A Review of Acceptance Sampling Schemes with Emphasis on the Economic Aspect

Ever since the pioneering work of Dodge and Romig (1929), acceptance sampling has rapidly gained wide application in industry, particularly in the following stages of manufacturing: incoming materials inspection, on-line production control, and finished product quality auditing. The purpose for which sampling inspection is being applied varies from case to case. For a producer, some possible aims are:

[1]  S. Ehrenfeld.  On Group Sequential Sampling , 1972 .

[2]  William C. Guenther,et al.  Use of the Binomial, Hypergeometric and Poisson Tables to Obtain Sampling Plans , 1969 .

[3]  G. B. Wetherill,et al.  Bayesian sequential analysis , 1961 .

[4]  V. Barnett,et al.  Economic Choice of Sample Size for Sampling Inspection Plans , 1974 .

[5]  Henry P Goode,et al.  Sampling inspection by variables , 1954 .

[6]  G. A. Barnard,et al.  Sampling Inspection and Statistical Decisions , 1954 .

[7]  I. D. Hill.  The Economic Incentive Provided by Sampling Inspection , 1960 .

[8]  O. L. Davies.  Some Statistical Aspects of the Economics of Analytical Testing , 1959 .

[9]  J. W. Schmidt,et al.  Economic Multiattribute Acceptance Sampling , 1972 .

[10]  H. C. Hamaker.  Defence Specification DEF-131: Sampling Procedures and Tables for Inspection by Attributes. , 1963 .

[11]  G. B. Wetherill,et al.  The Most Economical Sequential Sampling Scheme for Inspection by Variables , 1959 .

[12]  A. W. Wortham,et al.  A Technical Note on Average Outgoing Quality , 1970 .

[13]  A. Hald.  SINGLE SAMPLING INSPECTION PLANS WITH SPECIFIED ACCEPTANCE PROBABILITY AND MINIMUM AVERAGE COSTS , 1963 .

[14]  William C. Guenther,et al.  On the Determination of Single Sampling Attribute Plans Based upon a Linear Cost Model and a Prior Distribution , 1971 .

[15]  A. Hald.  Bayesian single sampling attribute plans for discrete prior distributions , 1964 .

[16]  Betty J. Flehinger,et al.  Incentive Contracts and Price Differential Acceptance Tests , 1964 .

[17]  A. Hald,et al.  The Compound Hypergeometric Distribution and a System of Single Sampling Inspection Plans Based on Prior Distributions and Costs , 1960 .

[18]  F. J. Anscombe,et al.  Tables of sequential inspection schemes to control fraction defective. , 1949, Journal of the Royal Statistical Society. Series A.

[19]  Joseph W. Foster.  PRICE ADJUSTING SAMPLING PLANS , 1970 .

[20]  G. Barrie Wetherill,et al.  Sequential methods in statistics , 1967 .

[21]  Henry Ellner,et al.  Validating Results of Sampling Inspechon by Attributes , 1963 .

[22]  F. J. Anscombe.  Notes on Sequential Sampling Plans , 1960 .

[23]  William C. Guenther.  A Procedure for Finding Double Sampling Plans for Attributes , 1970 .

[24]  David R. Cox,et al.  Serial Sampling Acceptance Schemes Derived From Bayes's Theorem , 1960 .

[25]  G. B. Wetherill,et al.  The Economic Design of Continuous Inspection Procedures: A Review Paper , 1973 .

[26]  G. E. G. Campling.  Serial sampling acceptance schemes for large batches of items where the mean quality has a normal prior distribution , 1968 .

[27]  H. C. Hamaker,et al.  The Efficiency of Double Sampling for Attributes , 1955 .

[28]  W. Chiu,et al.  A New Prior Distribution for Attributes Sampling , 1974 .

[29]  Eugene P. Durbin.  Pricing Policies Contingent on Observed Product Quality , 1966 .

[30]  Robert E. Sherman,et al.  Design and Evaluation of a Repetitive Group Sampling Plan , 1965 .

[31]  R. K. Zeigler,et al.  Double Sampling Plans where the Acceptance Criterion is the Variance , 1968 .

[32]  Søren Johansen,et al.  Asymptotic Properties of the Restricted Bayesian Double Sampling Plan , 1970 .

[33]  H. C. Hamaker.  Some Notes on Lot-by-Lot Inspection by Attributes , 1950 .

[34]  G. A. Barnard,et al.  Sequential Tests in Industrial Statistics , 1946 .

[35]  K. Sarkadi,et al.  On Preliminary Sampling with Special Reference to the Microbiological Control of Tomato Concentrates , 1960 .

[36]  William R. Pabst,et al.  Reviews of Standards and Specifications: MIL-STD-414 Sampling Procedures and Tables for Inspection by Variables for Percent Defective , 1971 .

[37]  I. D. Hill,et al.  Deferred Sentencing Schemes , 1959 .

[38]  M. K. Vagholkar.  The Process Curve and the Equivalent Mixed Binomial with Two Components , 1959 .

[39]  Herman D. Hughes,et al.  A Computer Program for the Solution of Double Sampling Plans , 1972 .

[40]  W. R. Pabst.  MIL-STD-105D , 1963 .

[41]  A. Hald,et al.  ASYMPTOTIC PROPERTIES OF BAYESIAN SINGLE SAMPLING PLANS , 1967 .

[42]  A. Hald.  The Mixed Binomial Distribution and the Posterior Distribution of p for a Continuous Prior Distribution , 1968 .

[43]  G. B. Wetherill,et al.  A Simplified Attribute Sampling Scheme , 1974 .

[44]  Joseph W. Foster,et al.  Price Adjusted Single Sampling with Linear Indifference , 1972 .

[45]  L. Weiss,et al.  Sampling Plans Which Approximately Minimize the Maximum Expected Sample Size , 1964 .

[46]  J. Pfanzagl,et al.  The Efficiency of Sequential Sampling Plans Based on Prior Distributions and Costs , 1970 .

[47]  William C. Guenther,et al.  Variables sampling plans for the Poisson and the binomial , 1972 .

[48]  M. T. Subrahmanya.  Equitable quality level and error-areas under the operating characteristic curves of normal single sampling inspection plans (with σ known) , 1976 .

[49]  I. D. Hill.  Sampling Inspection and Defence Specification Def‐131 , 1962 .

[50]  A. Cohen,et al.  Curtailed attribute sampling , 1970 .

[51]  W. J. Zimmer,et al.  Some Acceptance Sampling Plans Based on the Theory of Runs , 1962 .

[52]  Herbert T. David,et al.  Acceptance inspection by variables when the measurements are subject to error , 1959 .

[53]  Eugene L. Grant,et al.  Statistical Quality Control , 1946 .

[54]  V. Barnett,et al.  Bayesian, and Decision Theoretic, Methods Applied to Industrial Problems , 1973 .

[55]  R. K. Zeigler,et al.  A Double Sampling Plan for Comparing Two Variances , 1972 .

[56]  M. Johns,et al.  Bayes Acceptance Sampling Procedures for Large Lots , 1959 .

[57]  A. Hald,et al.  THE DETERMINATION OF SINGLE SAMPLING ATTRIBUTE PLANS WITH GIVEN PRODUCER'S AND CONSUMER'S RISK. A TABLE FOR SOLVING THE EQUATION B(C,N,P) = P FOR C = 0(1)100 AND 15 VALUES OF P , 1966 .

[58]  Donald B. Owen,et al.  Control of Percentages in Both Tails of the Normal Distribution , 1964 .

[59]  H. Raiffa,et al.  Applied Statistical Decision Theory. , 1961 .

[60]  H. C. Hamaker,et al.  Some Basic Principles of Sampling Inspection by Attributes , 1958 .

[61]  Gerald J. Lieberman,et al.  Sampling Plans for Inspection by Variables , 1955 .

[62]  A. Clifford Cohen.  Misclassified Data from a Binomial Population , 1960 .

[63]  V. Barnett.  A Bayesian Sequential Life Test , 1972 .

[64]  F. J. Anscombe.  Rectifying Inspection of Lots , 1961 .

[65]  I. G. Evans,et al.  Bayesian Acceptance-Sampling Schemes for Two-Sided Tests of the Mean of a Normal Distribution of Known Variance , 1973 .

[66]  G. B. Wetherill,et al.  The most economical binomial sequential probability ratio test , 1960 .

[67]  David C. Dellinger,et al.  On some economic concepts of multiple incentive contracting , 1968 .

[68]  W. Schuler.  Multistage Sampling Procedures Based on Prior Distributions and Costs , 1967 .

[69]  William C. Guenther,et al.  The Average Sample Number for Truncated Double Sample Attribute Plans , 1971 .

[70]  G. B. Wetherill.  Some Remarks on the Bayesian Solution of the Single Sample Inspection Scheme , 1960 .

[71]  A. Hald,et al.  ON THE THEORY OF SINGLE SAMPLING INSPECTION BY ATTRIBUTES BASED ON TWO QUALITY LEVELS , 1967 .

[72]  W. K. Chiu,et al.  Economic Design of Attribute Control Charts , 1975 .

[73]  G. Barrie Wetherill,et al.  Sampling Inspection and Quality Control , 1969 .

[74]  H. Weiler,et al.  The Use of Incomplete Beta Functions for Prior Distributions in Binomial Sampling , 1965 .

[75]  Norman R. Garner.  Curtailed Sampling for Variables , 1958 .

[76]  D. K. Shah,et al.  A Simplified Form of the ASN for a Curtailed Sampling Plan , 1972 .

[77]  H. F. Dodge,et al.  A method of sampling inspection , 1929 .

[78]  H. R. Singh.  Producer and Consumer Risks in Non-normal Populations , 1966 .

[79]  A. Hald,et al.  Some Limit Theorems for the Dodge-Romig LTPD Single Sampling Inspection Plans. , 1962 .

[80]  Irving W. Burr,et al.  Three Class Attributes Plans in Acceptance Sampling , 1973 .

[81]  G. B. Wetherill,et al.  The Decision Theory Approach to Sampling Inspection , 1966 .

[82]  David G. Champernowne,et al.  The Economics of Sequential Sampling Procedures for Defectives , 1953 .

[83]  Yukio Suzuki,et al.  On sampling inspection plans , 1959 .

[84]  B. E. Ellison.  Two Theorems for Inferences about the Normal Distribution with Applications in Acceptance Sampling , 1964 .

[85]  A. G. Rao,et al.  An application of least cost acceptance sampling schemes , 1965, Unternehmensforschung.

[86]  S. Gupta.  Gamma Distribution in Acceptance Sampling Based on Life Tests , 1961 .

[87]  Kenneth E. Case,et al.  The effects of inspection error on single sampling inspection plans , 1973 .

[88]  E. Wilson,et al.  Multiple Sampling Plans Viewed as Finite Markov Chains , 1971 .

[89]  J.P.P. Talbot,et al.  VARIATION ANALYSIS AND DESIGN OF EXPERIMENTS AS AN AID TO DESIGN QUALITY ASSURANCE , 1972 .

[90]  D. W. Beattie,et al.  The Variable Lot‐Size Acceptance Sampling Plan for Continuous Production , 1961 .

[91]  H. F. Dodge.  Notes on the Evolution of Acceptance Sampling Plans: Part I , 1969 .

[92]  A. Kaplan,et al.  Instantaneous Switching Procedure for MIL-STD-105D , 1969 .

[93]  Joan Keen,et al.  Essentials of Quality Control , 1965 .

[94]  Johin V. Breakwell,et al.  Economically Optimum Acceptance Tests , 1956 .

[95]  G. P. Steck,et al.  Percentage Points for the Distribution of Outgoing Quality , 1959 .

[96]  Gareth Horsnell.  The Determination of Single-Sample Schemes for Percentage Defectives , 1954 .

[97]  M. J. R. Healy,et al.  Economic Choice of the Amount of Experimentation , 1956 .

[98]  Arthur Schleifer,et al.  Two-Stage Normal Sampling in Two-Action Problems with Linear Economics , 1969 .

[99]  A. Hald,et al.  Bayesian Single Sampling Attribute Plans for Continuous Prior Distributions , 1968 .

[100]  C. C. Craig.  The Average Sample Number for Truncated Single and Double Attributes Acceptance Sampling Plans , 1968 .

[101]  A. W. Wortham,et al.  A backward recursive technique for optimal sequential sampling plans , 1971 .

[102]  D. M. Ellis,et al.  Quality Control and Industrial Statistics. 3rd Ed. , 1966 .

[103]  Donald B. Owen,et al.  Variables Sampling Plans Based on the Normal Distribution , 1967 .

[104]  Alexander M. Mood.  On the Dependence of Sampling Inspection Plans Upon Population Distributions , 1943 .

[105]  R. Perry,et al.  Skip-Lot Sampling Plans , 1973 .

[106]  Leonard H. C. Tippett,et al.  A Guide to Acceptance Sampling , 1958 .

[107]  K. C. Seal.  A Single Sampling Plan for Correlated Variables with a Single-Sided Specification Limit , 1959 .

[108]  K. T. Wallenius.  Sampling for Confidence , 1967 .

[109]  H. F. Dodge,et al.  Sampling inspection tables , 1945 .

[110]  J. W. Schmidt,et al.  A Dual Purpose Cost Based Quality Control System , 1973 .

[111]  J. L. Jaech.  On the Use of Tolerance Intervals in Acceptance Sampling by Attributes , 1972 .