Inference for a step-stress model with competing risks from the GE distribution under Type-I censoring

In reliability analysis, accelerated life-testing allows gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-_xed time points, allowing the experimenter to obtain information on the lifetime parameters more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the step-stress model under Type-I censoring when the lifetime distributions of the different risk factors are independent generalized exponential. Under this setup, we derive the maximum likelihood estimates of the unknown scale and shape parameters of the different causes with the assumption of cumulative damage. Using the asymptotic distributions and the parametric boot-strap method, we discuss the construction of confidence intervals for the parameters. The precision of the estimates and the performance of the confidence intervals are also assessed through extensive Monte Carlo simulations, and finally, the methods of inference discussed here is illustrated with an example.