Step-stress tests for interval-censored data under gamma lifetime distribution

Abstract

Inferential methods under extreme form of censoring are of interest in reliability theory because of their applicability to practical engineering problems. interval-censored data naturally appear in many situations wherein the exact failure times cannot be observed, but we can only know if the product has failed before a certain inspection time or not. In addition, some products are highly reliable with large mean lifetimes under normal operating conditions, and so accelerated lifetime tests (ALTs) need to be carried out for inferential purposes. Step-stress ALTs increase such stress factors at certain pre-fixed times, thus inducing early failure. Likelihood-based estimation methods are known to have a very good performance in the absence of contamination in the data, but they perform poorly when few observations do not follow the same distribution as the rest of the observations. In this work, we develop robust estimators and Wald-type test statistics based on density power divergence (DPD) method under step-stress ALT model and gamma lifetime distribution based on interval-censored test data. The performance of the proposed estimators and test statistics are then empirically examined through an extensive simulation study. Finally, the usefulness of the developed inferential methods is illustrated with a real kinetics data.