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.

翻译：加速寿命试验在可靠性分析中发挥着关键作用，可为高可靠性产品提供寿命估计。在加速寿命试验中，步进应力设计在预定时间点提高应力水平，同时在连续变化之间保持恒定应力水平。该方法加速了失效发生，缩短了实验时长并降低了成本。尽管许多研究假设寿命分布具有特定形式，但在某些应用中，应优先采用满足特定属性的一般形式。比例风险模型假设施加的应力对风险率呈乘性作用，因此风险函数可分解为两个因子，一个代表应力效应，另一个代表基线风险。本研究考察了两种特定形式的基线风险，即线性和二次型。此外，某些实验可能面临实际限制，致使对设备进行连续监测不可行。相反，被测设备会按预定时间间隔接受检查，从而产生区间删失数据。另一方面，近期研究表明，基于散度的估计量在效率与鲁棒性之间具有吸引人的权衡关系。本文提出了比例风险下的步进应力加速寿命试验模型，并构建了最小密度功率散度估计量的鲁棒族，用于估计设备可靠性及相关寿命特征（如平均寿命和分布分位数）。推导了这些估计量的渐近分布，并提供了近似置信区间。通过蒙特卡洛模拟进行的实证评估展示了其在鲁棒性和效率方面的表现。最后，通过一个示例说明了本文所提出模型及关联方法的实用性。