On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution

Abstract

This article deals with classical and Bayesian estimation of the parameters of a 1-out-of-k load-sharing parallel system model in which each component's lifetime follows modified Burr-III distribution. In the classical set up, the maximum likelihood estimates of the load-share parameters, system reliability and hazard rate functions with their bias, standard errors (SEs), average absolute bias (AABias) and width of the confidence interval along with coverage probability are obtained. Besides, two bootstrap confidence intervals for the parameters of the model are also obtained. Further, by assuming both gamma and noninformative priors for the unknown parameters, Bayes estimates of the parameters, system reliability and hazard rate functions with their bias, SEs, AABias and width of the Bayes credible interval along with coverage probability (C p ) are obtained. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. Finally, we analyze one real data set to illustrate the results derived.

Half circular modified burr−III distribution, application with different estimation methods

“…[ 49 ] developed MBIII-G Family of distributions based on odds ratio of any baseline distribution. The application of Modified Burr III distribution in reliability analysis was done by [ 50 ]. [ 51 ] originated the McDonald modified Burr–III.…”

Reliability analysis of the dynamic system for the Chen model through sequential order statistics

“…Many authors have studied the equal load‐sharing systems with the assumption that the systems' components are nonrepairable. See, for example, Amari and Misra, 5 Liu, 6 Kim and Kvam, 7 Singh et al, 8 Park, 9 Singh and Gupta, 10 Ali et al, 11 Singh and Goel, 12 Choudhary et al, 13, 14 and references cited therein.…”