Inference for a Step-Stress Model With Competing Risks for Failure From the Generalized Exponential Distribution Under Type-I Censoring

TLDR

Accelerated life testing, especially step‑stress designs, use higher stress levels at planned points to quickly estimate lifetime parameters, and failures often involve multiple risk factors such as mechanical or electrical causes. The study investigates a step‑stress model with Type‑I censoring for competing risks modeled by independent generalized exponential distributions. The authors derive maximum‑likelihood estimates of the scale and shape parameters for each cause and construct confidence intervals using asymptotic theory and parametric bootstrap. Monte Carlo simulations show that the estimators are precise and the confidence intervals perform well, and the inference method is illustrated with case examples.

Abstract

In a reliability experiment, accelerated life-testing allows higher-than-normal stress levels on test units. In a special class of accelerated life tests known as step-stress tests, the stress levels are increased at some pre-planned time points, allowing the experimenter to obtain information on the lifetime parameters more quickly than under normal operating conditions. Also, when a test unit fails, there are often several risk factors associated with the cause of failure (i.e., mechanical, electrical, etc.). In this article, the step-stress model under Type-I censoring is considered when the different risk factors have s-independent generalized exponential lifetime distributions. With the assumption of cumulative damage, the point estimates of the unknown scale and shape parameters of the different causes are derived using the maximum likelihood approach. Using the asymptotic distributions and the parametric bootstrap method, we also discuss the construction of confidence intervals for the parameters. The precision of the estimates and the performance of the confidence intervals are assessed through extensive Monte Carlo simulations, and lastly, the method of inference discussed here is illustrated with examples.