Sequential Order Statistics Used for Reliability Analysis of Dynamic System

Abstract

Reliability studies in several engineering domains have recently made extensive use of the general family of inverted exponentiated distributions. Using this family as a baseline model, in this work, we have obtained a number of statistical inferences on the power-trend mechanism-based composite dynamic system. In particular, the maximum likelihood estimates of the unknown parameters and baseline reliability function are computed. The asymptotic and bootstrapped confidence intervals of the baseline reliability function are proposed. A parametric hypothesis test is provided to ascertain, whenever the failed components change the hazard rate function. The Bayes estimates of the unknown model parameters and baseline reliability function with respect to the squared error and generalized entropy loss functions are obtained. Further, the Metropolis-Hastings algorithm is used to generate Markov chain Monte Carlo samples for the computation of the Bayes estimates. The highest posterior density credible interval of the baseline reliability function is also calculated. For illustration reasons, two real data sets are considered, and then analyzed. Finally, a simulation study is carried out to examine the behaviour of the proposed estimates.