Accelerated life-tests (ALTs) are used 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 the product's wear and inducing its failure. In some cases, due to cost or product nature constraints, continuous monitoring of devices is infeasible, and so the units are inspected for failures at particular inspection time points. In a such setup, 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 exponential distributions with scale parameters depending on the stress level. Under this setup, we present a family of robust estimators based on density power divergence, including the classical maximum likelihood estimator (MLE) as a particular case. We derive asymptotic and robustness properties of the Minimum Density Power Divergence Estimator (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 are then developed. Direct asymptotic, 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 then compared through Monte Carlo simulations. Moreover, the performance of the MDPDE family has been examined through an extensive numerical study and the methods of inference discussed here are finally illustrated with a real-data example concerning electronic devices.

翻译：加速寿命试验用于推断高可靠性产品的寿命特性。其中，步进应力加速寿命试验在预设时间点提高受测单元的应力水平，从而加速产品磨损并引发失效。在某些情况下，由于成本或产品性质的限制，无法对设备进行连续监测，因此需要在特定检查时间点对单元进行失效检测。在此设置下，加速寿命试验的响应属于区间删失数据。此外，当测试单元失效时，往往存在多个致命原因，即所谓的竞争风险。本文假设所有竞争风险相互独立，且服从尺度参数依赖于应力水平的指数分布。在此框架下，我们提出了一类基于密度幂散度的稳健估计量族，其中经典极大似然估计是特例。我们推导了最小密度幂散度估计量的渐近性和稳健性性质，证明其在大样本下的一致性。基于这些最小密度幂散度估计量，进一步开发了产品寿命特性以及原因特异性寿命特性的估计方法。提出了平均失效时间、任务时间可靠性与分布分位数的直接渐近置信区间、变换置信区间和自助置信区间，并通过蒙特卡洛模拟比较其性能。此外，通过广泛的数值研究检验了最小密度幂散度估计量族的性能，并最终通过电子设备的实际数据案例展示了本文讨论的推断方法。