Modeling of System Availability and Bayesian Analysis of Bivariate Distribution

Abstract

To meet the desired standard, it is important to monitor and analyze different engineering processes to obtain the desired output. The bivariate distributions have received a significant amount of attention in recent years due to their ability to describe randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed by compounding two independent asymmetric univariate distributions and by using the nesting approach to study the effect of each component on reliability for better understanding. Furthermore, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution like mean median and quantile function are discussed. We used inverse Gamma prior to study its frequentist properties by conducting a Monte Carlo Markov Chain (MCMC) sampling scheme.