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Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

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  • Huibing Hao
  • Chun Su

Abstract

A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.

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  • Huibing Hao & Chun Su, 2014. "Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, March.
    • Handle: RePEc:hin:jnlmpe:510929
    DOI: 10.1155/2014/510929
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    Cited by:

    1. Palayangoda, Lochana K. & Ng, Hon Keung Tony, 2021. "Semiparametric and nonparametric evaluation of first-passage distribution of bivariate degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 205(C).

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