Reliability assessment for products with two performance characteristics based on marginal stochastic processes and copulas. (English) Zbl 1497.62262
Summary: Many highly reliable products (systems) usually have multiple dependent degradation processes because of their complex structure. Therefore, it is important to investigate the multivariate degradation models along with the reliability assessment in the stochastic modeling. This article proposes a framework for bivariate degradation modeling based on hybrid stochastic processes for products with two performance characteristics (PCs), the dependence of which is captured by copula functions. Considering heterogeneities among product units, different random effects are introduced in marginal stochastic processes. Then two classes of reliability functions based on joint posterior distributions are derived. In addition, a simulation study indicates that the holistic Bayesian parameter estimation method is better than the two-step Bayesian parameter estimation method. Finally, this article concludes with a case application to demonstrate the effectiveness of the proposed model.
MSC:
| 62N05 | Reliability and life testing |
| 62F15 | Bayesian inference |
| 62M05 | Markov processes: estimation; hidden Markov models |
| 62P30 | Applications of statistics in engineering and industry; control charts |
Keywords:
Bayesian parameter estimation; bivariate degradation modeling; copula function; performance characteristic; reliability functionReferences:
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