基于马氏距离的二元退化可靠性分析

Reliability analysis for bivariate degradation process based on Mahalanobis distance

为解决二元退化产品可靠性建模困难,提出了基于马氏距离(Mahalanobis distance,MD)的二元退化产品可靠性分析方法。首先引入MD,将二元退化数据降维至一元MD,并采用蒙特卡罗方法确定MD失效阈值;然后分别采用了Wiener过程的基本模型和3个具有随机参数的Wiener过程模型进行退化建模,运用贝叶斯方法进行参数估计,并通过模型验证、分位数图(quantile-quantile plot,QQ图)和改进的留一法交叉验证等模型选择方法综合判断确定最优模型。最后采用裂纹增长数据实例验证了所提方法的有效性。

The reliability of many highly reliable products is usually evaluated by two or more performance characteristics. To address this concern, a reliability analysis method based on Mahalanobis distance (MD) is proposed. Firstly, MD is used to transform the bivariate degradation data to one dimensional MD data. The MD threshold is obtained by the Monte-Carlo method Then, a simple wiener process model and three wiener process models with random effects are investigated. The statiscal inference is performed via Bayesian approach. An integrated method of model selection is given, which considers not only the hypothesis testing model and the quantile-quantile (QQ) plot, but also the refined leave-one-out cross-validation value. Finally, for an illustration of the proposed method, a numerical example about fatigue cracks is discussed and some results are presented.