Bivariate unit inverse Weibull distribution with applications to multicomponent reliability

This paper is studied in two folds. Initially, we introduce a bivariate unit inverse Weibull distribution and discuss some of its probabilistic and structural properties. In sequel, reliability characteristics of this model are studied in a multicomponent stress-strength (MSS) model. An MSS system comprises k statistically independent and identically distributed strength components. We further assume that components are constructed using a pair of statistically dependent elements which follow bivariate unit inverse Weibull distributions. Also, each component undergoes a common stress following a unit inverse Weibull distribution. Reliability estimation of such systems is highly useful in safety management and in preventing catastrophic disasters. Accordingly, we obtain estimates of MSS reliability using both classical and Bayesian approaches. As the corresponding posterior distribution does not appear in known form, and so we employ Lindley’s approximation and Markov Chain Monte Carlo methods to approximate it. The performance of studied estimators are assessed through simulation studies and conclusions are drawn. We analyse a numerical example to illustrate application viewpoints. Finally, we present concluding remarks to summarize our findings.