Robust Statistical Modeling of Heterogeneity for Repairable Systems Using Multivariate Gaussian Convolution Processes

A main challenge in reliability analysis of repairable systems is to model the heterogeneity in their failure behavior, which can be reflected by the corresponding recurrent failure-time data. To capture the system heterogeneity for data analysis, a system-specific random effect is typically introduced in most existing statistical models. In practice, the random effect of repairable systems tends to be time varying; for example, each repair action could change system's physical properties. Prior studies, however, generally do not take account of this time-varying nature and few of them circumvent the risk of model misspecification on the parametric distribution of frailty. In this article, we propose a semiparametric model that uses multivariate Gaussian convolution processes (MGCPs) to meet the above challenges. First, we use the trend RP to model the baseline intensity function of each repairable system. Based on the baseline intensity function, we then introduce MGCPs to simultaneously factor in heterogeneity and infer commonalities across multiple systems. A Bayesian framework is used for parameter estimation and time-to-failure prediction. Simulation studies show the advantages of our model in terms of robustness and estimation accuracy. A group of oil and gas well systems are used to illustrate the application of the proposed model.