Order Restricted Bayesian Analysis of a Simple Step Stress Model

TL;DR

This paper develops a Bayesian inference framework for a simple step stress model assuming generalized exponential distributions, incorporating order restrictions and extending to censored data, with simulation and real data applications.

Contribution

It introduces order restricted Bayesian analysis for step stress models with generalized exponential distributions, including methods for censored data and optimal stress change time estimation.

Findings

Bayes estimates and credible intervals are effectively computed using importance sampling.

The proposed methods perform well in simulations for both complete and censored data.

Application to real data demonstrates practical utility of the approach.

Abstract

In this article we consider a simple step stress set up under the cumulative exposure model assumption. At each stress level the lifetime distribution of the experimental units are assumed to follow the generalized exponential distribution. We provide the order restricted Bayesian inference of the model parameters by considering the fact that the expected lifetime of the experimental units are larger in lower stress level. Analysis and the related results are extended to different censoring schemes also. The Bayes estimates and the associated credible intervals of the unknown parameters are constructed using importance sampling technique. We perform extensive simulation experiments both for the complete and censored samples to see the performances of the proposed estimators. We analyze two simulated and one real data sets for illustrative purposes. An optimal value of the stress changing time is obtained by minimizing the total posterior coefficient of variations of the unknown parameters.