Reliability Acceptance Sampling Plans with Sequentially Supplied Samples

시료가 축차적으로 공급되는 상황에서의 신뢰성 샘플링검사 계획

  • Koo, Jung-Seo (Department of Industrial Engineering, Korea Advanced Institute of Science and Technology) ;
  • Kim, Min (Department of Industrial Engineering, Korea Advanced Institute of Science and Technology) ;
  • Yum, Bong-Jin (Department of Industrial Engineering, Korea Advanced Institute of Science and Technology)
  • 구정서 (한국과학기술원 산업공학과) ;
  • 김민 (한국과학기술원 산업공학과) ;
  • 염봉진 (한국과학기술원 산업공학과)
  • Published : 2007.03.31

Abstract

A reliability acceptance sampling plan (RASP) consists of a set of life test procedures and rules for eitheraccepting or rejecting a collection of items based on the sampled lifetime data. Most of the existing RASPs areconcerned with the case where test items are available at the same time. However, as in the early stage ofproduct development, it may be difficult to secure test items at the same time. In such a case, it is inevitable toconduct a life test using sequentially supplied samples.In this paper, it is assumed that test items are sequentially supplied, the lifetimes of test items follow anexponential disthbution, failures are monitored continuously, arrival times of test items are known, and thenumber of test items at each arrival time is given. Under these assumptions, RASPs are developed by deter-mining the test completion time and the critical value for the maximum likelihood estimator of the mean lifetimesuch that the producer and consumer risks are satisfied. Then, the developed plans are compared to thetraditional Type-I censored RASPs in terms of the test completion time. Computational results indicate that thetest completion time of the developed RASP is shorter than that of the traditional Type-I censored plan in mostcases considered. It is also found that the superiority of the developed RASP becomes more prominent as theinter-arrival times of test items increase and/or the total number of test items gets larger.

Keywords

References

  1. Bartholomew, D. J. (1963), The Sampling Distribution of an Estimate Arising in Life-Testing, Technometrics, 5, 361-374 https://doi.org/10.2307/1266339
  2. Bernardo, M. V. P. and Ibrahim, J. G. (2000), Group Sequential Designs for Cure Rate Models with Early Stopping in Favor of Null Hypothesis, Statistics in Medicine, 19, 3023-3035 https://doi.org/10.1002/1097-0258(20001130)19:22<3023::AID-SIM638>3.0.CO;2-X
  3. Epstein, B. (1954), Truncated Life Tests in the Exponential Case, The Annals of Mathematical Statistics, 25, 555-564 https://doi.org/10.1214/aoms/1177728723
  4. Epstein, B. and Sobel, M. (1953), Life Testing, Journal of the American Statistical Association, 48, 486-502 https://doi.org/10.2307/2281004
  5. Epstein, B. and Sobel, M. (1955), Sequential Life Tests in the Exponential Case, The Annals of Mathematical Statistics, 26, 82-93 https://doi.org/10.1214/aoms/1177728595
  6. Hauck, D. J. and Keats, J. B. (1997), Robustness of the Exponential Sequential Probability Ratio Test (SPRT) when Weibull Distributed Failures are Transformed Using a 'Known' Shape Parameter, Microelectronics and Reliability, 37,1835-1840 https://doi.org/10.1016/S0026-2714(96)00287-9
  7. Jeong, H. S. (1994), Development and Comparisons of Reliability Acceptance Sampling Plans for Exponential and Gamma Lifetime Distributions, Ph. D. Dissertation, KAIST, Daejeon, Korea
  8. Kao, P., Kao, E. P. C. and Mogg, J. M. (1979), A Simple Procedure for Computing Performance Characteristics of Truncated Sequential Tests with Exponential Lifetimes, Technometrics, 21, 229-232 https://doi.org/10.2307/1268520
  9. Kim, S. H. and Yum, B. J. (2000), Comparisons of Exponential Life Test Plans with Intermittent Inspections, Journal of Quality Technology, 32, 217
  10. Lawless, J. F. (2003), Statistical Models and Methods for Lifetime Data, 2nd Ed., John Wiley & Sons, New York, USA
  11. Pocock, S. J. (1977), Group Sequential Methods in the Design and Analysis of Clinical Trials, Biometrika, 64, 191-199 https://doi.org/10.1093/biomet/64.2.191
  12. Sharma, K. K. and Rana, R. S. (1993), Robustness of Sequential Weibull Life-Test Plans, Microelectronics and Reliability, 33, 467-470 https://doi.org/10.1016/0026-2714(93)90311-L
  13. Sprott, D. A. (1973), Normal Likelihoods and Relation to a Large Sample Theory of Estimation, Biometrika, 60, 457-465 https://doi.org/10.1093/biomet/60.3.457
  14. Spurrier, J. D. and Wei, J. J. (1980), A Test of Parameter of the Exponential Distribution in the Type I Censoring Case, Journalof the American Statistical Association, 75, 405-409 https://doi.org/10.2307/2287467
  15. Wald, A. (1947), Sequential Analysis, Dover Publications, New York, USA