A Bayesian Analysis of Reliability in Accelerated Life Tests Using Gibbs Sampler
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In this paper MCMC (Markov Chain Monte Carlo) techniques are proposed to perform Bayesian inference to evaluate the reliability of units with Weibull lifetime, submitted to accelerated and censored life tests. A full Bayesian analysis is done via Gibbs sampling. The marginal posterior of the main parameters and other unobserved quantities of interest derived from them are obtained. Two numerical applications using real and artificially generated data are discussed.
KeywordsBayesian analysis Gibbs sampler Reliability Accelerated life tests Weibull distribution
We are grateful to the referees and the editor for helpful comments. The second author would also like to thank the Brazilian research agencies CNPq, Faperj and Ministry of Science and Technology for the continuing support of his research work.
- Best, N., Cowles, M. K. and Vines, K. (1997). CODA — Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output- version 0.4. Technical Report, Biostatistics Unit-MRC, Cambridge, UK.Google Scholar
- Gilks, W. R., Richardson, S. and Spiegehalter, D. J. (1996). Markov Chain Monte Carlo in Practice. Chapman and Hall, London.Google Scholar
- Louzada-Neto, F and Achcar, J.A. (1991). Uso de Dados Acelerados no Controle da Qualidade de Produtos Industriais Assumindo Uma Distribuição Exponential e um Modelo Estresse-resposta Gerat Technical Report, FCMSC, USP, São Carlos, São Paulo, Brazil.Google Scholar
- Mann, N. R., Schaffer, R. E. and Singpurwalla, N. D. (1974). Methods for Statistical Analysis of Reliability and Life Data. John Wiley, New York.Google Scholar
- Mattos, N. M. C. and Migon, H.S. (1998). Análise da Confiabilidade de Itens Submetidos a Testes Acelerados via Simulação Estocástica: o Efeito da Ortogonalização de Parâmetros. Technical Report, EP-01/98-P.O. COPPE-UFRJ, Rio de Janeiro, Brazil.Google Scholar
- Nelson, W. (1990). Accelerated Testing, Statistical Models Tests Plans and data Analysis. John Wiley, New York.Google Scholar
- Raftery, A. E. and Lewis, S. (1992) How Many Iterations in Gibbs Sampler? in: Bayesian Statistics, J.O. Berger, J.M. Berardo, A.P. David and A.F.M. (eds), 4, 763–773, Oxford University Press, Oxford.Google Scholar
- Ripley, B. D. (1992). Introductory Guide to S-Plus. University of Oxford.Google Scholar
- Spiegehalter, D., Thomas, A., Best, N. and Gilks, W. (1997). BUGS-Bayesian Inference Using Gibbs Sampling — version 0.6. Technical Report, Biostatistics Unit-MRC, Cambridge, UK.Google Scholar