A semiparametric approach for simple step-stress model

In many life-testing experiments, interest often lies in examining the effect of extreme or varying stress factors such as frequency, voltage, temperature, load, etc. on the lifetimes of the experimental units. An experimenter often then performs the step-stress accelerated life-testing (SSALT) experiment, a special case of the more general accelerated life-testing (ALT) experiment, to get an insight about various reliability characteristics of the lifetime distribution much quickly compared to that obtained under normal operating conditions. An extensive amount of work has been performed analyzing data obtained from a simple SSALT experiment based on different parametric models. We propose here a flexible data-driven semiparametric approach based on a piecewise constant approximation (PCA) of the baseline hazard function (HF) in order to analyze failure time data obtained from a simple SSALT experiment when the data are Type-I censored. It is assumed that the associated lifetime distribution satisfies the failure rate- based model assumptions. We provide both the classical and Bayesian solutions to this problem. In particular, methodologies to obtain the point and interval estimates of the associated model parameters are discussed. Extensive simulation studies are carried out to see the effectiveness of the proposed method. A real-life data example is considered for illustrative purposes.