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Reliability Demonstration Test for a Finite Population Based on the Conjugacy of the Beta-Binomial Distribution  

Jeon, Jong-Seon (Department of Industrial and Management Engineering, Hanyang University)
Ahn, Sun-Eung (Department of Industrial and Management Engineering, Hanyang University)
Publication Information
Journal of Korean Society of Industrial and Systems Engineering / v.35, no.2, 2012 , pp. 98-105 More about this Journal
Abstract
This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to produce the posterior distribution. In this paper, the hypergeometric distribution is adopted as a likelihood function for a finite population. The conjugacy of the beta-binomial distribution and the hypergeometric distribution is shown and is used to make a decision about whether to accept or reject the finite population judging from a viewpoint of faulty goods. A numerical example is also given.
Keywords
Bayesian Approach; Hypergeometric Distribution; Beta-Binomial Distribution; Finite Population; Reliability Demonstration Test;
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1 Ahn, S. E. and Kim, W. H., "Diagnosis of Lead Time Demand Based on the Characteristics of Negative Binomial Distribution," Journal of the Society of Korea Industrial and Systems Engineering, 28(2) : 146-151, 2005.
2 Borgonovo, E.; "A new uncertainty importance measure," Reliability engineering and system safety, 92(6) : 771-784, 2007.   DOI   ScienceOn
3 Borgonovo, E.; "Epistemic uncertainty in the ranking and categorization of probabilistic safety assessment model elements : Issues and findings," Risk analysis, 28(4) : 983-1001, 2008.   DOI   ScienceOn
4 Childs, A. and Chen, Y.; "Multilevel Fixed and Sequential Acceptance Sampling : The R Package MFSAS," Journal of Statistical Software, 43(6) : 2011.
5 Coolen, F. and Coolen-Schrijner, P.; Bayesian reliability demonstration, Wiley encyclopedia of statistics in quality and reliability, 2006.
6 Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B.; "Bayesian data analysis," Champman and Hall, New York, 2000.
7 Guérin, F., Dumon, B., and Usureau, E.; "Reliability estimation by Bayesian method : Definition of prior distribution using dependability study," Reliability Engineering and System Safety, 82(3) : 299-306, 2003.   DOI   ScienceOn
8 Kim, D.; "On the actual coverage probability of hypergeometric parameter," Journal of the Korea Data Information Science Society, 21(6) : 1109-1115, 2010.
9 Kim, H. M. and Ahn, S. E.; "Hazard Rate Estimation from Bayesian Approach," Journal of the Society of Korea Industrial and Systems Engineering, 28(3) : 26- 35, 2005.
10 Kleyner, A., Bhagath, S., Gasparini, M., Robinson, J., and Bender, M.; "Bayesian techniques to reduce the sample size in automotive electronics attribute testing," Microelectronics reliability, 37(6) : 879-883, 1997.   DOI
11 Krolo, A., Rzepka, B., and Bertsche, B.; "Application of Bayes statistics to reduce sample-size considering a lifetime-ratio," Proceedings of annual reliability and maintainability symposium, 577-583, 2002.
12 Lu, M. W. and Rudy, R. J.; "Reliability demonstration test for a finite population," Quality and Reliability Engineering International, 17(1) : 33-38, 2001.   DOI   ScienceOn
13 Martz, H. F. and Waller, R. A.; "Bayesian reliability analysis of complex series/parallel systems of binomial subsystems and components," Technometrics, 32(4) : 407-416, 1990.   DOI   ScienceOn
14 Martz, H. F., Waller, R. A., and Fickas, E. T.; "Bayesian reliability analysis of series systems of binomial subsystems and components," Technometrics, 30(2) : 143-154, 1988.   DOI   ScienceOn
15 Percy, D. F.; "Subjective priors for maintenance models," Journal of quality in maintenance engineering, 10(3) : 221-227, 2004.   DOI   ScienceOn
16 Ten, L. M. and Xie, M.; "Bayes reliability demonstration test plan for series-systems with binomial subsystem data," Proceedings of annual reliability and maintainability symposium, 241-246, 1998.
17 Vicens, G. J., Rodriguez-Iturbe, I., and Schaake, J. C.; "A Bayesian framework for the use of regional information in hydrology," Water Resources Research, 11(3) : 405-414, 1975.   DOI   ScienceOn