ABSTRACT

This paper proposes a simple statistical approach for analyzing reliability data arising from double-stage Accelerated Life Tests (ALT). The main motivation is to develop a workable solution, which can be easily understood and implemented by quality and reliability engineers, for incorporating existing engineering knowledge on life-stress relationship into ALT data analysis. We focus on the most general scenario where the lifetime follows the log-location-scale distribution and the life-stress relationship is log-linear. The proposed approach, which is based on the shrinkage estimation technique, utilizes the prior knowledge on the slope parameter in the form of an initial estimate or guessed value. The risk of incorporating such knowledge is investigated in terms of the bias, variance, and mean squared error of the estimator of a certain life quantile at use condition. The applications of the proposed method are illustrated by numerical examples. Comprehensive comparison study between the proposed method and Maximum Likelihood estimation is performed based on three real-life ALT examples. The proposed approach can be easily implemented in any statistical packages. In particular, the computer program, both in the MATLAB Graphical User Interface Design Environment (GUIDE) and R, is available on GitHub.

摘要

本文提出了一种简单的统计方法，用于分析双阶段加速寿命试验（ALT）产生的可靠性数据。主要动机是开发一种可行的解决方案，质量和可靠性工程师可以轻松理解和实施该解决方案，以将有关生命压力关系的现有工程知识整合到ALT数据分析中。我们将重点放在最一般的情况下，即寿命遵循对数位置尺度分布，并且生活压力关系呈对数线性关系。所提出的方法基于收缩率估计技术，以初始估计值或猜测值的形式利用了对斜率参数的先验知识。根据偏见，方差，使用条件下某个寿命分位数的估计量的均方误差。数值实例说明了该方法的应用。基于三个实际的ALT示例，对建议的方法与最大似然估计进行了全面的比较研究。所提出的方法可以在任何统计软件包中轻松实现。特别是，可以在GitHub上使用MATLAB图形用户界面设计环境（GUIDE）和R中的计算机程序。