On Classical and Bayesian Reliability of Systems Using Bivariate Generalized Geometric Distribution

Abstract

Abstract The study of system safety and reliability has always been vital for the quality and manufacturing engineers of varying fields for which generally the continuous probability distributions are proposed. Bivariate and multivariate continuous distributions are the candidates while studying more than one characteristic of the system. In this article, an attempt is made to address this issue when the reliability systems generate bivariate and correlated count datasets. The bivariate generalized geometric distribution (BGGD) is believed to serve as a potential candidate to model such types of datasets. Bayesian approach of data analysis has the potential of accommodating the uncertainty associated with the model parameters of interest using uninformative and informative priors. A real life bivariate correlated dataset is analyzed in Bayesian framework and the results are compared with those produced by the classical approach. Posterior summaries including posterior means, highest density regions, and predicted expected frequencies of the bivariate data are evaluated. Different information criteria are evaluated to compare the inferential methods under study. The entire analysis is carried out using Markov chain Monte Carlo (MCMC) set-up of data augmentation implemented through WinBUGS.

Keywords

• Bayesian analysis
• Bivariate generalized geometric distribution
• Correlated count data
• Maximum likelihood estimation
• MCMC methods
• Model selection criteria