Bayesian analysis of series system with dependent causes of failure

References

• AL-Hussaini, E. K., Abdel-Hamid, A. H., & Hashem, A. F. (2015). Bayesian prediction intervals of order statistics based on progressively type-II censored competing risks data from the half-logistic distribution. Journal of the Egyptian Mathematical Society, 23, 190–196.
   Google Scholar
• Bemis, B., Bain, L. J., & Higgins, J. J. (1972). Estimation and hypothesis testing for the parameters of a bivariate exponential distribution. Journal of the American Statistical Association, 67, 927–929.
   Web of Science ®Google Scholar
• Berger, J. O., & Bernardo, J. M. (1992). On the development of reference priors (with discussion). In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian statistics (Vol. 4, pp. 35–60). Oxford: Clarendon Press.
   Google Scholar
• Berger, J. O., Bernardo, J. M., & Sun, D. (2015). Overall objective priors (with discussion). Bayesian Analysis, 10, 189–221.
   Web of Science ®Google Scholar
• Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion). Journal of the Royal Statistical Society B, 41, 113–147.
   Google Scholar
• Cramer, E., & Schmiedt, A. B. (2011). Progressively type-II censored competing risks data from Lomax distributions. Computational Statistics and Data Analysis, 55, 1285–1303.
   Web of Science ®Google Scholar
• Csorgo, S., & Welsh, A. H. (1989). Testing for exponential and Marshall-Olkin distribution. Journal of Statistical Planning and Inference, 23, 287–300.
   Web of Science ®Google Scholar
• Dijoux, Y. D., & Gaudoin, O. (2009). The alert-delay competing risks model for maintenance analysis. Journal of Statistical Planning and Inference, 139, 1587–1603.
   Web of Science ®Google Scholar
• Dimitrova, D. S., Haberman, S., & Kaishev, V. K. (2013). Dependent competing risks: Cause elimination and its impact on survival. Insurance: Mathematics and Economics, 53, 464–477.
   Web of Science ®Google Scholar
• Feizjavadian, S. H., & Hashemi, R. (2015). Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall-Olkin bivariate Weibull distribution. Computational Statistics and Data Analysis, 82, 19–34.
   Web of Science ®Google Scholar
• Ghosh, J. K., & Mukerjee, R. (1991). Characterization of priors under which Bayesian and frequentist bartlett corrections are equivalent in the multiparameter case. Journal of Multivariate Analysis, 38, 385–393.
   Web of Science ®Google Scholar
• Gilks, W. R., & Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41, 337–348.
   Web of Science ®Google Scholar
• Guan, Q., Tang, Y. C., & Xu, A. C. (2013). Objective Bayesian analysis for bivariate Marshall-Olkin exponential distribution. Computational Statistics and Data Analysis, 64, 299–313.
   Web of Science ®Google Scholar
• Jeffreys, H. (1961). Theory of probability. London: Oxford University Press.
   Google Scholar
• Kozumi, H. (2004). Posterior analysis of latent competing risk models by parallel tempering. Computational Statistics and Data Analysis, 46, 441–458.
   Web of Science ®Google Scholar
• Kundu, D., & Dey, A. K. (2009). Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm. Computational Statistics and Data Analysis, 53, 956–965.
   Web of Science ®Google Scholar
• Kundu, D., & Gupta, A. K. (2013). Bayes estimation for the Marshall-Olkin bivariate Weibull distribution. Computational Statistics and Data Analysis, 57, 271–281.
   Web of Science ®Google Scholar
• Kundu, D., Kannan, N., & Balakrishnan, N. (2003). Analysis of progressively censored competing risks data. In N. Balakrishnan & C. R. Rao (Eds.), Handbook of statistics on survival analysis (Vol. 23, pp. 331–348). New York: Elsevier Publications.
   Google Scholar
• Laplace, P. (1812). Analytical theory of probability. Paris: Courcier Press.
   Google Scholar
• Lindqvist, B. H., & Skogsrud, G. (2009). Modeling of dependent competing risks by first passage times of Wiener processes. IIE Transactions, 41(1), 72–80.
   Web of Science ®Google Scholar
• Marshall, A. W., & Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association, 62, 30–44.
   Web of Science ®Google Scholar
• Mazucheli, J., & Achcar, J. A. (2011). The Lindley distribution applied to competing risks lifetime data. Computer Methods and Programs in Biomedicine, 104, 188–192.
   PubMed Web of Science ®Google Scholar
• Pareek, B., Kundu, D., & Kumar, S. (2009). On progressively censored competing risks data for Weibull distributions. Computational Statistics and Data Analysis, 53, 4083–4094.
   Web of Science ®Google Scholar
• Wang, C. P., & Ghosh, M. (2003). Bayesian analysis of bivariate competing risks models with covariates. Journal of Statistical Planning and Inference, 115, 441–459.
   Web of Science ®Google Scholar
• Xu, A. C., Basu, S, & Tang, Y. C. (2014). A full Bayesian approach for masked data in step-stress accelerated life testing. IEEE Transactions on Reliability, 63, 798–806.
   Web of Science ®Google Scholar
• Xu, A. C, & Tang, Y. C (2010). Reference analysis for Birnbaum-Saunders distribution. Computational Statistics & Data Analysis, 54, 185–192.
   Web of Science ®Google Scholar
• Xu, A. C., & Tang, Y. C. (2011). Objective Bayesian analysis of accelerated competing failure models under type-I censoring. Computational Statistics & Data Analysis, 55, 2830–2839.
   Web of Science ®Google Scholar
• Xu, A. C, Tang, Y. C, & Sun, D. C. (2015). Objective Bayesian analysis for masked data under symmetric assumption. Statistics and its Interface, 8, 227–237.
   Web of Science ®Google Scholar
• Yang, R., & Berger, J. O. (1994). Estimation of a covariance matrix using the reference prior. The Annals of Statistics, 22, 1195–2111.
   Web of Science ®Google Scholar