A Bayesian Approach to Order-Restricted Inference and Design Optimization for Simple Step-Stress Accelerated Life Testing under Progressive Type-I Censoring

In this work, we investigate a conjugate-like prior to perform order-restricted Bayesian inference and design optimization for progressively Type-I censored simple step-stress accelerated life tests with exponential lifetimes under continuous inspections. This prior is a joint distribution of Gamma (Erlang) distributions, which incorporates the use of a shift parameter. The conjugate-like structure provides computational simplicity. Utilizing the shift parameter in this distribution allows us to ensure that the rate parameters increase as the stress level increases. For inference, we compute the means, variances, covariance and credible intervals from the marginal and joint posterior distributions. We also explore two competing modes of failure. For design optimization, we consider various design criteria based on Shannon information gain and the posterior variance-covariance matrix. We further explore incorporating a cost constraint where we derive the formula for expected termination time and expected total cost and propose estimation procedures for each. For each chapter, we include results from illustrative examples and/or simulation studies.