Reliability Modeling and Inference with Multiple Performance Characteristics

Huibing Hao and Chun Su


Bivariate degradation, Random effect Wiener process, Copula function, Inference for margins method, MCMC method


Light emitting diode (LED) lamp has attracted increasing interest in the field of lighting systems due to its low energy and long lifetime. For different functions (i.e. illumination and color), it may have two or more performance characteristics. When the multiple performance characteristics are dependent, it creates a challenging problem to accurately analyze the system reliability. In this paper, we assume that a product has two performance characteristics, and each performance characteristic is governed by a random effected Wiener process where random effects capture the unit to unit differences. The random effected model is fitted to the actual data and corresponding goodness of fit tests are carried out. The dependency of performance characteristics is described by a Frank copula function. The inference for margins method and Markov chain Monte Carlo method are used to obtain the estimators of the corresponding model unknown parameters. A numerical example about an actual LED lamps experiment data is given to demonstrate the usefulness and validity of the proposed model and method.

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