A Bivariate Gamma Model for a Latent Degradation Process

Abstract

A model is presented in this article based on a bivariate gamma process in which, the first component is latent and determines the failure time and the second represents the marker. This process is a more realistic model for a degradation process. After introducing the model, we obtain failure and survival probability distributions and discuss parametric and predictive inferences based on the Maximum Likelihood method and in a Bayesian setup.

Keywords:

• Bivariate gamma process
• Degradation process
• Marker process
• First-hitting time
• Prediction
• Reliability
• Statistical inference
• MCMC method.

Mathematics Subject Classification:

• Primary 60K10
• Secondary 62M09.