A classical and Bayesian estimation of a [formula omitted]-components load-sharing parallel system

Abstract

The present study proposes the classical and Bayesian treatment to the estimation problem of parameters of a k -components load-sharing parallel system in which some of the components follow a constant failure-rate and the remaining follow a linearly increasing failure-rate. In the classical setup, the maximum likelihood estimates of the load-share parameters with their variances are obtained. ( 1 − γ ) 100 % individual, simultaneous, Bonferroni simultaneous and two bootstrap confidence intervals for the parameters have been constructed. Further, on recognizing the fact that life testing experiments are very time consuming, the parameters involved in the failure time distributions of the system are expected to follow some random variations. Therefore, Bayes estimates along with their posterior variances of the parameters are obtained by assuming gamma and Jeffrey’s invariant priors. Markov Chain Monte Carlo techniques such as a Gibbs sampler have also been used to obtain the Bayes estimates and highest posterior density credible intervals when all the parameters follow gamma priors.