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

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, which are called recurrent events. To model the recurrent event data, the renewal process (RP), the nonhomogeneous 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 paper, we propose a general class of models to describe replacement events in a multilevel repairable system by extending the TRP model. We also develop procedures for estimation of model parameters and 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.