Bivariate degradation modelling with marginal heterogeneous stochastic processes. (English) Zbl 07192059
Summary: In this paper, we consider that the degradation of two performance characteristics of a product can be modelled by stochastic processes and jointly by copula functions, but different stochastic processes govern the behaviour of each performance characteristic (PC) degradation. Different heterogeneous and homogeneous models are presented considering copula functions and different combinations of the most used stochastic processes in degradation analysis as marginal distributions. This is an important aspect to consider because the behaviour of the degradation of each PC may be different in its nature. As the joint distributions of the proposed models result in complex distributions, the estimation of the parameters of interest is performed via MCMC. A simulation study is performed to compare heterogeneous and homogeneous models. In addition, the proposed models are implemented to crack propagation data of two terminals of an electronic device, and some insights are provided about the product reliability under heterogeneous models.
MSC:
| 60Gxx | Stochastic processes |
| 62N05 | Reliability and life testing |
| 62Nxx | Survival analysis and censored data |
Keywords:
degradation process; bivariate modelling; heterogeneous processes; stochastic process; copula functionReferences:
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