竞争失效场合加速试验(AT)技术是加速试验由简单结构产品向复杂结构产品推广应用的基础。但目前的方法主要针对恒定应力加速试验,而对竞争失效场合步进应力加速试验缺乏相关研究。针对这一问题,对最一般形式(突发型失效和退化型失效并存)的竞争失效场合步进应力试验进行建模与分析。充分考虑了试验数据由于试验截尾和失效样本对应的失效模式不确定而产生的非完整性,在此基础上分别采用基于期望最大化(EM)算法的极大似然估计(MLE)和伪失效寿命MLE,对突发型失效模式和退化型失效模式进行统计分析。最后应用实例验证了方法的有效性。
The technology of accelerated testing (AT) with competing failure modes is the foundation of application extending from products with simple structures to products with complex structures. However, most of the methods proposed in relevant literature are for constant stress AT, and there is scarcely any study concerning methods for step stress AT. This article proposes a model and a method for analyzing a common type of step stress AT with competing failure modes in which both hard failures and soft failures exist. Full consideration is given to the incompleteness of testing data, which may be due to censoring as well as masking that occurs when the failure time is observed, but its corresponding failure mode is not identified. Then maximum likelihood estimation (MLE) based on expectation maximum (EM) algorithm and pseudo-lifetime MLE are proposed for analyzing respectively the hard failure modes and soft failure modes. Finally, case studies are performed to check the validity of the model and the method.
[1] Jayatille S, Okogbaa O G. Accelerated life testing for speedier product development: problems and strategies//Proceedings of Reliability and Maintainability Symposium. 2006: 318-324.
[2] Nelson W B. Accelerated testing: statistical models, test plans, and data analyses[M]. New York: John Wiley & Sons, Inc., 1990.
[3] Klein J P, Basu A P. Weibull accelerated life test when there are competing causes of failure[J]. Communications in Statistics Theory and Methods, 1981, 10(20): 2073-2100.
[4] 张志华, 茆诗松. 竞争失效产品加速寿命试验的广义线性模型分析[J]. 华东师范大学学报: 自然科学版, 1997(1): 29-35. Zhang Zhihua, Mao Shisong. GLM of accelerated life test with competing causes of failure[J]. Journal of East China Normal University: Natural Science, 1997(1): 29-35. (in Chinese)
[5] Kim C M, Bai D S. Analyses of accelerated life test data under two failure modes[J]. International Journal of Reliability, Quality and Safety Engineering, 2002, 9(2): 111-125.
[6] 高伟, 赵选民. 混合指数分布恒定应力加速寿命试验的统计分析[J]. 机械科学与技术, 2006, 25(8): 913-916. Gao Wei, Zhao Xuanmin. Statistical analysis of constant stress accelerated life testing of mixture exponential distribution[J]. Mechanical Science and Technology, 2006, 25(8): 913-916. (in Chinese)
[7] Tan Y Y, Zhang C H, Chen X. Analysis of incomplete data of accelerated life testing with competing failure modes[J]. Chinese Journal of Mechanical Engineering, 2009, 22(6): 883-889.
[8] Meeker M Q, Escobar L A. Statistical methods for reliability data[M]. New York: John Wiley & Sons, Inc., 1998.
[9] Bousquet N, Bertholon H, Celeux G. An alternative competing risk model to the Weibull distribution for modeling aging in lifetime data analysis[J]. Lifetime Data Analysis, 2006, 12(4): 481-504.
[10] Dempster A P, Laird N M, Rubin D B. Maximum likelihood for incomplete data via the EM algorithm[J]. Journal of the Royal Statistical Society: Series B (Methodological), 1977, 39(1): 1-38.
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