Accelerated life-tests (ALTs) are applied for inferring lifetime characteristics of highly reliable products. In particular, step-stress ALTs increase the stress level at which units under test are subject at certain pre-fixed times, thus accelerating product wear and inducing its failure. In some cases, due to cost or product nature constraints, continuous monitoring of devices is infeasible but the units are inspected for failures at particular inspection time points. In such setups, the ALT response is interval-censored. Furthermore, when a test unit fails, there are often more than one fatal cause for the failure, known as competing risks. In this paper, we assume that all competing risks are independent and follow an exponential distribution with scale parameter depending on the stress level. Under this setup, we present a family of robust estimators based on the density power divergence, including the classical maximum likelihood estimator as a particular case. We derive asymptotic and robustness properties of the MDPDE, showing its consistency for large samples. Based on these MDPDEs, estimates of the lifetime characteristics of the product as well as estimates of cause-specific lifetime characteristics have been developed. Direct, transformed and bootstrap confidence intervals for the mean lifetime to failure, reliability at a mission time, and distribution quantiles are proposed, and their performance is empirically compared through simulations. Besides, the performance of the MDPDE family has been examined through an extensive numerical study and the methods of inference discussed here are illustrated with a real-data example regarding electronic devices.

翻译：加速寿命试验（ALTs）用于推断高可靠性产品的寿命特征。特别地，步进应力ALTs会在预先设定的时间点提高受试单元承受的应力水平，从而加速产品磨损并诱发其失效。在某些情形下，受成本或产品性质限制，对设备进行连续监测不可行，仅在特定检查时间点对单元进行失效检测。在此类设置中，ALT响应为区间删失。此外，当测试单元失效时，通常存在多个致命失效原因，即竞争风险。本文假设所有竞争风险相互独立且服从指数分布，其尺度参数依赖于应力水平。基于该设定，我们提出一类基于密度幂散度的稳健估计量，经典极大似然估计量作为其特例。我们推导了最小密度幂散度估计（MDPDE）的渐近性与稳健性性质，证明其在大样本下的一致性。基于MDPDE，进一步开发了产品寿命特征及原因特异性寿命特征的估计量。针对平均失效时间、任务时间可靠性与分布分位数，提出了直接、变换及Bootstrap置信区间，并通过模拟实验对其性能进行经验比较。此外，通过广泛的数值研究考察了MDPDE族的表现，并利用电子设备的实际数据示例说明了本文讨论的推断方法。