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Optimal Design of Reliability Acceptance Sampling Plan Based on Sequential Order Statistics

Author

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  • Kumar Mahesh

    (Department of Mathematics, National Institute of Technology, Calicut, Kerala, India)

  • Ramyamol P. C.

    (Department of Mathematics, National Institute of Technology, Calicut, Kerala, India)

Abstract

The concept of sequential order statistics were introduced by Kamps in 1995. In this article, we derive an acceptance sampling plan, for units having exponentially distributed lifetime, using sequential order statistics. Based on data obtained from progressive type II censoring using constant stress accelerated life tests, we obtain the maximum likelihood estimates of the parameters of the exponential distribution. Further, a log linear life-stress relationship is assumed to derive the exact distributions of the estimators of the parameters of exponential distribution. The parameters of the sampling scheme are obtained by minimizing expected total testing cost satisfying usual probability requirements. Some numerical results are presented in a table to illustrate our plans.

Suggested Citation

  • Kumar Mahesh & Ramyamol P. C., 2019. "Optimal Design of Reliability Acceptance Sampling Plan Based on Sequential Order Statistics," Stochastics and Quality Control, De Gruyter, vol. 34(2), pages 87-94, December.
    • Handle: RePEc:bpj:ecqcon:v:34:y:2019:i:2:p:87-94:n:5
    DOI: 10.1515/eqc-2019-0012
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    References listed on IDEAS

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    1. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    2. Erhard Cramer & Udo Kamps, 2001. "Estimation with Sequential Order Statistics from Exponential Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 307-324, June.
    3. Bing Wang & Keming Yu, 2009. "Optimum plan for step-stress model with progressive type-II censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 115-135, May.
    4. Erhard Cramer & Udo Kamps, 1996. "Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 535-549, September.
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