Many modern products exhibit high reliability under normal operating conditions. Conducting life tests under these conditions may result in very few observed failures, insufficient for accurate inferences. Instead, accelerated life tests (ALTs) must be performed. One of the most popular ALT designs is the step-stress test, which shortens the product's lifetime by progressively increasing the stress level at which units are subjected to at some pre-specified times. Classical estimation methods based on the maximum likelihood estimator (MLE) enjoy suitable asymptotic properties but they lack robustness. That is, data contaminationcan significantly impact the statistical analysis. In this paper, we develop robust inferential methods for highly reliable devices based on the density power divergence (DPD) for estimating and testing under the step-stress model with intermittent monitoring and Weibull lifetime distributions. We theoretically and empirically examine asymptotic and robustness properties of the minimum DPD estimators and associated Wald-type test statistics. Moreover, we develop robust estimators and confidence intervals for some important lifetime characteristics. The effect of temperature in solar lights, medium power silicon bipolar transistors and LED lights using real data arising from an step-stress ALT is analyzed applying the robust methods proposed.

翻译：许多现代产品在正常操作条件下表现出高可靠性。在这些条件下进行寿命测试可能导致观测到的失效极少，不足以进行准确推断。因此，必须执行加速寿命测试（ALT）。最流行的ALT设计之一是步进应力测试，它通过在预先指定的时间点逐步提高施加于产品的应力水平来缩短产品寿命。基于最大似然估计量（MLE）的经典估计方法具有良好的渐近性质，但缺乏稳健性。也就是说，数据污染会显著影响统计分析。本文针对高可靠性设备，基于密度功率散度（DPD），为具有间歇监测和威布尔寿命分布的步进应力模型下的估计与检验开发了稳健的推断方法。我们从理论和实证上研究了最小DPD估计量及相关Wald型检验统计量的渐近性质与稳健性。此外，我们还为一些重要的寿命特征开发了稳健估计量与置信区间。应用所提出的稳健方法，分析了步进应力ALT中真实数据所反映的温度对太阳能灯、中功率硅双极晶体管和LED灯的影响。