Robust inference for an interval-monitored step-stress experiment under proportional hazards

Abstract

Accelerated life tests (ALTs) play a crucial role in reliability analyses, providing lifetime estimates of highly reliable products. Among ALTs, step-stress design increases the stress level at predefined times, while maintaining a constant stress level between successive changes. This approach accelerates the occurrence of failures, reducing experimental duration and cost. While many studies assume a specific form for the lifetime distribution, in certain applications instead a general form satisfying certain properties should be preferred. Proportional hazard model assumes that applied stresses act multiplicatively on the hazard rate, so the hazards function may be divided into two factors, with one representing the effect of the stress, and the other representing the baseline hazard. In this work we examine two particular forms of baseline hazards, namely, linear and quadratic. Moreover, certain experiments may face practical constraints making continuous monitoring of devices infeasible. Instead, devices under test are inspected at predetermined intervals, leading to interval-censoring data. On the other hand, recent works have shown an appealing trade-off between the efficiency and robustness of divergence-based estimators. This paper introduces the step-stress ALT model under proportional hazards and presents a robust family of minimum density power divergence estimators (MDPDEs) for estimating device reliability and related lifetime characteristics such as mean lifetime and distributional quantiles. The asymptotic distributions of these estimates are derived, providing approximate confidence intervals. Empirical evaluations through Monte Carlo simulations demonstrate their performance in terms of robustness and efficiency. Finally, an illustrative example is provided to demonstrate the usefulness of the model and associated methods developed.