A Bivariate Degradation Model Based on Gamma Processes with Dependent Scale Parameters

Lots of products have more than one performance characteristic (PC), which makes it difficult to model their degradation processes and assess their reliabilities. In this paper, a bivariate degradation model is proposed based on nonlinear gamma processes, and the scale parameters are regarded as random variables that share a common item. A parameter estimation method based on maximum likelihood is proposed, and the reliability function of the product can be calculated after an analytical integral. The simulation study shows the good validities of the parameter estimation method and the reliability function. In the end, a case study based on a group of fatigue crack development data is presented, which demonstrates the application of the proposed model.