Title: Order Restricted Bayesian Analysis of a Simple Step Stress Model

Author(s): Debashis Samanta, Debasis Kundu and Ayon Ganguly
Issue: Volume 80 Series B Part 2 Year 2018
Pages: 195 -- 221
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.
AMS (2000) subject classification. Primary 62N02; Secondary 62F15, 62F30.
Keywords and phrases: Step-stress life-tests, Cumulative exposure model, Bayes estimate, Generalized Exponential distribution, Credible interval, Censoring scheme, Optimality