Statistical analysis of double stress accelerated life testing under adaptive type-Ⅱ progressive censoring

自适应Ⅱ型逐步截尾双应力恒加试验统计分析

School of Power and Energy, Northwestern Polytechnical University, Xi'an 710072, China

Received: 31 May 2023

Abstract

Aiming at the traditional accelerated life test only considering the single stress and single failure cause, the inference method of double stress accelerated competing risks data is studied under the adaptive type-Ⅱ progressively censored and the life of test units follow Weibull distribution. The maximum likelihood estimations and the asymptotic confidence intervals of unknown parameters are obtained by using the Newton-Raphson iteration and asymptotic likelihood theory. A Gibbs sampling combining with Metropolis-Hasting algorithm method is developed to obtain Bayes estimations, and the Monte Carlo method is employed to construct the HPD credible intervals. The simulated results show that the present method has good statistical inference performance, meanwhile the failure sample size and the expected experimentation time have significant effect on the estimations.

摘要

针对传统加速寿命试验仅考虑单一加速应力和单一失效模式的问题, 研究寿命服从Weibull分布且失效模式相互独立的竞争失效产品, 在自适应Ⅱ型逐步截尾下建立双应力恒加试验的统计分析方法。通过Newton-Raphson迭代和渐进似然理论得到未知参数的极大似然估计和渐进置信区间。采用Gibbs抽样与M-H抽样混合算法获得参数的Bayes估计并基于MC方法构建HPD可信区间。数值模拟结果表明所提的方法具有良好的统计推断性能且失效样本数和试验时间对估计效果有显著影响。