Bivariate degradation modelling with marginal heterogeneous stochastic processes |
| |
Authors: | Luis Alberto Rodríguez-Picón Víctor Hugo Flores-Ochoa Luis Carlos Méndez-González Manuel Arnoldo Rodríguez-Medina |
| |
Institution: | 1. Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Autonomous University of Ciudad Juárez, Ciudad Juárez, Mexicoluis.picon@uacj.mx;3. Technological Institute of Ciudad Juárez, Ciudad Juárez, Mexico;4. Department of Industrial Engineering and Manufacturing, Institute of Engineering and Technology, Autonomous University of Ciudad Juárez, Ciudad Juárez, Mexico |
| |
Abstract: | 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. |
| |
Keywords: | Degradation process bivariate modelling heterogeneous processes stochastic process copula function |
|
|