In reliability engineering, there are numerous examples of units with two performance characteristics (PCs) that degrade over time. Here, a flexible model is developed for bivariate degradation data where the degradation processes corresponding to the PCs are likely dependent on each other. The degradation corresponding to the PCs are marginally modelled by gamma processes, and the dependence between them is captured by a shared frailty term that is assumed to follow the generalized gamma distribution. It is shown that the proposed model is far more flexible and efficient than many of the commonly used models used for this purpose. A Monte Carlo simulation-based technique for the computation of maximum likelihood estimates is developed for fitting the proposed model to bivariate degradation data. Then, the method of estimation is evaluated through an elaborate Monte Carlo simulation study. The joint reliability function of the unit with two PCs and its estimation are also discussed in this general setting. The proposed model is then extended to the case of multiple PCs. A case study is presented in which a real degradation data pertaining to fatigue cracks is analyzed through the proposed model to demonstrate its usefulness.
CO Author: Sandip Barui and Narayanaswamy Balakrishnan
Journal: Reliability Engineering & System Safety
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