Bayesian Estimate of Strength Analysis for Downton's Bivariate Exponential Distribution Under Type II Censoring

• Activity Number: 612
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Yuhlong Lio*+ and Yu-Jau Lin and Hon Keung Tony Ng
• Companies: University of South Dakota and Chung Yuan Christian University and Southern Methodist University
• Keywords: Censored Data ; Importance Sampling ; MCMC ; Reliability

Abstract

Downton's bivariate exponential (DBVE) distribution is commonly used for modeling bivariate reliability and lifetime data with positive correlation. Bayesian estimator of $\delta=P(X< Y)$ is studied based on Type II censored or unrestricted samples when the random variate (X, Y) follows DBVE. Several computation algorithms are developed to estimate $\delta$ based on Monte Carlo method and importance sampling. Viewing $\delta$ as a latent variable, the Markov chain sequence of the estimates of $\delta$ can be obtained by the Gibbs samplers. Then, the empirical distribution can be used to obtain credible interval of $\delta$. An extensive simulation study is conducted to investigate the performance of the developed methods. Finally, the proposed approaches are applied to bivariate data sets for illustration.