Abstract

To inference the reliability of product at normal stress conditions, accelerated life test (ALT) is usually used to obtain failure information rapidly. However, most of the researches on ALT are focused on the statistical inference with single stress, which makes it difficult to gain accurate reliability through applying ALT method in single stress case. In this article, statistical inference is considered on dual constant-stress accelerated life test (DCSALT) model for the Weibull distribution with Type-I censored data. On the assumption that the Weibull distribution has constant shape parameter, and a log-linear acceleration model between its scale parameter and the test stress level combination. Using the profile maximum likelihood estimation (PMLE) method to estimate the unknown parameters in DCSALT model for Weibull distribution, and this process is completed by Newton-Raphson algorithm. Moreover, the observed information matrix is obtained in order to construct asymptotic confidence intervals of the unknown parameters. Finally, the numerical study is presented to illustrate the effectiveness of the maximum likelihood estimators (MLEs).

摘要

为了推断产品在正常应力条件下的可靠性，通常采用加速寿命试验（ALT）来快速获取失效信息。然而，关于ALT的研究大多集中在单一应力的统计推断上，使得在单一应力情况下应用ALT方法难以获得准确的可靠性。在本文中，考虑了对具有 I 型删失数据的 Weibull 分布的双恒应力加速寿命试验 (DCSALT) 模型的统计推断。假设 Weibull 分布具有恒定的形状参数，并且在其尺度参数和测试应力水平组合之间存在对数线性加速度模型。使用轮廓最大似然估计（PMLE）方法估计威布尔分布的DCSALT模型中的未知参数，而这个过程是由Newton-Raphson算法完成的。此外，为了构建未知参数的渐近置信区间，获得了观测信息矩阵。最后，提出了数值研究来说明最大似然估计器（MLE）的有效性。