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A new statistical inference method for multi-stress accelerated life testing based on random variable transformation

机译：一种新的基于随机变换的多应力加速寿命测试的新统计推理方法

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摘要

The limited sample size in multi-stress accelerated life testing makes the conventional large-sample-based inference methods inefficient. To overcome this problem, this paper develops a new statistical inference method based on random variable transformation for multi-stress accelerated life testing with Weibull distribution and progressive Type-Ⅱ censoring. Firstly, a x~2 statistic is constructed using the random variable transformation method, and the exact point estimates of model parameters are derived based on the x~2 statistic. Subsequently, based on the x~2 statistic, the exact confidence interval of shape parameter is provided, while the generalized confidence intervals of the accelerated model parameters are calculated by constructing the new multivariate generalized pivotal quantities. Furthermore, the generalized confidence intervals of some commonly used reliability indexes are provided for better reliability management and decision making. Finally, a simulation study and a real case study are conducted to illustrate the implementation and effectiveness of the proposed method.
机译：多应力加速寿命测试中的有限样本量使得传统的基于大样本的推断方法效率低下。为了克服这个问题，这篇论文开发了一种基于随机变换的新统计推理方法，用于多应力加速寿命测试与威布尔分布和逐步Ⅱ型审查。首先，使用随机变换方法构建X〜2统计，基于X〜2统计来导出模型参数的精确点估计。随后，基于X〜2统计，提供了形状参数的确切置信区间，而通过构建新的多变量通用枢转量来计算加速模型参数的广义置信区间。此外，提供了一些常用可靠性指标的广义置信区间，用于更好的可靠性管理和决策。最后，进行了模拟研究和实际情况研究以说明所提出的方法的实施和有效性。

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