by other agencies.

This report is a companion to FHWA-RD-02-095, Optimal Procedures for Quality Assurance Specifications. While FHWA-RD-02-095 is a manual intended to provide guidance to highway agencies, this report summarizes the research work that was performed and contains the analyses to explain and justify the provided guidance. This report will be of interest to those materials, construction, specifications, and research engineers who wish to gain a better understanding of any specific procedures recommended in the manual.

Sufficient copies of this report are being distributed to provide three copies to each FHWA Resource Center, a minimum of one copy to each FHWA Division, and a minimum of two copies to each State highway agency. Direct distribution is being made to the division offices. Additional copies for the public are available from the National Technical Information Services (NTIS), 5285 Port Royal Road, Springfield, VA 22161.

T. Paul Teng, P.E.
Director, Office of Infrastructure
Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document.

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the object of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.

Technical Report Documentation Page

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized

SI (Modern Metric) Conversion Factors

Preface

It is important to note that two documents have been prepared for this project-a manual for use by State highway administrations (SHAs), and this technical report, which summarizes the procedures and findings of the project. The manual is intended to be a comprehensive guide that a SHA can use when developing new or modifying existing acceptance plans and quality assurance (QA) specifications. While the focus and objectives of these documents are quite different, they are not entirely stand-alone documents. In preparing the two documents, an attempt has been made to minimize duplication of the contents. As such, this technical report should be read in conjunction with and as a companion to the QA specifications manual, Optimal Procedures for Quality Assurance Specifications (Report No. FHWA-RD-02-095), which also resulted from this project.

The focus of the manual is on what should be done when developing QA specifications. The reasons for the various steps and possible decisions are explained and easy-to-follow examples are included to assist in understanding the process that is involved. The manual does not explain what was done during the project, nor what analytical and simulation analyses were conducted, unless it was necessary to clarify why certain steps in the process were necessary. This technical report contains the detailed descriptions and summaries of the results for the analyses that were conducted to arrive at the decisions and recommendations included in the manual.

Table of Contents

1. INTRODUCTION
   • BACKGROUND
   • PROJECT OBJECTIVE
   • METHODOLOGY
     • Review of the Literature
     • Development of the Process
     • Analysis of Specific Options
     • Development of the Manual
   • ORGANIZATION OF THIS REPORT
2. LITERATURE AND SPECIFICATION REVIEW
   • LITERATURE REVIEW
     • Search Methodology
     • Results
     • Summary
   • SPECIFICATION REVIEW
     • HMAC Specifications
     • Superpave Specifications
     • PCC Specifications
     • Summary
3. SPECIFICATIONS DEVELOPMENT PROCESS
   • METHODOLOGY FOR DEVELOPING THE PROCESS
   • THE PROCESS
   • FLOWCHARTS AS A GUIDE TO REQUIRED ANALYSES
4. SELECTING TOPICS FOR DETAILED ANALYSES
   • FIRST PANEL MEETING
   • SURVEY OF TOPICS FOR DETAILED ANALYSES
     • Survey Results
   • TOPICS SELECTED FOR DETAILED ANALYSES
5. QUALITY MEASURES: ACCURACY AND PRECISION
   • INTRODUCTION
   • ACCURACY AND PRECISION
   • PWL EVALUATION
     • Simulation Analyses
   • AAD EVALUATION
     • Simulation Analyses
   • CI EVALUATION
     • Simulation Analyses
   • CONCLUSION
6. QUALITY MEASURES: NORMALITY ASSUMPTION
   • INTRODUCTION
   • SKEWED DISTRIBUTIONS
     • PWL Evaluation
     • AAD Evaluation
     • Comparison of PWL and AAD
   • BIMODAL DISTRIBUTIONS
     • PWL Evaluation
     • AAD Evaluation
   • CONCLUSION
7. VERIFICATION PROCEDURES
   • INTRODUCTION
   • HYPOTHESIS TESTING AND LEVELS OF SIGNIFICANCE
   • TEST METHOD VERIFICATION
     • Maximum Allowable Difference
     • Paired t-Test
   • PROCESS VERIFICATION
     • AASHTO Appendix G Method
     • AASHTO Appendix H Method
   • CONCLUSIONS AND RECOMMENDATIONS
     • Recommendation for Test Method Verification
     • Recommendation for Process Verification
8. QUALITY MEASURES AND PAYMENT
   • CANDIDATE QUALITY MEASURES
   • ANALYSES PERFORMED
   • PAYMENT FOR A SINGLE QUALITY CHARACTERISTIC
     • PWL Payment Factors
     • AAD Payment Factors
     • Matching PWL and AAD Payment Equations
   • PAYMENT FOR MULTIPLE QUALITY CHARACTERISTICS
     • Simulating Correlated Variables
     • Correlated Quality Characteristics
   • SELECTION OF THE QUALITY MEASURE
9. EVALUATING RISKS
   • INTRODUCTION
     • Types of Risk
     • OC and EP Curves
   • CALCULATING RISKS FOR A SINGLE QUALITY CHARACTERISTIC
     • Example
     • Effect of Sample Size
     • Distribution of Estimated PWL Values
   • CALCULATING RISKS FOR MULTIPLE QUALITY CHARACTERISTICS
     • Calculating EP Contours
   • EFFECT OF ADDED PROVISIONS
   • CLOSING COMMENTS ON RISK
10. THE COMPOSITE PAYMENT FACTOR
    • TRADITIONAL COMPOSITE PAYMENT FACTORS
    • ANALYSES PROCEDURES
    • ANALYSES RESULTS
      • Comparing the Methods
    • CONCLUSION: TRADITIONAL COMPOSITE QUALITY MEASURES
11. RELATING PAYMENT TO PERFORMANCE
    • BACKGROUND
    • PERFORMANCE-RELATED SPECIFICATIONS (PRS)
      • Decision Regarding PRS
    • LCC BASIS FOR PAYMENT ADJUSTMENTS
      • LCC Approach
      • Performance Relationships
      • Composite Quality Measure
12. BRIEF SUMMARY AND RECOMMENDATIONS
    • PROJECT OBJECTIVE
    • QA SPECIFICATIONS DEVELOPMENT PROCESS
    • RESULTS OF DETAILED ANALYSES

APPENDIX A: ANNOTATED BIBLIOGRAPHY OF SELECTED ITEMS FROMTHE INITIAL LITERATURE SEARCH

APPENDIX B: SUMMARY OF AGENCY HMAC SPECIFICATIONS RECEIVED

APPENDIX C: SUMMARY OF AGENCY SUPERPAVE SPECIFICATIONS RECEIVED

APPENDIX D: SUMMARY OF AGENCY PCC SPECIFICATIONS RECEIVED

APPENDIX E: MINUTES FROM THE FIRST PANEL MEETING

APPENDIX F: ILLUSTRATIONS OF POSSIBLE RANGES FOR PD OR PWL ESTIMATES

APPENDIX G: BIAS HISTOGRAMS FROM THE SIMULATION PROGRAM

APPENDIX H: DISTRIBUTION OF SAMPLE PWL ESTIMATES

REFERENCES

List of Figures

• 1. States that provided funding for the study
• 2. Flowchart for phase I-Initiation and planning
• 3. Flowchart for phase II-Specifications development
• 4. Flowchart for phase III-Implementation
• 5. Survey sent to panel members
• 6. Graphical presentation of survey results for the first ranking method
• 7. Graphical presentation of survey results for the second ranking method
• 8. Plot of how the standard deviation of PWL estimates varies with the population PWL
• 9a. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 90 PWL, sample 3
• 9b. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 90 PWL, sample 5
• 9c. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 90 PWL, sample 10
• 10a. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 70 PWL, sample 3
• 10b. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 70 PWL, sample 5
• 10c. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 70 PWL, sample 10
• 11a. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 50 PWL, sample 3
• 11b. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 50 PWL, sample 5
• 11c. Histogram illustrating the distribution of estimated PWL values for 1000 simulated lots from a population with 50 PWL, sample 10
• 12a. Illustration 1 of accuracy and precision of PWL estimates
• 12b. Illustration 2 of accuracy and precision of PWL estimates
• 12c. Illustration 3 of accuracy and precision of PWL estimates.
• 13. Plot of average difference of simulated PWL values versus actual PWL values for sample sizes = 3, 5, and 10
• 14a. Plots of the 95^th percentile for the average estimated PWL minus the actual PWL at 50 versus the number of lots per project
• 14b. Plots of the 95^th percentile for the average estimated PWL minus the actual PWL at 70 versus the number of lots per project
• 14c. Plots of the 95^th percentile for the average estimated PWL minus the actual PWL at 90 versus the number of lots per project
• 15. Plot of average difference of simulated AAD values versus actual AAD values for sample sizes = 3, 5, and 10
• 16. Plot of how the standard deviation of AAD estimates varies with the population AAD value
• 17. Plot of average difference of simulated CI values versus actual CI values for sample sizes = 3, 5, and 10
• 18. Plot of how the standard deviation of CI estimates varies with the population CI value
• 19a. Plots of bias versus actual PWL for 10,000 simulated lots with 3 tests per lot and one-sided limits showing positive skewness
• 19b. Plots of bias versus actual PWL for 10,000 simulated lots with 3 tests per lot and one-sided limits showing negative skewness
• 20a. Plots of bias versus actual PWL for 10,000 simulated lots with 5 tests per lot and one-sided limits showing positive skewness
• 20b. Plots of bias versus actual PWL for 10,000 simulated lots with 5 tests per lot and one-sided limits showing negative skewness
• 21a. Plots of bias versus actual PWL for 10,000 simulated lots with 10 tests per lot and one-sided limits with positive skewness
• 21b. Plots of bias versus actual PWL for 10,000 simulated lots with 10 tests per lot and one-sided limits with negative skewness
• 22a. Plot of bias versus actual PWL for 10,000 simulated lots with various tests per lot and one-sided limits with +1 skewness
• 22b. Plot of bias versus actual PWL for 10,000 simulated lots with various tests per lot and one-sided limits with +2 skewness
• 22c. Plot of bias versus actual PWL for 10,000 simulated lots with various tests per lot and one-sided limits with +3 skewness
• 23a. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=8/0)
• 23b. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=7/1)
• 23c. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=6/2)
• 23d. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=5/3)
• 23e. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=4/4)
• 23f. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=3/5)
• 23g. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=2/6)
• 23h. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=1/7)
• 23i. Illustration of the divisions that SKEWBIAS2H uses to calculate bias in the PWL estimate for two-sided specification limits (skewness coefficient = +1.0, split=0/8)
• 24a. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 10, sample=3, and two-sided limits
• 24b. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 10, sample=5,and two-sided limits
• 24c. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 10, sample=10, and two-sided limits
• 25a. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 30, sample = 3, and two-sided limits
• 25b. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 30, sample = 5, and two-sided limits
• 25c. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 30, sample = 10, and two-sided limits
• 26a. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 50, sample = 3, and two-sided limits
• 26b. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 50, sample = 5, and two-sided limits
• 26c. Plot of bias versus PDL/PDU divisions for 10,000 simulated lots with PD = 50, sample = 10, and two-sided limits
• 27a. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots with PD = 10, skewness = 1, and two-sided limits
• 27b. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots with PD = 10, skewness = 2, and two-sided limits
• 28a. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots with PD = 30, skewness = 1, and two-sided limits
• 28b. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots with PD = 30, skewness = 2, and two-sided limits
• 29a. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots with PD = 50, skewness = 1, and two-sided limits
• 29b. Plot of bias versus SKEWBIAS2H divisions for 10,000 simulated lots with PD = 50, skewness = 2, and two-sided limits
• 30. Comparison of a normal population with a population with a skewness coefficient = +1.0
• 31. Sample program output screen for a population with PD = 10, skewness coefficient = 0.00, and sample size = 5
• 32a. Portion of program output screens for PD = 10, skewness coefficient = 0.00, and sample sizes = 3
• 32b. Portion of program output screens for PD = 10, skewness coefficient = 0.00, and sample sizes = 5
• 32c. Portion of program output screens for PD = 10, skewness coefficient = 0.00, and sample sizes = 10
• 33. Sample program output screen for a population with PD = 30, skewness coefficient = 1.00, and sample size = 5
• 34a. Portion of program output screens for PD = 30, skewness coefficient = 1.00, and sample sizes = 3
• 34b. Portion of program output screens for PD = 30, skewness coefficient = 1.00, and sample sizes = 5
• 34c. Portion of program output screens for PD = 30, skewness coefficient = 1.00, and sample sizes = 10
• 35a. Examples of shapes and actual AAD values for populations centered on the target and skewness coefficient of 0
• 35b. Examples of shapes and actual AAD values for populations centered on the target and with skewness coefficients between .5 and 1.5
• 35c. Examples of shapes and actual AAD values for populations centered on the target and with skewness coefficients between 2.0 and 3.0
• 36a. Comparison of the shapes and spread of estimated AAD values for populations centered on the target and with various skewness coefficients
• 36b. Comparison of the shapes and spread of estimated AAD values for populations centered on the target and with various skewness coefficients, sample size = 3
• 36c. Comparison of the shapes and spread of estimated AAD values for populations centered on the target and with various skewness coefficients, sample size = 5
• 36d. Comparison of the shapes and spread of estimated AAD values for populations centered on the target and with various skewness coefficients, sample size = 10
• 37. Comparison of the shapes and spread of estimated AAD values for normal populations centered on and offset from the target
• 38. Example 1 of populations that are very dissimilar in shape, but have approximately the same AAD
• 39a. Bias of the AAD sample estimates for populations centered on the target, but with various levels of skewness
• 39b. Spread of the AAD sample estimates for populations centered on the target, but with various levels of skewness
• 40a. Bias of the AAD sample estimates for normal populations with various offsets from the target and n = 5
• 40b. Spread of the AAD sample estimates for normal populations with various offsets from the target and n = 5
• 41a. Bias of the AAD sample estimates for normal populations centered on the target, with various standard deviation values, and n = 5
• 41b. Spread of the AAD sample estimates for normal populations centered on the target, with various standard deviation values, and n = 5
• 42. Sample output screen from the simulation program for bimodal distributions
• 43a. Program output screens for sample size = 5 and mean offsets = 1
• 43b. Program output screens for sample size = 5 and mean offsets = 2
• 43c. Program output screens for sample size = 5 and mean offsets = 3
• 43d. Program output screens for sample size = 5 and mean offsets = 4
• 43e. Program output screens for sample size = 5 and mean offsets = 5
• 44a. Illustration 1 of program output screens when combining distributions with equal means for sample size = 5
• 44b. Illustration 2 of program output screens when combining distributions with equal means for sample size = 5
• 44c. Illustration 3 of program output screens when combining distributions with equal means for sample size = 5
• 44d. Illustration 4 of program output screens when combining distributions with equal means for sample size = 5
• 45. OC surface for the maximum allowable difference test method verification method (assuming the smaller s = stest)
• 46. OC surface for the maximum allowable difference test method verification method (assuming the smaller s = 0.5stest)
• 47. OC surface for the maximum allowable difference test method verification method (assuming the smaller s = 2stest)
• 48a. Example 1 of some of the cases considered in the average run length analysis for the maximum allowable difference method
• 48b. Example 2 of some of the cases considered in the average run length analysis for the maximum allowable difference method
• 48c. Example 3 of some of the cases considered in the average run length analysis for the maximum allowable difference method
• 49. OC curves for a two-sided t-test (a = 0.05)
• 50. OC curves for a two-sided t-test (a = 0.01)
• 51a. OC surfaces (also called power surfaces) for the appendix G method for 5 contractor tests compared to a single agency test
• 51b. OC surfaces (also called power surfaces) for the appendix G method for 6 contractor tests compared to a single agency test
• 51c. OC surfaces (also called power surfaces) for the appendix G method for 7 contractor tests compared to a single agency test
• 51d. OC surfaces (also called power surfaces) for the appendix G method for 8 contractor tests compared to a single agency test
• 51e. OC surfaces (also called power surfaces) for the appendix G method for 9 contractor tests compared to a single agency test
• 51f. OC surfaces (also called power surfaces) for the appendix G method for 10 contractor tests compared to a single agency test
• 52. OC curves for the two-sided F-test for level of significance a = 0.05
• 53. OC curves for the two-sided F-test for level of significance a = 0.01
• 54a. EP curves for PWL payment schedule with sample size = 3
• 54b. EP curves for PWL payment schedule with sample size = 5
• 54c. EP curves for PWL payment schedule with sample size = 10
• 55a. Distribution of individual lot PWL = 90, sample = 3, and the resulting payment factors
• 55b. Distribution of individual lot PWL = 50, sample = 3, and the = resulting payment factors
• 55c. Distribution of individual lot PWL = 90, sample = 5, and the resulting payment factors
• 55d. Distribution of individual lot PWL = 50, sample = 5, and the resulting payment factors
• 55e. Distribution of individual lot PWL = 90, sample = 10, and the resulting payment factors
• 55f. Distribution of individual lot PWL = 50, sample = 10, and the resulting payment factors
• 56. EP curve with the 90^th and 10^th payment percentiles for the AAD payment schedule
• 57. Illustration of measuring AAD in standard deviation units (ZTarg) from the mean
• 58. Example illustrating the PWL specification limits and the offset in s units between the population mean and the target
• 59. EP curves for matched PWL and AAD payment equations for sample size = 5
• 60. Standard deviations for individual payment factors for matched PWL and AAD payment equations for sample size = 5
• 61a. Illustration 1 of two normal variables with various values for the correlation coefficient
• 61b. Illustration 2 of two normal variables with various values for the correlation coefficient
• 61c. Illustration 3 of two normal variables with various values for the correlation coefficient
• 61d. Illustration 4 of two normal variables with various values for the correlation coefficient
• 61e. Illustration 5 of two normal variables with various values for the correlation coefficient
• 61f. Illustration 6 of two normal variables with various values for the correlation coefficient
• 61g. Illustration 7 of two normal variables with various values for the correlation coefficient
• 61h. Illustration 8 of two normal variables with various values for the correlation coefficient
• 62. Expected combined weighted average payment factors for various weights and correlation coefficients based on PWL.
• 63. Standard deviations of weighted average payment factors for various weights and correlation coefficients based on PWL.
• 64. Expected combined weighted average payment factors for various weights and correlation coefficients based on AAD
• 65. Standard deviations of weighted average payment factors for various weights and correlation coefficients based on AAD
• 66. Expected average payment factors for two populations with various correlation coefficients based on PWL
• 67. Expected average payment factors for two populations with various correlation coefficients based on AAD
• 68. Standard deviations of individual payment factors for two populations with various correlation coefficients based on PWL
• 69. Standard deviations of individual payment factors for two populations with various correlation coefficients based on AAD
• 70. Bias for the average payment for two populations with various actual PWL values
• 71. Bias for the average payment for two populations with various actual AAD values
• 72. Standard deviation for the individual average payment values for two populations with various actual PWL values
• 73. Standard deviation for the individual average payment values for two populations with various actual AAD values
• 74. OC curve for an acceptance plan that calls for rejection if the estimated PWL is less than 60, for sample size = 4
• 75. OC curves for the probabilities of receiving at least some payment and at least 100-percent payment, sample size = 4
• 76. OC curves for the probability of receiving various payments, sample size = 4
• 77. EP curve for the payment relationship Pay = 55 + 0.5PWL, with an RQL provision, sample size = 4
• 78a. Distribution of estimated PWL values for an AQL population
• 78b. Distribution of payment factors for an AQL population
• 79. EP curve for the payment relationship Pay = 55 + 0.5PWL, sample size = 4
• 80. Distributions of sample PWL estimates for a population with 90 PWL
• 81a. Distributions of sample PWL estimates for a population with 50 PWL and one-sided speculations
• 81b. Distributions of sample PWL estimates for a population with 50 PWL and two-sided speculations
• 82a. Distribution of sample standard deviations for a sample size, n = 3, based on 1000 simulated samples
• 82b. Distribution of sample standard deviations for a sample size, n = 5, based on 1000 simulated samples
• 82c. Distribution of sample standard deviations for a sample size, n = 10, based on 1000 simulated samples
• 83. EP contours for the values in table 53
• 84. EP surface for the values in table 53
• 85. EP curves for the values in table 53
• 86. OC curve for an acceptance plan that calls for rejection if the estimated PWL is less than 60, sample sizes = 5
• 87a. Simulation results of expected payment for the averaging method, combining two populations with equal PWL values
• 87b. Simulation results of standard deviation values for the averaging method, combining two populations with equal PWL values
• 88a. Simulation results of expected payment for the weighted average method, combining two populations with equal PWL values
• 88b. Simulation results of standard deviation values for the weighted average method, combining two populations with equal PWL values
• 89a. Simulation results of expected payment for the multiplication method, combining two populations with equal PWL values
• 89b. Simulation results of standard deviation values for the multiplication method, combining two populations with equal PWL values
• 90a. Simulation results of expected payment for the summation method, combining two populations with equal PWL values
• 90b. Simulation results of standard deviation values for the summation method, combining two populations with equal PWL values
• 91a. Simulation results of expected payment for the maximum method, combining two populations with equal PWL values
• 91b. Simulation results of standard deviation values for the maximum method, combining two populations with equal PWL values
• 92a. Simulation results of expected payment for the minimum method, combining two populations with equal PWL values
• 92b. Simulation results of standard deviation values for the minimum method, combining two populations with equal PWL values
• 93a. Comparison of simulation results for various methods for combining individual expected payment factors for two populations with PWL = 90
• 93b. Comparison of simulation results for various methods for combining individual standard deviation payment factors for two populations with PWL = 90
• 94a. Comparison of simulation results for various methods for combining individual expected payment factors for two populations with PWL = 70
• 94b. Comparison of simulation results for various methods for combining individual standard deviation factors for two populations with PWL = 70
• 95a. Comparison of simulation results for various methods for combining individual expected payment factors for two populations with PWL = 50
• 95b. Comparison of simulation results for various methods for combining individual standard deviation payment factors for two populations with PWL = 50
• 96. Flowchart of the PRS process
• 97. Illustration of the net impact of rescheduling an overlay 2 years earlier than originally planned
• 98. Spread of possible sample means for a normal distribution with 10 PD below the lower specification limit and sample size = 3
• 99. Spread of possible sample means for a normal distribution with 10 PD below the lower specification limit and sample size = 10
• 100. Spread of possible sample means for a normal distribution with 5 PD outside each specification limit and sample size = 3
• 101. Spread of possible sample means for a normal distribution with 5 PD outside each specification limit and sample size = 10
• 102. Spread of possible sample means for a normal distribution with 50 PD below the lower specification limit and sample size = 3
• 103. Spread of possible sample means for a normal distribution with 50 PD below the lower specification limit and sample size = 10
• 104. Spread of possible sample means for a normal distribution with 25 PD outside each specification limit and sample size = 3
• 105. Spread of possible sample means for a normal distribution with 25 PD outside each specification limit and sample size = 10
• 106. Spread of possible sample means for a distribution with skewness = 1.0, 10 PD below the lower specification limit, and sample size = 3
• 107. Spread of possible sample means for a distribution with skewness = 1.0, 10 PD below the lower specification limit, and sample size = 10
• 108. Spread of possible sample means for a distribution with skewness = 1.0, 5 PD outside each specification limit, and sample size = 3
• 109. Spread of possible sample means for a distribution with skewness = 1.0, 5 PD outside each specification limit, and sample size = 10
• 110. Spread of possible sample means for a distribution with skewness = 1.0, 50 PD below the lower specification limit, and sample size = 3
• 111. Spread of possible sample means for a distribution with skewness = 1.0, 50 PD below the lower specification limit, and sample size = 10
• 112. Spread of possible sample means for a distribution with skewness = 1.0, 25 PD outside each specification limit, and sample size = 3
• 113. Spread of possible sample means for a distribution with skewness = 1.0, 25 PD outside each specification limit, and sample size = 10
• 114. Sample output screen for a population with PD = 10, skewness coefficient = 0.00, and sample size = 5
• 115. Portions of output screens for PD = 10, skewness coefficient = 0.00, and sample sizes = 3, 5, and 10
• 116. Sample output screen for a population with PD = 10, skewness coefficient = 1.00, and sample size = 5
• 117. Portions of output screens for PD = 10, skewness coefficient = 1.00, and sample sizes = 3, 5, and 10
• 118. Sample output screen for a population with PD = 10, skewness coefficient = 2.00, and sample size = 5
• 119. Portions of output screens for PD = 10, skewness coefficient = 2.00, and sample sizes = 3, 5, and 10
• 120. Sample output screen for a population with PD = 30, skewness coefficient = 0.00, and sample size = 5
• 121. Sample output screen for a population with PD = 50, skewness coefficient = 0.00, and sample size = 5
• 122. Sample output screen for a population with PD = 30, skewness coefficient = 0.00, and sample size = 10
• 123. Sample output screen for a population with PD = 50, skewness coefficient = 0.00, and sample size = 10
• 124. Portions of output screens for PD = 50, sample size = 5, and skewness coefficients = 0.00, 1.00, 2.00, and 3.00
• 125. Sample output screen for a population with PD = 10, skewness coefficient = 3.00, and sample size = 5
• 126. Sample output screen for a population with PD = 30, skewness coefficient = 3.00, and sample size = 5
• 127. Sample output screen for a population with PD = 50, skewness coefficient = 3.00, and sample size = 5
• 128a. Distribution of sample means for 1000 samples from a normal population with μ = 0.00, σ =1.00
• 128b. Distribution of standard deviations for 1000 samples from a normal population with μ = 0.00, σ =1.00
• 129a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 90, one-sided specifications
• 129b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 90, two-sided specifications
• 130a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 80, one-sided specifications
• 130b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 80, two-sided specifications
• 131a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 70, one-sided specifications
• 131b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 70, two-sided specifications
• 132a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 60, one-sided specifications
• 132b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 60, two-sided specifications
• 133a. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 50, one-sided specifications
• 133b. Distribution of sample PWL values for 1000 samples from a normal population with PWL = 50, two-sided specifications
• 134. Illustration of the populations for which the distributions of sample PWL values are shown in figures 129 through 133

List of Tables

• 1. Project team
• 2. Panel members
• 3. Agencies that provided copies of their specifications
• 4. Survey results for the first ranking method
• 5. Survey results for the second ranking method
• 6. Overall rankings of the survey topics
• 7. Quality index values for estimating PWL
• 8. Accuracy and precision for PWL estimates (based on the results of 10,000 simulated lots)
• 9. Results of simulation analyses with actual PWL = 90 (distribution of the results from 1000 simulated projects)
• 10. Results of simulation analyses with actual PWL = 70 (distribution of the results from 1000 simulated projects)
• 11. Results of simulation analyses with actual PWL = 50 (distribution of the results from 1000 simulated projects)
• 12. Distributions of sample AAD values for a population centered on the target and for sample sizes = 1, 3, 5, and 10
• 13. Distributions of sample AAD values for sample size = 3 and population means offset from the target by 0.50, 1.00, 1.50, 2.00, and 2.50 standard deviations
• 14. Accuracy and precision for AAD estimates (based on the results of 10,000 simulated lots)
• 15. Accuracy and precision for CI estimates (based on the results of 10,000 simulated lots)
• 16. Distributions with various levels of skewness
• 17. Bias in estimating PWL for various skewness coefficients and one-sided limits (3 tests per lot and 10,000 simulated lots)
• 18. Bias in estimating PWL for various skewness coefficients and one-sided limits (5 tests per lot and 10,000 simulated lots)
• 19. Bias in estimating PWL for various skewness coefficients and one-sided limits (10 tests per lot and 10,000 simulated lots)
• 20. Bias in estimating PWL for various skewness coefficients, sample sizes, and one-sided limits (10,000 simulated lots)
• 21. Results of simulations with PD = 10, 10,000 simulated lots, sample sizes = 3, 5, and 10, and two-sided limits
• 22. Results of simulations with PD = 30, 10,000 simulated lots, sample sizes = 3, 5, and 10, and two-sided limits
• 23. Results of simulations with PD = 50, 10,000 simulated lots, sample sizes = 3, 5, and 10, and two-sided limits
• 24. Bias and spread of the AAD sample estimates for populations centered on the target, but with various levels of skewness
• 25. Bias and spread of the AAD sample estimates for normal populations with various offsets from the target and n = 5
• 26. Bias and spread of the AAD sample estimates for normal populations with various standard deviation values and n = 5
• 27. Bias results for combining two populations with equal s with one-sided limits
• 28. Bias results for combining two populations with equal s with two-sided limits equidistant from the mean
• 29. Shapes of combined distributions when the combined distributions have different means and standard deviations
• 30. Bias in estimating PD when two populations are combined (sample size = 5, 10,000 simulated lots)
• 31. Average run length results for the single split-sample method (5000 simulated lots)
• 32. Allowable intervals for the AASHTO appendix G method
• 33. Average run length results for the appendix G method (5000 simulated lots)
• 34. F-test power values for n = 3-10 and s-ratio l = 1-5
• 35. F-test power values for n = 3-10 and s-ratio l = 0-1
• 36. F-test power values for n = 5-100 and s-ratio l = 1-3
• 37. Average run length results for the appendix H method (5 contractor tests and 1 agency test per lot) for 1000 simulated lots
• 38. Simulated EP factors and correct payment factors based on AAD
• 39. Relationship between ZTarg, AAD, and PWL for a normal population when the PWL specification limits are set at 1.645s
• 40. Relationship between AAD, ZTarg, and PWL for a normal population when the PWL specification limits are set at 1.645s
• 41. Relationship between PWL, AAD, and ZTarg for a normal population when the PWL specification limits are set at 1.645s
• 42. AAD values equivalent to the corresponding PWL payment factors
• 43. Results of the simulation of matched PWL and AAD payment equations for sample size = 5
• 44. Demonstration of the simulation of three correlated normal variables with selected values for correlation coefficients
• 45. Demonstration of the simulation of four correlated normal variables with selected values for correlation coefficients
• 46. Results of PWL simulation analyses for two correlated normal variables.
• 47. Results of AAD simulation analyses for two correlated normal variables.
• 48. Bias in EP for two populations with equal PWL values and various correlation coefficients
• 49. Bias in EP for two populations with equal AAD values and various correlation coefficients
• 50. Standard deviations of individual payment factors for two populations with equal PWL values and various correlation coefficients
• 51. Standard deviations of individual payment factors for two populations with equal AAD values and various correlation coefficients
• 52. EP values using Pay = 55 + 0.5PWL for two individual payment factors and then averaging them, sample size = 5
• 53. EP values using Pay = 55 + 0.5PWL for two individual payment factors and then multiplying them, sample size = 5, correlation coefficient = +0.5
• 54. Probabilities that populations with various quality levels would require removal and replacement for the example in figure 86
• 55. Completed data matrix for the example of an exponential model
• 56. Examples of computed PD* values for selected individual PD values
• 57. Illustration of the problem with separate RQL provisions
• 58. Alaska weight factors
• 59. Alaska QC/QA tests
• 60. Arkansas QC/QA tests
• 61. Colorado pay factor equations
• 62. Colorado QC/QA tests
• 63. Idaho QC/QA tests
• 64. Illinois smoothness pay factors
• 65. Illinois QC/QA tests
• 66. Iowa pay factors for density
• 67. Iowa pay factors for thickness
• 68. Iowa QC/QA tests
• 69. Maryland profile index adjustment (normal projects)
• 70. Maryland profile index adjustment (incentive projects)
• 71. Maryland QC/QA tests
• 72. Michigan QC/QA tests
• 73. Minnesota payment schedule
• 74. Minnesota determination of lots for density
• 75. Minnesota adjusted payment schedule for maximum density (disincentive)
• 76. Minnesota adjusted payment schedule for maximum density (incentive)
• 77. Minnesota payment schedule for smoothness
• 78. Minnesota QC/QA tests
• 79. Montana price reduction factors
• 80. Montana QC/QA tests
• 81. Nebraska density of asphalt concrete (first lot)
• 82. Nebraska density of asphalt concrete (subsequent lots)
• 83. Nebraska QC/QA tests
• 84. Nevada pay factors for profile index
• 85. Nevada pay factors for gradation
• 86. Nevada pay factors for asphalt content
• 87. Nevada pay factors for in-place air voids
• 88. Nevada QC/QA tests
• 89. North Dakota QC/QA tests.
• 90. Ohio QC/QA tests
• 91. Ontario QC/QA tests
• 92. Oregon weighting factors
• 93. Oregon QC/QA tests
• 94. Pennsylvania adjustment of contract price relative to the specification limits
• 95. Pennsylvania QC/QA tests
• 96. South Carolina required QC tests and verifications
• 97. South Carolina required acceptance tests
• 98. Texas pay factors for flexural strength
• 99. Texas pay factors for thickness
• 100. Texas QC/QA tests
• 101. Virginia QC/QA tests
• 102. Washington QC/QA tests
• 103. Wisconsin sampling frequencies
• 104. Wisconsin percent payment for mixture
• 105. Wisconsin QC/QA tests
• 106. Wyoming QC/QA tests
• 107. Connecticut M.A.D. from job-mix formula for consecutive tests
• 108. Connecticut pay factors for joint and mat density
• 109. Connecticut QC/QA tests
• 110. Kansas pay factors for specified density
• 111. Kansas pay factors for air voids (lot size of four tests)
• 112. Kansas pay factors for air voids (lot size of three tests)
• 113. Kansas pay factors for air voids (lot size of five tests)
• 114. Kansas pay factors for air voids (lot size of six tests)
• 115. Kansas QC/QA tests
• 116. Louisiana payment adjustment schedule
• 117. Louisiana QC/QA tests
• 118. Maine QC/QA tests
• 119. Minnesota payment schedule
• 120. Minnesota determination of lots for density
• 121. Minnesota payment schedule for density
• 122. Minnesota payment schedule for smoothness
• 123. Minnesota QC/QA tests
• 124. Mississippi sampling frequency
• 125. Mississippi lot determination for density
• 126. Mississippi pay factors for mixture quality
• 127. Mississippi pay factors for density
• 128. Mississippi pay factors for smoothness
• 129. Mississippi QC/QA tests
• 130. New York QC/QA tests
• 131. North Carolina testing frequency
• 132. North Carolina payment for mix produced in warning bands
• 133. North Carolina pay factor
• 134. North Carolina QC/QA tests
• 135. Kansas concrete thickness and comprehensive strength pay adjustment
• 136. Kansas QC/QA tests
• 137. Illinois QC/QA tests
• 138. Iowa pay factors for thickness
• 139. Iowa pay factors for flexural strength
• 140. Iowa QC/QA tests
• 141. North Carolina pay factors for thickness
• 142. North Carolina pay factors for flexural strength
• 143. North Carolina QC/QA tests
• 144. Oregon pay factors for thickness
• 145. Oregon QC/QA tests
• 146. Pennsylvania QA/QC tests.
• 147. Texas pay factors for flexural strength.
• 148. Texas pay factors for thickness
• 149. Texas QC/QA tests
• 150. Wisconsin pay factors for compressive strength
• 151. Wisconsin pay factors for the profile index
• 152. Wisconsin pay factors for thickness
• 153. Wisconsin QC/QA tests

FHWA-HRT-04-046

Events

• View all Upcoming Pavements Events

More Information

• Pavement Publications

Contact

Peter Kopac
Turner Fairbank
202-493-3151
E-mail Peter