Analysis of Weibull Step-Stress Model In Presence of Competing Risk

Abstract

In this paper, we mainly consider the inference of a simple step-stress model based on a complete sample, when the stress changes after a prefixed number of failures. It is assumed that there is more than one cause of failure, and the lifetime of the experimental units at each stress level follows Weibull distribution with the same shape parameter and different scale parameters. The distribution function under different stress levels are connected through the generalized Khamis–Higgins model. The maximum likelihood estimates of the model parameters and the associated asymptotic confidence intervals are obtained. Further, we consider the Bayesian inference of the unknown model parameters based on fairly general prior distributions. We have also provided the results for Type-I censored data also. We assess the performances of the estimators through extensive simulation study for complete sample, and the analyses of one complete (simulated) data set and one Type-I censored solar lighting device data set have been performed for illustrative purpose. We propose different classical and Bayesian optimal criteria, and based on them we obtain the optimum stress changing time. Finally, we have indicated how the assumption on the common shape parameter of two competing causes can be relaxed.