Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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Single and Sequential Dependent Sampling Plans for the Polya Process Model

폴랴 과정 모델에 대한 단일 및 축차 종속 샘플링 계획법

  • 김원경 (경남대학교 벤처창업학부)
  • Published : 2002.12.31
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Abstract

In this paper, stochastically dependent single and sequential acceptance sampling plans are dealt when the process follows a Polya process model. A Monte-Cairo algorithm is used to find the acceptance and rejection probabilities of a lot. The number of defectives for the test to be accepted and rejected in a probability ratio sequential test can be found by using these probabilities. The formula to measure performance of these sampling plans is developed. Type I and II error probabilities are estimated by simulation. Dependent multiple acceptance sampling plans can be derived by extending the sequential sampling procedure. In numerical examples, single and sequential sampling plans of a Polya dependent process are examined and the characteristics are compared according to the change of the dependency factor.

Keywords

References

  1. Baker, A. G. (1950), Properties of Some Tests in Sequential Analysis, Biometrika, 37, 334-346
  2. Bhat, U. Narayan and Lal, Ram (1988), Number of Successes in Markov Trials, Advances in Applied Probability, 20, 677-680
  3. Bhat, U. Narayan and Lal, Ram and Mahinda Karunaratne (March 1990), A Sequential Inspection Plan for Markov Dependent Production Processes, IIE Transactions, 22(1)
  4. Broadbent, S. R. (1958), The Inspection of a Markov Process, Journal of Royal Statistics Society, B20, 111-119
  5. Comeliussen, A. H. and Ladd, D. W. (1970), On Sequential Tests of the Binomial Distribution, Technometrics, 12, 635-646
  6. Johnson, N. L. (1961), Sequential Analysis: A Survey, Journal of Royal Statistics Society, A, 124, 372-411
  7. Kemp, K. W. (1958), Formulae for Calculating the Operating Characteristic and the Average Sample Number of Some Sequential Tests, Journal of Royal Statistics Society, B, 20, 379-386
  8. Nelson, B. (1987), On Control Variate Estimators, Computer and Operations Research, 14(3),219-225 https://doi.org/10.1016/0305-0548(87)90024-4
  9. Nelson, B. (1993), Estimating Acceptance-Sampling Plans for Dependent Production Processes, IIE Transactions, 25(6), 11-18 https://doi.org/10.1080/07408179308964323
  10. Page, E. S. (1954), An Improvement to Wald's Approximation for Some Properties of Sequential Tests, Journal of Royal Statistics Society, B, 16, 136-139
  11. Ripley, Brian D. (1987), Stochastic Simulation, John Wiley & Sons, N.Y
  12. Sarkadi, K. and Vincze (1974), I., Mathematical Methods of Statistical Quality Control, Academic Press, N.Y.
  13. Wald, A. (1947), Sequential Analysis, John Wiley, N.Y
  14. Wald, A. and Wolfowitz (1948), Optimum Character of the Sequential Probability Ratio Test, Annals of Mathematical Statistics, 19, 326-339
  15. Wilson, J. R.(1984), Variance Reduction Techniques for Digital Simulation, American Journal of Mathematical Management Science, 4, 277-312