Bivariate degradation analysis of products based on Wiener processes and copulas

By Zhengqiang Pan, Narayanaswamy Balakrishnan, Quan Sun, Jinglun Zhou. 2013

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Residual life estimation based on bivariate Wiener degradation process with time-scale transformations (2014, methodology): “[32], it is assumed that a product has two possible fatigue crack positions with initial crack length of 0.”
Residual life estimation based on bivariate non-stationary gamma degradation process (2015, methodology): “Moreover, as in [21], the expected cumulative crack lengths of each PC over time can be assumed to be proportional according to a power law.”
RUL Prediction of Deteriorating Products Using an Adaptive Wiener Process Model (2017, background): “degradation of these characteristics are generally correlated due to the complicated interactions of different failure mechanisms [44], [45].”
Reliability Modeling for Systems with Multiple Degradation Processes Using Inverse Gaussian Process and Copulas (2014, background): “[10] proposed a bivariate Wiener degradation process to describe the dependence between degradation characteristics, where marginal distribution and multivariate dependence can be modeled separately, and marginal distribution functions of degradation measures may follow different distributions famil”