Bivariate Constant-Stress Accelerated Degradation Model and Inference Based on the Inverse Gaussian Process

Modern highly reliable products may have two or more quality characteristics (QCs) because of their complex structures and abundant functions. Relations between the QCs should be considered when assessing the reliability of these products. This paper conducts a Bayesian analysis for a bivariate constant-stress accelerated degradation model based on the inverse Gaussian (IG) process. We assume that the product considered has two QCs and each of the QCs is governed by an IG process. The relationship between the QCs is described by a Frank copula function. We also assume that the stress on the products affects not only the parameters of the IG processes, but also the parameter of the Frank copula function. The Bayesian MCMC method is developed to calculate the maximum likelihood estimators (MLE) of the model parameters. The reliability function and the mean-time-to-failure (MTTF) are estimated through the calculation of the posterior samples. Finally, a simulation example is presented to illustrate the proposed bivariate constant-stress accelerated degradation model.