Robust Tests for Step-Stress Models under Exponential Lifetimes

RESUMO

Highly reliable products with extended lifetimes present a challenge in reliability analysis: obtaining enough failure data under normal operating conditions is often incompatible with reasonable time and cost constraints. Step-Stress Accelerated Life Tests (SSALTs) offer a practical solution by progressively increasing stress levels to accelerate product degradation, allowing results to be extrapolated to normal conditions. However, the small sample sizes and Type-I censoring inherent to these experiments render classical maximum likelihood-based inference vulnerable to data contamination. Robust point estimation has been studied in the literature. However, robust test statistics have not yet been developed in this context. In this paper, we propose robust test statistics for SSALTs under exponential lifetime distributions, based on the minimum density power divergence estimator (MDPDE). This paper directly works with the exact failure times recorded before the end of the experiment. Once this limit time is reached, all surviving components are censored. This creates a mixed discrete-continuous distribution, which is a major analytical breakthrough in the context of SSALT. We introduce the restricted version of the MDPDE, establish its asymptotic properties, and construct Z-type and Rao-type test statistics for linear hypotheses on the model parameters. The proposed tests are shown to maintain their nominal significance levels and statistical power under data contamination, where classical MLE-based procedures fail. An extensive simulation study confirms the robustness gains of the proposed methods, and a real data application illustrates their practical value.