Abstract Many moderns products have a long life before failure. Reliability analyses for such highly reliable devices therefore present a practical challenge as obtaining sufficient failure information to adequately assess lifetime behavior will require extended experimental duration. As an alternative, accelerated life testing (ALT) is commonly used to shorten the time to failure of units under test, with the results subsequently extrapolated to normal operating conditions. This paper provides a comprehensive review of robust inferential methods based on density power divergence for analyzing step-stress ALT data. Point estimates and approximate confidence intervals for model parameters, along with robust estimates of some important lifetime characteristics are developed for general lifetime distributions. Subsequently, explicit expressions are derived for four most prominent parametric lifetime distributions: exponential, Weibull, gamma, and lognormal. A semi-parametric approach based on the proportional hazards model and a competing risks scenario are also discussed as extensions of the proposed model. Throughout the manuscript, several open problems are highlighted, along with significant gaps in the literature, to motivate readers and also to promote further research in this important research area. Moreover, to illustrate the importance of step-stress ALTs and the practical utility of robust estimators, we also present some real data sets used in the literature and analyze one of them using robust methods. By analyzing real data, we demonstrate the stability of the Minimum Density Power Divergence Estimator (MDPDE) for different values of the tuning parameter in the presence of outliers. We also analyze the implications of distributional assumptions on parameter estimation. Confidence intervals, including transformed intervals, are examined, with transformed intervals resulting in confidence levels close to nominal level and also provide better interpretability. Our results highlight the importance of robust estimation techniques in the presence of data contamination and also in a careful selection of parametric models for modeling the lifetime data, as these choices significantly influence predictions of lifetime characteristics under normal operating conditions.
Balakrishnan et al. (Mon,) studied this question.