Median ranked acceptance sampling plans for exponential distribution
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We develop a ranked acceptance sampling plan by attribute for exponential distribution assuming that the life test is truncated at a pre-assigned time. Two main requirements are essential for the proposed ranked sampling plans; namely; the life times of the test units are assumed to follow the exponential distribution; and the data are selected by using a free cost sampling method, the median ranked set sampling scheme from a large lot. The main advantage of using the median rank set sampling is to reduce producer’s risk, and it is one of the ranked scheme that produces a judgment order statistics that are mutually independent and identically distributed random variables to meet the binomial theory assumptions. The distribution function characterization under the median ranked set sampling scheme is derived assuming that the set size is known; then the minimum sample size necessary to ensure the specified average life are obtained and the operating characteristic values of the sampling plans based on the ranked samples and producer’s risk are presented. A comparisons with sampling plan based on simple random sampling and an illustrative example are given.
KeywordsMedian ranked set sampling Acceptance sampling plans Exponential distribution Operating characteristic function value Producer’s risk Consumer’s risk
Mathematics Subject Classification60D05 62G30
The authors would like to thank the chief editor and all referees for their helpful comments and valuable suggestions which improved the presentation of this paper.
- 6.Al-Omari, A.I.: Acceptance sampling plan based on truncated life tests for three parameter kappa distribution. Stoch. Qual. Control 29(1), 53–62 (2014)Google Scholar
- 11.Baklizi, A., El-Masri, A., Al-Nasser, A.D.: Acceptance sampling plans in the Raleigh Model. Korean Commun. Stat. 12(1), 11–18 (2005)Google Scholar
- 14.Ciavolino, E., Al-Nasser, A.D.: Information theoretic estimation improvement to the nonlinear Gompertz’s Model based on ranked set sampling. J. Appl. Quant. Methods 5(2), 317–330 (2010)Google Scholar
- 20.Habib, E.: Linear moments study under ranked set sampling. Electron. J. Appl. Stat. Anal. 3(2), 134–149 (2010)Google Scholar
- 29.Sobel, M., Tischendrof, J.A.: Acceptance sampling with new life test objectives. In: Proceedings of the fifth national symposium on reliability and quality control, pp. 108–118. Philadelphia, Pennsylvania (1959)Google Scholar