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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
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Publication Number: FHWAHRT04046 Date: October 2004 
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Afferton, K.C.; Freidenrich, J.; and Weed, R.M. "Managing Quality: Time for a National Policy," Transportation Research Record 1340, 1992, pp. 339.
Statistical quality assurance (SQA) (currently in use or under development in approximately threequarters of the States) has proven to be a very effective tool for encouraging highquality construction. However, although statistical specifications writing must now be recognized as a thoroughly scientific activity, there is great disparity in its application on the State level and many current practices and published standards are far from optimal. Part 1 of this paper stresses the need for sweeping reforms and suggests that the establishment of a uniform national policy on transportation QA is overdue. Part 2 describes a variety of obstacles that must be overcome if such a transformation is to be made. Part 3 outlines an extensive series of principles that must be understood in order to derive the maximum benefit from a QA program. And finally, Part 4 presents a plan of action that, if conscientiously followed, will significantly increase the effectiveness of transportation QA practices nationwide.
Allen, O.B. and Newcombe, P.A. "A ThreeClass Procedure for Acceptance Sampling by Variables," Technometrics, Vol. 30, No. 4, 1988, pp. 415421.
A threeclass procedure for acceptance sampling by variables is introduced as an alternative to both the three class attributes plan and the twoclass variables plan. The procedure, which requires that the quality characteristic be normally distributed, has the advantage of requiring a smaller sample size than a threeclass attributes plan with approximately the same OC surface. The advantage of the threeclass variables plan over the twoclass variables plan is the ability to discriminate between lots with high and low percentages of marginally conforming products. Two equivalent methods of stating the decision rules for the plan are suggested. It is shown that the OC surface for the threeclass variables procedure may be constructed with a special case of bivariate, noncentral tdistribution. The motivation and methods for choosing a plan are discussed and illustrated.
Aminzadeh, M.S. "InverseGaussian Acceptance Sampling Plans by Variables," Communications in Statistics: Theory and Method, Vol. 125, No. 5, 1996, pp. 923935.
Variable sampling plans to control the defective fraction are obtained using the InverseGaussian distribution. OC curves are obtained and the impact of the sample size and the specification limits on these curves are discussed. Simulation studies are used to investigate the sensitivity of the sampling plans under the more commonly used normal distribution.
Amirkhanian, S.N.; Burati, J.L.; and Mirchandani, H.C. "Effect of Testing Variability on Contractor Payment for Asphalt Pavements," Journal of Construction Engineering and Management, Vol. 120, No. 3, September 1994, pp. 579592.
Acceptance of asphalt pavements on a lotbylot basis depends on how well the material conforms to specified quality characteristics. If a lot does not fall within the specified tolerance limits for a given characteristic, the payment to the contractor for that lot may be adjusted according to a predetermined payment schedule. This study evaluated the effects of the variability of the test method on the payment to the contractor. Payment factors based on selected State highway agency specifications, typical of the most commonly used type of acceptance plans, were estimated using simulation techniques. The results were illustrated by plotting the OC in terms of the expected payment. The OC plots show that the contractor might receive a reduced payment even when there is no material variability and the process mean is on target. This reduction was a result of the relatively large magnitude of the testing variability as compared with the tolerance range specified in the simulated acceptance plans. With suitable modifications, the simulation routine developed to estimate contractor payment can be used for any acceptance plan.
Balamurali, S. and Kalyanasundaram, M. "Determination of an Attribute Single Sampling Scheme," Journal of Applied Statistics, Vol. 24, No. 6, 1997, pp. 689695.
A procedure for the selection of a new sampling scheme, called the Single Sampling Scheme, is presented. Additionally, a table for the selection of a single sampling scheme, which is indexed by various combinations of entry parameters, is given. The method of table construction and the advantages of single sampling schemes are discussed.
Barros, R.T.; Weed, R.M.; and Willenbrock, J.H. "Software Package for Design and Analysis of Acceptance Procedures Based on Percent Defective," Transportation Research Record 924, 1983, pp. 8593.
The trend toward statistical endresult specifications (ERS) has led to the development of construction specifications based on the concept of PD. To analyze the risks and determine the effectiveness of the acceptance procedures associated with these specifications, OC curves must be constructed. However, many potential users do not have a working knowledge of the noncentral t and beta distributions necessary for this development. The underlying theory, several useful references, and a conversational computer program that greatly simplifies the design and analysis of specifications of this type are presented.
Benson, P.E. "Comparison of End Result and Method Specifications for Managing Quality," Transportation Research Record 1491, 1995, pp. 310.
The results of a statistically designed experiment in which AC cores and nuclear gauge readings were taken from five California projects are reported. Relative compaction for the projects was controlled with a method specification. Analysis of variance is used to separate test error and the locational components of variance for specific gravity, asphalt content, lift thickness, and grading. Compaction results are compared with similar results from 16 ERS jobs studied previously. Relative compaction on the endresult jobs averages 3.1 percent higher in value. Findings on test precision, increased lot size, and material variability are discussed.
Benson, P.E. "Performance Review of a Quality Control/Quality Assurance Specification for Asphalt Concrete," Transportation Research Record 1654, 1999, pp. 8894.
A statistical review of 50 jobs recently completed by using California's QC/QA specification for AC is presented. Performance is contrasted to the quality achieved under method specification and ERS. A cost analysis is made and issues related to verification are discussed. Improvements to the current specification are proposed. The data present clear evidence that the allowable tolerance of ±0.5 percent for asphalt content is too broad for current practices. Also, an increase in compaction variability for many QC/QA jobs could be controlled by adding an upper specification limit or adopting a twosided volumetric specification. The cost for QC/QA jobs went up approximately 3 percent to pay for bonuses allowed under the specification. An analysis of the contractor's QC test data indicate that this increase is more than compensated for by projected reductions in future rehabilitation costs. However, a significant lack of agreement between the contractor QC and agency QA tests brings this finding into question. More rigorous verification of contractorprovided test results must be incorporated into the specification and the results must be analyzed before costeffectiveness can be determined.
Budwig, J.L. "Bituminous Pavement Smoothness: Statistically Based Approach to Acceptance," Transportation Research Record 1544, 1996, pp. 125134.
Since 1987, the Federal Lands Highway (FLH) branch of FHWA has been evaluating acceptance of newly constructed bituminous pavements using Californiatype profilograph measurements. California Test Method 526 and FLH T504, as well as various acceptance plans, have been used in this evaluation. This study examined: (1) whether operator trace reduction variability was too large for acceptance testing, (2) which type of acceptance plan should be incorporated into the Standard Specifications for Construction of Roads and Bridges on Federal Highway Projects (FP 92), and (3) two commercially available computerized trace reduction systems. The study concludes that when used in conjunction with statistical evaluation procedures, the test method is suitable for acceptance purposes and that computerized trace reduction is superior to manual reduction. Also presented are some fundamentals of statistically based acceptance that are not widely known or understood by highway engineers.
Burati, J.L.; Antle, C.E.; and Willenbrock, J.H. "Development of a Bayesian Acceptance Approach for Bituminous Pavements," Transportation Research Record 924, 1983, pp. 6471.
Traditional approaches for estimating the percentage of a lot that is within specification limits (PWL) are based on random samples taken from the lot being evaluated. These approaches suffer from the small sample size necessitated by the destructive and timeconsuming tests that are usually used in determining the quality of the materials. The development of a Bayesian approach for estimating PWL, which incorporates information concerning the contractor's past performance on the project and the current sample results that determine the estimate for the PWL of the current lot, is presented. The procedure assumes that the daily population mean is a random variable that follows a normal distribution, that the production process is also normally distributed, and that the process variance is constant. These assumptions are confirmed by using goodnessoffit tests on data collected from 13 bituminous runway paving projects. Computer simulation shows that the Bayesian PWL estimators are slightly biased in comparison with the traditional quality index method, but that the PWL estimators exhibit smaller variances than the traditional method.
Burati, J.L.; Bridges, W.C.; and Ackerman S.A. "Evaluation of Quality Assurance Programs for Bituminous Paving Mixtures," Report No. FHWASC95002, South Carolina DOT, May 1995.
The South Carolina DOT QA program currently consists of the Record Sample, Independent Assurance (known as the Green Tag program), and SplitSample programs. Because these three programs were developed at different times and possibly for different reasons, a study was needed to determine how the three programs meshed together, if there are overlaps or gaps in these programs, and if they are serving the function or functions for which they were intended. The study consisted of: (1) a review of the documentation of the existing programs, (2) interviews with FHWA and South Carolina DOT personnel to establish the objectives for each program, (3) a survey of other State highway agency independent assurance practices, and (4) an analysis of historical data from each of the programs. ASTM precision statements were also considered when evaluating the allowable tolerances for comparing test results. This report recommends that the Record Sample and Split Sample programs be maintained with some modification in the procedures, including using independently obtained samples (as opposed to split samples) for the Record Sample program and slightly modified allowable comparison tolerances for both programs. It was concluded that the Green Tag program is not necessary for the purpose of independent assurance. It primarily serves as an enforcement function and is not needed unless the South Carolina DOT believes that it is necessary to provide an external psychological inducement to ensure that its inspectors properly perform their job functions.
Burati, J.L. and Willenbrock, J.H. "Acceptance Criteria for Bituminous Surface Course on Civil Airport Pavements," Report No. FAARD79089, Federal Aviation Administration, 1981.
Research was undertaken to extend the use of statistically based airport pavement materials specifications that incorporate priceadjustment features. During the course of the project, data on the physical characteristics of the pavement materials were collected from 13 airport pavement construction projects. A statistical analysis of this data permitted the determination of the parameters (mean and standard deviation) of existing airport projects, and these parameters were then used to develop acceptance plans and priceadjustment factors. OC curves and the curves of expected payment were used to determine the appropriate acceptance plans, which were based on the percentage of material falling within the specification limits (PWL). By using a continuous rather than a discrete priceadjustment schedule, it was possible to avoid the problem of large differences in payment associated with relatively small differences in quality (as measured by the PWL). A computer program was developed to approximate the expected payment curves associated with different continuous price adjustment systems. This program is applicable to onesided specification limits such as density. For properties such as air voids, which require both an upper and lower specification limit, the OC curves were determined by computer simulation of 10,000 randomly drawn samples.
Chang, LM. and Hsie, M. "Developing Acceptance Sampling Methods for Quality Construction," Journal of Construction Engineering and Management, Vol. 121, No. 2, 1995, pp. 246253.
The role that the acceptance sampling method plays in designing the QA specification is discussed. The acceptance sampling method applies statistics to specify the number of measurements needed and determines how to make an acceptance or rejection decision based on measured data. Four acceptance sampling methods are presented, including the variable single sampling method, quality index sampling method, attribute double sampling method, and attribute proportion sampling method. The theories are derived and the applications of the four quality acceptance sampling methods are described. The advantages and disadvantages of the different sampling methods are compared.
Darter, M.I.; Hoerner, T.E.; Smith, K.D.; Okamoto, P.A.; and Kopac, P.A. "Development of Prototype PerformanceRelated Specification for Concrete Pavements," Transportation Research Record 1544, 1996, pp. 109115.
The development of a prototype PRS for concrete pavement is summarized. The prototype PRS requires that the pavement lot be divided into consistent sublots for the measurement of quality characteristics that are then used to estimate future performance and lifecycle costs. The difference between the lifecycle costs of the target (as designed) pavement and the actual (asconstructed) pavement lot is used to determine a rational pay adjustment. Both the means and the variations of all of the quality characteristics are directly considered in the pay factor determination. A Microsoft^{®} Windows^{®}based computer program, PaveSpec, was developed for use with the specification simulation and for generating pay adjustments. However, additional work is required to make this a fully practical PRS.
Dobrowolski, J. and Bressette, T. "Development of Quality Control/Quality Assurance Specifications by Using Statistical Quality Assurance for Asphalt Concrete Pavements in California," Transportation Research Record 1632, 1998, pp. 1321.
In 1996, Caltrans implemented QC/QA specifications for AC paving. These specifications require contractor QC and provide rewards or penalties based on statistical quality analysis of eight quality characteristics. These specifications were developed through a joint Caltrans/industry group and are supplemented with a QC manual. In March 1996, the first project using the specifications went to bid and, in the first year, six projects were completed. Since then, revisions to the specifications have been developed. The specifications and manual issues, recommendations based on 1996 projects, changes that Caltrans has made, and anticipated additional endeavors in areas of QC/QA and materials testing are discussed.
Douglas, K.D.; Coplantz, J.; Lehman, R.; and Bressette, T. "Evaluation of Quality Control/Quality Assurance Implementation for Asphalt Concrete Specifications in California," Transportation Research Record 1654, 1999, pp. 95101.
Caltrans has implemented a new QC/QA specification for AC pavement. As part of this implementation, Caltrans realized the need for objective feedback on its design and implementation, and selected Nichols Consulting Engineers to perform this study. The study objective, the research approach used, a description of the projects included in the study, and recommendations and findings are presented. Lessons learned from the Caltrans experience are shared to the benefit of other States implementing QC/QA specifications for AC pavement.
Elliott, R.P. "A Value Concept for Pavement Construction Pay Adjustment Schedules," Transportation Research Record 1040, 1985, pp. 4548.
A value concept is presented that can serve as a basis for developing rational payment schedules for pavement construction. Provisions are made for incorporating both the average and the standard deviation of the materials tests into a payment determination scheme that is based on the relative pavement life effects. The concept is based on the recognition that, at the time the pavement is considered to have failed, only a small percentage of the surface actually exhibits severe distress. As a result, the life of the pavement is controlled not by the average or 50^{th} percentile of the material, but by a lower percentile representative of the actual surface distress.
Elliott, R.P. and Qiu, Yanjun. "Analysis of Contractor Pay Adjustment Schedule Using Simulation," Transportation Research Record 1544, 1996, pp. 109115.
A common provision in QC/QA construction contracts is the adjustment of the contractor's pay on the basis of the quality of the construction. The expected impact of the provision on payment should be examined to ensure that the adjustments are neither unduly severe nor excessively lenient. Most pay adjustment plans have been developed around a quality index by using a PD approach. Analyses of these plans are complex, but reasonably well defined. Other plans are more complex and do not lend themselves to direct analysis. Computer simulation can be used to examine these plans. An example is given. It is shown that the simulation process can provide a better, more detailed examination of the pay schedule than is possible by simply determining the expected payment. In particular, the simulation process can indicate the variability of payment at various quality levels and can identify the factors most responsible for the pay adjustment.
Fan, DY. "Bayesian Acceptance Sampling Scheme for PassFail Components," Communications in Statistics: Theory and Method, Vol. 20, No. 8, 1995, pp. 23512355.
An approach is given for determining the choice of a prior distribution for the design of a Bayesian acceptance sampling scheme. The appropriate prior distribution is selected from confidence coefficients corresponding to classical lower confidence bounds. A numerical example is provided.
Gentry, C. and Yrjanson, W.A. "Specifications for Quality Control: A Case Study," Transportation Research Record 1126, 1987, pp. 3741.
One of the essential qualities of a specification is reasonableness. Court decisions and their economic consequences demand that specifications be based on reasonable requirements. Specifications that call for unnecessary perfection are hardly reasonable; furthermore, they do not ensure performance. Specifications that attempt to control quality through extremely limited tolerances may, in fact, be counterproductive. When QC efforts are directed to comply with such specifications, quality may be compromised, contract administration may be difficult, and additional costs may be incurred, all without improving the performance of the completed work. A case study is presented to illustrate the problems created by an excessively restrictive specification. Alternatives and comments for improvement of the specification are offered.
Gibra, I.N. "Recent Developments in Control Chart Techniques," Journal of Quality Technology, Vol. 7, No. 4, 1975, pp. 183192.
In the last three decades, several control chart procedures were developed. Prominent among these are the Cumulative Sum, Economic Design of XControl, and Acceptance and Multicharacteristic charts. Descriptions and analyses of these charts are presented in an attempt to bring past research into current perspective.
Govindaraju, K. "Certain Observations on LotSensitive Sampling Plan," Communications in Statistics: Theory and Method, Vol. 19, No. 2, 1990, pp. 617627.
A comparison of the samplesize efficiency of the lotsensitive plan with the double and multiple sampling plans is presented. It is shown that a fully curtailed lotsensitive plan will involve a smaller average sample number than the equivalent double and multiple sampling plans.
Govindaraju, K. and Kuralmani, V. "A Note on the Operating Characteristic Curve of the Known Sigma Sampling Variables Plan," Communications in Statistics: Theory and Method, Vol. 21, No. 8, 1992, pp. 23392347.
The OC curves of certain known sigma sampling plans may not be satisfactory in that they have a tendency to reject lots of acceptable quality. The theory and a method to identify such known sigma variables plans possessing unsatisfactory OC curves are presented.
Govindaraju, K. and Subramani, K. "Selection of Double Sampling Attributes Plan for Given Acceptable Quality Level and Limiting Quality Level," Communications in Statistics: Simulation and Computation, Vol. 21, No. 1, 1992, pp. 221242.
Tables and procedures are given for finding the double sampling plan, conditional double sampling plan, link sampling plan, and ChSP4 and ChSP4A chain sampling plans involving a minimum sum of the producer's and consumer's risks for the specified acceptable quality level and the limiting quality level.
Govindaraju, K. and Subramani, K. "Selection of Single Sampling Attributes Plan for Given Acceptable Quality Level and Limiting Quality Level Involving Minimum Risk," Communications in Statistics: Simulation and Computation, Vol. 19, No. 4, 1990, pp. 1293 1302.
A table and a procedure are given for finding the single sampling attributes plan involving a minimum sum of the producer's and the consumer's risk for the specified acceptable quality level and the limiting quality level.
Hamaker, H.C. "Acceptance Sampling for Percent Defective by Variable and by Attributes," Journal of Quality Technology, Vol. 11, No. 3, 1979, pp. 139148.
Various methods for adjusting variables and attributes sampling plans so that they possess nearly identical OC curves are reviewed and extended. It is demonstrated that the OC curve for the Smethod plans can be adequately derived from a normal approximation and that the more complicated use of the noncentral tdistribution can be avoided. The relative efficiencies of the different types of single sampling plans are shown to be practically functions of the indifference quality alone. The relationships between these efficiencies and the choice of the specification limit are discussed in detail.
Hawkes, C.J. "Curves for Sample Size Determination in LotSensitive Sampling Plans," Journal of Quality Technology, Vol. 11, No. 4, 1979, pp. 205210.
Curves are given for determining the required sample size for zero acceptance number sampling plans for specified values of lot size and lot tolerance PD. These allow a quick and easy assessment of the minimum required sample size to obtain lot PD protection for 1percent, 5percent, 10percent, 20percent, and 50percent consumer risk.
Hughes, C.S. "Incentive and Disincentive Specification for Asphalt Concrete Density," Transportation Research Record 986, 1984, pp. 3842.
The background for a specification that includes both positive and negative price adjustments for the density of AC is presented. The results that have been obtained since the specification was introduced in 1978 are described. The incentive features of the specification are emphasized because it is believed that they are unique and have been the primary reason that improved densities have been obtained in Virginia for the past 6 years.
Hughes, C.S. "Variability in Highway Pavement Construction," NCHRP Synthesis 232, 1996.
This synthesis addresses variability questions and the importance of defining the variability of materials and construction processes. For potential users of these measures of variability, an update of the typical materials and construction variability and the use of incentive and disincentive pay schedules for acceptance are presented.
Irick, P.E. "A Conceptual Framework for the Development of a PerformanceRelated Materials and Construction Specification," Transportation Research Record 1126, 1987, pp. 127. Pavement design and performance concepts that provide a systematic basis for the development of specifications for materials and construction (M&C) are presented. It is assumed that the conceptual framework for specifications includes eight sets of relationships among the process variables and nine sets of inputs or outputs for the relationships. Independent variables are selected that have predictable effects on performance related output variables. From these independent variables, variables appearing explicitly in prediction functions (EPF) are selected and subdivided into traffic factors, environmental factors, and pavement structure factors. EPF variables can be replaced by surrogate variables (SPF) when M&C control for these secondary variables is easier to provide. Other secondary variables are the control factors (CF), which have predictable effects on the EPF of SPF variables. EPF variables related to the M&C process are denoted as MCF. In general, a stochastic prediction model consists of a prediction function that may be completely known from mechanistic considerations; may be partially known except for undetermined constants; or may be assumed to be a linear combination of linear, curvilinear, and interaction effects among independent variables. General forms of prediction equations for stress and distress, stressload equivalence relationships, traffic prediction relationships, relationships among M&C specification factors, and performancecost relationships are presented. Pavement design criteria and M&C specification factors are added as the initial conditions for the definition of a pavement design for a given requirement.
Kandahl, P.S.; Cominsky, R.J.; Maurer, D.; and Motter, J.B. "Development and Implementation of Statistically Based EndResult Specifications for HotMix Asphalt in Pennsylvania," Transportation Research Record 1389, 1993, pp. 916.
In the past, Pennsylvania DOT used the concept of single samples and tests to determine the quality of hotmix asphalt (HMA) mixtures. This study develops a statistically based ERS for HMA pavements that makes the contractor responsible for QC and Pennsylvania DOT responsible for QA. Field data from several HMA paving projects were analyzed statistically to establish realistic numerical limits for the various test parameters used in the specification. Three pay items (asphalt content, percent passing #200, and mat density) are included in the specification. The specifications have provided Pennsylvania DOT with a means of evaluating and comparing the dollar value of the yearbyyear improvement in HMA quality.
Kirkpatrick, R.L. "Confidence Limits on a Percent Defective Characterized by Two Specification Limits," Journal of Quality Technology, Vol. 2, No. 3, 1970, pp. 150155.
A quality problem is to assess the performance of a production process with respect to specifications. A solution is obtained by estimating PD and placing confidence limits on the PD for each product characteristic. Tables are presented for determining a point estimate of PD and 90, 95, and 99percent confidence limits on the PD of a characteristic with both upper and lower or single specification limits. On the assumption of normality, only the specification limits, sample size, sample mean, and standard deviation are needed to give a solution to the problem.
Kopac, P.A. "Current Practices in Acceptance of Bituminous Concrete Compaction," Transportation Research Record 986, 1984, pp. 4346.
Current procedures employed by State highway agencies to determine the acceptability of bituminous concrete compaction are discussed. Both statistical and nonstatistical acceptance plans are covered. Statistical acceptance plans can provide a clear indication of the quality levels that are desired with the estimation of the construction quality. However, many of the statistical acceptance plans currently in use are inadequate because they are inefficient or statistically unsound, or both. Also, there is a considerable lack of uniformity among acceptance plans and the price adjustment schedules they contain. Recommendations are made to improve acceptance plans.
Kuralmani, V. and Govindaraju, K. "Modified Tables for the Selection of the Double Sampling Attributes Plan Indexed by AQL and LQL," Communications in Statistics: Theory and Method, Vol. 24, No. 7, 1995, pp. 18971921.
Modified tables are presented for the selection of double sampling plans for a given AQL, producer's risk, LQL, and consumer's risk, giving the minimum sum of the average sample numbers at the AQL and LQL under the conditions of the Poisson model for the OC curve.
Kuralmani, V. and Govindaraju, K. "Selection of Conditional Sampling Plans for Given AQL and LQL," Journal of Applied Statistics, Vol. 20, No. 4, 1993, pp. 467479.
Procedures and tables for the selection of conditional sampling plans are given. The sampling plans discussed include the conditional double sampling plan, chaindeferred sampling plan, link sampling plan, and ChSP4A chain sampling plan. The procedures and tables for each are provided for a given AQL, producer's risk, limiting quality level (LQL), and consumer's risk, giving a minimum sample size at AQL under the conditions of the Poisson model for the OC curve.
Moore, R.M.; Mahoney, J.P.; Hicks, R.G.; and Wilson, J.E. "Overview of PayAdjustment Factors for Asphalt Concrete Mixtures," Transportation Research Record 821, 1981, pp. 4956.
In fall 1979, the Oregon State Highway Division and Oregon State University, with participation from the University of Washington, initiated a research project to study the impact of variations in material properties on asphalt pavement life. The study was aimed at developing a rational approach to assessing the effects of variations from specification limits so that a firm basis could be established for the development of pay factors. Analysis of the results indicates the following: (1) most State agencies will accept one or more property characteristics that are outside of specification tolerances, (2) most State agencies apply a pay factor for accepted material outside of specification tolerances, (3) only 26 percent of the State agencies consider their pay factor to be proportional to reduced pavement serviceability, (4) approximately half of the agencies consider payfactor plans to be effective in encouraging compliance with specifications, and (5) there is a wide disparity in the payadjustment factors used by the different agencies.
Nachlas, J.A. and Kim, SI. "Generalized Attribute Acceptance Sampling Plans," Journal of Quality Technology, Vol. 21, No. 1, 1989, pp. 3240.
The imposition of acceptance criteria upon realizations of generalized sampling plans is described and has been shown to yield a large variety of new attribute acceptance sampling plans. The resulting generalized attribute acceptance sampling plans can be constructed to yield the same OC curve as that for conventional single sampling plans with lower expected total cost. An example is presented.
Nelson, L.S. "Factors for Confidence Limits on Standard Deviation," Journal of Quality Technology, Vol. 29, No. 4, 1997, pp. 485487.
Tables are presented for easily determining both onesided and twosided confidence limits on standard deviations, assuming that the sample is random and from a normal population.
Patel, A.; Thompson, M.; Harm, E.; and Sheftick, W. "Developing QC/QA Specifications for HotMix Asphalt Concrete in Illinois," Transportation Research Record 1575, 1997, pp. 6674.
The Illinois DOT has recently undertaken a quality management program to improve the quality of construction, allow more innovation, and reduce the department's management of industry construction programs. The AC QC/QA program is a significant part of this quality management program. The Illinois DOT credits the success of the AC QC/QA program to gradual implementation, and contractor and industry involvement. In 1991, four projects were constructed under a newly developed QC/QA specification. After reviewing and evaluating feedback, the specification was revised for 1992. In 1992, 30 projects were constructed using the QC/QA specification and, in 1993, 65 projects used the specification. In 1994 and 1995, most projects over 225 Mg used the specification. In conjunction with this effort, an aggregate certification program was implemented. Training programs for contractor QC and aggregate certification were also implemented. Analysis of the data indicates an increase in the uniformity of the HMA, potentially leading to a 15percent increase in fatigue life. The Illinois DOT is now examining the implications of developing ERS and PRS for the AC QC/QA program. In summer 1996, one QC/QA project was shadowed and evaluated based on newly developed ERS/PRS.
Pham, T.G. and Turkkan, N. "Bayes Binomial Sampling by Attributes With a GeneralBeta Prior Distribution," IEEE Transactions on Reliability, Vol. 41, No. 2, 1992, pp. 310316.
In binomial sampling, the standard beta is frequently used as a prior because of its conjugate property for a sample from a Bernoulli distribution. The case where the prior is a general beta is examined. Practical advantages in the elicitation of expert opinion (to obtain a prior) and a convenient expression of the posterior are presented. A computer program on an IBM^{®} personal computer (or a compatible computer) permits simple use of the general beta and is available from the authors. This program is used to solve the numerical examples, showing the advantages of using the general beta as a prior.
Schmitt, R.L.; Russell, J.S.; Hanna, A.S.; Bahia, H.U.; and Jung, G.A. "Summary of Current Quality Control/Quality Assurance Practices for HotMix Asphalt Construction," Transportation Research Record 1632, 1998, pp. 2231.
State highway agencies and contractors have been implementing QC/QA specifications in recent years to advance the quality of HMA construction. During their continued development, the attributes of these QC/QA specifications have varied among the States. This paper provides a compilation of stateoftheart practices in QC/QA for HMA construction and provides recommendations for State highway agencies and contractors when modifying or developing a QC/QA specification.
Seeds, S.B.; Basavaraju, R.; Epps, J.A.; and Weed, R.M. "Development of PerformanceRelated Specifications for HotMix Asphalt Pavements Through WesTrack," Transportation Research Record 1575, 1997, pp. 8591.
The primary purpose of the FHWAsponsored WesTrack project is to further the development of PRS for HMA construction. This objective is being achieved, in part, through the accelerated loading of a fullscale test track facility in northern Nevada. Twentysix HMA test sections that were constructed to meet the criteria set forth in a statistically based experimental design are providing performance data that will be used to improve (or develop new) pavement performance prediction relationships that better account for the effects that offtarget values of asphalt content, air voids, and aggregate gradation have on such distress factors as fatigue cracking, permanent deformation, roughness, raveling, and tirepavement friction. The concept of the planned PRS and how it will incorporate the modified pavement performance prediction models are described. The current plan for assessing contractor pay adjustments based on data collected from the asconstructed pavement is also discussed.
Semenov, V.A. "Quality Control in Highway Construction and Maintenance When the Measurement Parameters Are Highly Nonuniform," Transportation Research Record 1126, 1987, pp. 2836.
An original method is presented for QC based on Weibull's law for the distribution of random quantities with variable parameters. The nomographs obtained for determining the extreme values of the parameters and the defectiveness index can be used for various cases in the statistical reduction of research results. The proposed method can be used for QC for both highly uniform data (normal distribution) and highly nonuniform data. The method described is widely used in the former Soviet Union for QC in the construction and maintenance of roads.
Sheng, Z. and Fan, DY. "Bayes Attribute Acceptance Sampling Plan," IEEE Transactions on Reliability, Vol. 41, No. 2, 1992, pp. 307309.
An approach is reviewed for choosing a prior distribution for a Bayes attribute acceptance sampling plan. A prior distribution is chosen from confidence levels corresponding to classical lower confidence bounds. Where a Bayes plan is acceptable, the sample size can be reduced.
Soundararajan, V. "Maximum Allowable Percent Defective (MAPD) Single Sampling Inspection by Attributes Plan," Journal of Quality Technology, Vol. 7, No. 4, 1975, pp. 173182.
Single sampling attribute plans indexed by maximum allowable percent defective (MAPD) are given. A table allowing the transitioning from one set of parameters to match the OC curve to other similar sets is given.
Soundararajan, V. and Arumainayagam, S.D. "Lot Sensitive Double Sampling Plan," Communications in Statistics: Theory and Method, Vol. 21, No. 10, 1992, pp. 29312948.
A sampling plan is derived for compliance testing, which provides consumer protection.
Suresh, K.K. and Ramkumar, T.B. "Selection of a Sampling Plan Indexed With Maximum Allowable Average Outgoing Quality," Journal of Applied Statistics, Vol. 23, No. 6, 1996, pp. 645654.
A new concept of maximum allowable average outgoing quality (MAAOQ), which is the average outgoing quality at the inflection point, is introduced. The procedure for designing a single sampling plan indexed through the MAPD and MAAOQ is stated. Tables are constructed for the selection of parameters for the plan and parametric conversions are studied.
Suresh, R.P. and Ramamathan, T.V. "Acceptance Sampling Plans by Variables for a Class of Symmetric Distributions," Communications in Statistics: Simulation and Computation, Vol. 26, No. 4, 1997, pp. 13791391.
The estimation of PD using a normal sampling plan is not appropriate when the assumption of normality is violated. A sampling plan based on a more general symmetrical family of distributions with the parameters estimated using the modified maximum likelihood (MML) procedures is presented. Some numerical studies are also presented, showing that the sampling plan works well for most of the symmetrical nonnormal distributions.
Vlatas, D.A. and Smith, R.E. "Implications of LifeCycle Performance Specifications," Transportation Research Record 1215, 1989, pp. 2530.
The professional, managerial, and legal implications of using lifecycle performance specifications are presented. Changes in the roles of the parties using lifecycle performance specifications are discussed. This approach can improve quality, reduce costs, and expedite the construction process. The basis of the process is the development of models of expected performance. These models will be used to predict whether the pavement will perform as required over the life of the project. Tests are performed at the end of construction to determine whether the expected performance is likely to be achieved. Adjustments in payment can be made, based on the performance model predictions. The ramifications of adopting lifecycle performance specifications are discussed.
Wasserman, G.S. "Matching Performance of Continuous Sampling Plans With Single Sampling Plans," Communications in Statistics: Simulation and Computation, Vol. 19, No. 4, 1990, pp. 13031317.
Single sampling plans are widely used for appraising product quality. However, for situations where a continuous product flow exists, lotbylot demarcations may not exist, and it may be necessary to use alternate procedures, such as Continuous Sampling Plan 1 (CSP1), for continuous processes. In this case, one would like to understand how the average performance of the continuous sampling procedures compares to the more commonly used single sampling plans. A model is devised that can be used to relate plan performance between single sample lot acceptance procedures and CSP1. It is shown that it is generally not possible to match up performance based on OC expressions for the two plans. Instead, the plans are matched by equating expressions for π (p), the long run proportion of the product that is accepted, under both procedures. This is shown to be equivalent to matching properties on an average outgoing quality basis. Tables are generated that may be used to look up equivalent CSP1 plans. The tables may also be used to match up plan performance around two target quality levels (p_{o} and p_{1}).
Weed, R.M. "Adjusted Pay Schedules: New Concepts and Provisions," Transportation Research Record 986, 1984, pp. 3238.
Shortly after the American Association of State Highway Officials (AASHO) Road Test had furnished a wealth of statistical data on pavement construction and performance, highway agencies began to use this data to develop ERS based on statistical concepts. These specifications usually included adjusted pay schedules, the development of which was sometimes quite arbitrary. More recently, attempts have been made to improve both the accuracy with which the pay schedules are established and the fairness with which they are administered. The rationale underlying several recent advances in the stateoftheart is discussed. Included are the use of the principal liquidated damages to relate pay reductions to the anticipated monetary loss resulting from substandard work, the development of the crediting concept to overcome a basic inequity of many existing pay schedules, and the establishment of bonus provisions that provide additional incentive by awarding payment slightly in excess of the contract price for superior quality work.
Weed, R.M. "Analysis and Application of Correlated Compound Probabilities," Transportation Research Record 792, 1981, pp. 4953.
Many statistical applications require the calculation of compound probabilities and, frequently, the individual probabilities are not independent. The failure to recognize that a correlation exists in cases such as these has resulted in numerous errors in published literature. Although an exact analytical solution is not known, problems of this type can often be handled effectively by calculating lower and upper bounds for the desired probabilities. Bounds for both positively and negatively correlated cases are derived and then applied in the analysis of statistical acceptance procedures. The results of several computer simulation tests are presented to demonstrate the validity of the theoretically derived results.
Weed, R.M. "Composite Pay Equations: General Approach," Transportation Research Record 1465, 1994, pp. 915.
Highway construction specifications involving the acceptance testing of several different quality characteristics are sometime confusing and difficult to administer. A procedure is developed by which multiple quality measures may be combined in a rational manner in a single, composite pay equation. This approach is scientifically sound and may be applied to almost any construction specification for which a relationship between quality and performance is known or can be approximated. An example based on PCC pavement is presented to illustrate the practicality of this method.
Weed, R.M. "ComputerAssisted Random Sampling," Transportation Research Record 1034, 1985, pp. 140152.
Many State transportation agencies use SQA specifications to govern construction work. A vital step in the application of these and other types of specifications is the selection of random samples to obtain a valid estimate of the quality received. Random sampling procedures are often tedious and timeconsuming, but can be considerably simplified with computer assistance, either by using special forms generated by computer or by working directly at an interactive terminal. Examples of several applications are presented.
Weed, R.M. "Development of Air Voids Specification for Bituminous Concrete," Transportation Research Record 1491, 1995, pp. 3339.
The New Jersey DOT has been using SQA specifications for various construction products since the 1960s. Throughout this period, there has been a continuing process leading to a better understanding of the operation and implementation of SQA procedures. The New Jersey DOT specification for air voids in bituminous concrete was one of the first to be developed and, as such, is a prime candidate for upgrading. A major change is to base the acceptance procedure on the PD rather than on the average of the test values in order to control both the level and the variability of the air voids in a statistically efficient way. Doing this required new definitions of AQL and rejectable quality level (RQL), and a reexamination of the adjusted pay schedule to be applied when other than AQL work is received. It was decided to use a bonus provision for superior quality, an approach that has worked well with other recently developed New Jersey DOT specifications. Another change is to use a continuous (equationtype) pay schedule to provide a smooth progression of payment as quality varies, thus avoiding potential disputes over measurement precision when a quality estimate falls just onto one side or the other of a boundary in a stepped pay schedule. The various developmental steps are described, including the construction of the OC curve to verify the performance of the specification and the field trials leading to its successful implementation.
Weed, R.M. "Development of Multicharacteristic Acceptance Procedures for Rigid Pavement," Transportation Research Record 885, 1982, pp. 2536.
The manner in which the AASHTO design can be used to develop multicharacteristic acceptance procedures for rigid pavement is outlined. The AASHTO equation is used to compute both the expected loadbearing capacity based on the asbuilt characteristics of the pavement and the desired loadbearing capacity based on the design parameters. The ratio of these two values is then used to determine the appropriate pay adjustment, which may be either positive or negative. Sensitivity tests are performed to verify the reliability of this approach and computer simulation is used to demonstrate the effectiveness of several different acceptance procedures of this type. A secondary study is conducted to determine how the procedure based on the AASHTO equation compares with several other methods of treating multiple pay factors to obtain a single overall pay factor. Under the assumption that the AASHTO method is the fundamentally correct approach, the method of multiplying individual pay factors together is shown to be among the best of the other methods that were tested.
Weed, R.M. "Method to Establish Pay Schedules for Rigid Pavement," Transportation Research Record 885, 1982, pp. 1824.
An equation is derived to compute the appropriate pay factor for any quality level of rigid pavement. The measure of quality used in this development is the estimated loadbearing capacity of the pavement, although the results may be applied to specifications based on other quality measures. The appropriate pay adjustment is considered to be the present worth of any expense or savings expected to occur in the future as the result of a departure from the specified level of quality and may be positive or negative. Sensitivity tests demonstrate that the method is reliable provided that the input variables are determined with reasonable accuracy. By using input values typical of a relatively urbanized area, this procedure indicates that a minimum pay factor of 60 percent is appropriate for the poorest quality work and a maximum pay factor of 115 percent is justified for work of truly superior quality. Additional factors are cited that, though unquantified, would tend to lower the minimum pay factor and raise the maximum pay factor. Finally, pay schedules are developed, the OC curves of which closely approximate the theoretically derived relationship.
Weed, R.M. "OCPLOT: Program to Generate Operating Characteristic Curves for Statistical Construction Specifications," Transportation Research Record 1491, 1995, pp. 1826.
The performance of the Nation's highway system is inexorably linked to the quality of the design and the quality of the construction. To control the quality of the construction, transportation agencies have developed elaborate QA programs, most of which employ ERS that rely on statistical sampling and acceptance procedures to ensure that the work is done in accordance with the plans and specifications. Whether the acceptance procedure leads to a simple pass/fail decision or an adjustment in contract price, the proper design of such plans is critical to their performance. Poorly conceived plans may be totally ineffective or impractically severe, and both extremes have been found in published or proposed national standards. To encourage the design of plans that are both effective and fair, an interactive software program has been developed that enables the user to construct OC curves to analyze the performance of a wide range of acceptance plans. An example is presented to demonstrate the versatility of the program and the ease with which it can be applied.
Weed, R.M. "Practical Framework for PerformanceRelated Specifications," Transportation Research Record 1654, 1999, pp. 8187.
As highway agencies moved away from the older prescriptiontype specifications and began to develop ERS and PRS, several different statistical measures of quality have been used. These include sample mean, PD or its complement, PWL, and AAD. The CI is yet another measure that has been proposed. What has not been undertaken during this developmental period is any sort of formal analysis to determine which, if any, of these measures accurately reflects the expected performance of the construction products to which they are applied. Specialized computer programs were developed to demonstrate the potential weaknesses of the current quality measures and to explore alternate approaches that may overcome these weaknesses. It was found that pay equations based on the mean and standard deviation computed from the sample can be tailored to closely match the value of the constructed product as estimated by lifecycle cost techniques. It is believed that this forms a practical starting point for the development of construction acceptance procedures more closely linked to quantified performance models.
Weed, R.M. "Quality Assurance Software for Personal Computer," Transportation Research Record 1544, 1996, pp. 116124.
Demonstration Project 89 on Quality Management was created to provide guidance on the use of practical and effective procedures to ensure that the level of quality designed into the plans and specifications is accurately achieved in the constructed product. One part of this effort is the distribution of a software package consisting of several interactive programs developed for use on a personal computer. These extremely userfriendly programs make it possible to analyze both pass/fail and payadjustment acceptance procedures, construct OC curves, plot control charts, experiment with computer simulation, perform statistical comparisons of data sets, demonstrate the unreliability of decisions based on a single test result, and explore the effectiveness of stratified random sampling. This comprehensive software package provides highway engineers with the necessary tools for learning why some statistical procedures are inherently superior to others and how to incorporate this knowledge into fair and effective construction specifications.
Weed, R.M. "A Rational Method for Relating AsBuilt Quality to Pavement Performance and Value," Transportation Research Record 1632, 1998, pp. 3139.
Highway construction specifications routinely use adjustedpayment provisions to award payment in proportion to the level of quality received. Work that is defined as acceptable is eligible for 100percent payment, whereas work that fails to meet the desired quality level, but is not sufficiently deficient to warrant removal and replacement, typically receives some degree of pay reduction. There is not yet consistency in the practices regarding the magnitude of the pay adjustment that is judged as being appropriate for varying levels of asbuilt quality. There needs to be a method for relating asbuilt quality to expected performance, which can then be related to value by engineering economics procedures. The extension and refinement of earlier work are described and an example structured around one of the performance relationships in the AASHTO Guide for Design of Pavement Structures is provided.
Weed, R.M. "Revision of a Flawed Acceptance Standard," Transportation Research Record 1056, 1986, pp. 2135.
A major revision of AASHTO Standard R984, Acceptance Sampling Plans for Highway Construction, has been completed. The primary goals were to correct a major conceptual error and to reduce the level of complexity. In this paper, the flaws in the original version are discussed, the basic changes that were made are described, and a significant addition to the new standard is presented. This addition is OC tables that enable the user to quickly and easily select acceptance plans that will provide the desired degree of QA. Computer simulation is used to demonstrate that singlelimit variable OC curves are sufficiently accurate for most double limit applications. Two examples are included to illustrate the use of the revised standard.
Weed, R.M. "Stratified Random Sampling From a Discrete Population," Transportation Research Record 792, 1981, pp. 4144.
In the development of statistical acceptance procedures for products whose quantity is measured on a continuous scale by using units such as length, area, volume, or weight, QA engineers usually specify stratified random sampling plans to ensure a more uniform coverage of the product than is often achieved by pure random sampling. Stratified plans divide the total quantity of the product into an appropriate number of equalsized sublots and require that a single random sample be taken from each. Not only is it desirable to develop an equivalent procedure for products that are measured in discrete units, but, in many cases, such a procedure will prove to be more convenient for continuous products that are delivered in discrete units, such as batches or truckloads. However, the development of such a procedure is not as straightforward as might be expected. The weaknesses of some of the more obvious approaches are discussed and then a method is presented that achieves the desired result.
Weed, R.M. and Strawderman, W.E. "Method to Exclude the Effect of Testing Error When Estimating the Percentage Defective of a Continuous Normal Population," Transportation Research Record 792, 1981, pp. 4549.
The quality of a product is often characterized by the percentage of the population that falls outside of specific limits. Although established methods for estimating PD are accurate as far as the overall distribution of test results is concerned, part of the variability of this distribution is caused by the presence of testing errors that cause the PD of the product itself to be overestimated. A method has been developed to overcome this problem and computer simulation has been used to demonstrate that it is effective for situations in which the testing error is no larger than about onehalf of the variability associated with the product. The results of several unsuccessful attempts to improve on this technique are also presented and described briefly.
Weingarten, H. "Confidence Intervals for the Percent Nonconforming Based on Variables Data," Journal of Quality Technology, Vol. 14, No. 4, 1982, pp. 207210.
Sampling inspection by variables for percent nonconforming, such as with the use of MILSTD414, also provides the data for estimating the population percent nonconforming. A method is provided for obtaining a confidence interval for the population value by means of an OC curve. This OC curve is achieved from the data and is not that of the original sampling plan.
White, T.D. and Brown, E.R. "Statistical Quality Control Procedures for Airfield Pavement Materials and Construction," Transportation Research Record 652, 1977, pp. 3642.
The interaction of materials, construction, and the environment makes projections of pavement performance difficult. To increase the confidence with which these projections can be made, a simplified statistical QC plan for airfield pavement materials and construction was developed. Test results based on a specific number of samples can be extended with the desired confidence limits based on probability theory to evaluate an entire lot of material. This statistical QC plan evaluates pavement quality much better than do conventional specifications. It also describes how to handle materials or construction of borderline acceptability. When test results indicate that the material or construction meets the desired quality, it is accepted at 100percent payment. If it is below the minimum requirements, it is rejected. When material or construction is found to be below the desired quality, but above the minimum requirement, it is accepted at a reduced price. The evaluation is done on a daily basis so that the engineer and the contractor know the level of acceptability as the project progresses.
Willenbrock, J.H. and Kopac, P.A. "Development of PriceAdjustment Systems for Statistically Based Highway Construction Specifications," Transportation Research Record 652, 1977, pp. 5258.
A methodology is presented that can be used to develop priceadjustment systems for use in statistically based highway construction specifications. Three approaches are proposed for the development of the price adjustment system: (1) the serviceability approach, (2) the cost of production approach, and (3) the OC curve approach. The three approaches are discussed and compared, and their most appropriate applications are recommended. A fourth approach, the cost of QC approach, is also discussed, but is not fully developed because of the limited cost data available.
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Topics: research, infrastructure, pavements and materials Keywords: research, infrastructure, pavements and materials, quality assurance, quality control, specifications, statistical specifications, QA, QC, payment adjustments TRT Terms: research, facilities, transportation, highway facilities, roads, parts of roads, pavements , pavementsunited statesquality controlhandbooks, manuals, etc, quality assuranceunited stateshandbooks, manuals, etc, quality assurance, statistical quality control, acceptance sampling, manuals Updated: 04/23/2012
