A Multi-Level Trend-Renewal Process for Modeling Systems With Recurrence Data

ABSTRACT

A repairable system is a system that can be restored to an operational state after a repair event. The system may experience multiple events over time that are called recurrent events. To model the recurrent event data, the renewal process (RP), the nonhomogenous Poisson process (NHPP), and the trend-renewal process (TRP) are often used. Compared to the RP and NHPP, the TRP is more flexible for modeling, because it includes both RP and NHPP as special cases. However, for a multi-level system (e.g., system, subsystem, and component levels), the original TRP model may not be adequate if the repair is effected by a subsystem replacement and if subsystem-level replacement events affect the rate of occurrence of the component-level replacement events. In this article, we propose a general class of models to describe replacement events in a multi-level repairable system by extending the TRP model. We also develop procedures for parameter estimation and the prediction of future events based on historical data. The proposed model and method are validated by simulation studies and are illustrated by an industrial application. This article has online supplementary materials.

KEYWORDS:

• Multi-level repairable systems
• Nonhomogenous Poisson process
• Random effect
• Renewal process
• Time-dependent covariate
• Trend-renewal process

Supplementary Materials

• Additional details: Additional details on covariate prediction, subsystem event simulation, and procedure for prediction intervals (pdf file).

Acknowledgments

The authors thank the editor, an associate editor, and two referees, for their valuable comments that helped in improving the presentation of the article significantly. The authors acknowledge Advanced Research Computing at Virginia Tech for providing computational resources.