发表机构
UNED, Madrid, Spain; Complutense University of Madrid, Spain（西班牙国立远程教育大学; 马德里康普顿斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对指数寿命下步进应力加速寿命试验，提出基于最小密度幂散度估计的稳健检验统计量，在数据污染下保持显著性水平和功效。
AI 中文摘要
具有长寿命的高可靠性产品在可靠性分析中提出了一个挑战：在正常操作条件下获取足够的失效数据往往与合理的时间和成本限制不相容。步进应力加速寿命试验（SSALTs）通过逐步增加应力水平以加速产品退化，提供了一种实用的解决方案，使得结果可以外推到正常条件。然而，这些实验固有的小样本量和I型删失使得经典的基于最大似然的推断容易受到数据污染的影响。文献中已经研究了稳健点估计。然而，在此背景下，稳健检验统计量尚未被开发。在本文中，我们基于最小密度幂散度估计器（MDPDE），提出了指数寿命分布下SSALTs的稳健检验统计量。本文直接处理实验结束前记录的精确失效时间。一旦达到这个极限时间，所有幸存的组件都被删失。这产生了一个混合离散-连续分布，这是SSALT背景下的一个重大分析突破。我们引入了MDPDE的受限版本，建立了其渐近性质，并为模型参数的线性假设构造了Z型和Rao型检验统计量。所提出的检验被证明在数据污染下保持其名义显著性水平和统计功效，而经典的基于MLE的程序则失效。一项广泛的模拟研究证实了所提出方法的稳健性增益，一个真实数据应用说明了它们的实用价值。
英文摘要
Highly reliable products with extended lifetimes present a challenge in reliability analysis: obtaining enough failure data under normal operating conditions is often incompatible with reasonable time and cost constraints. Step-Stress Accelerated Life Tests (SSALTs) offer a practical solution by progressively increasing stress levels to accelerate product degradation, allowing results to be extrapolated to normal conditions. However, the small sample sizes and Type-I censoring inherent to these experiments render classical maximum likelihood-based inference vulnerable to data contamination. Robust point estimation has been studied in the literature. However, robust test statistics have not yet been developed in this context. In this paper, we propose robust test statistics for SSALTs under exponential lifetime distributions, based on the minimum density power divergence estimator (MDPDE). This paper directly works with the exact failure times recorded before the end of the experiment. Once this limit time is reached, all surviving components are censored. This creates a mixed discrete-continuous distribution, which is a major analytical breakthrough in the context of SSALT. We introduce the restricted version of the MDPDE, establish its asymptotic properties, and construct Z-type and Rao-type test statistics for linear hypotheses on the model parameters. The proposed tests are shown to maintain their nominal significance levels and statistical power under data contamination, where classical MLE-based procedures fail. An extensive simulation study confirms the robustness gains of the proposed methods, and a real data application illustrates their practical value.
Comments21 pages, 9 figures
