Imperfect preventive maintenance policies for two-process cumulative damage model of degradation and random shocks

In numerous applications, the system may fail due to multiple competing risks, especially degradation processes and random shocks. In this paper, we develop a two-process combination model for degraded system subject to cumulative effect from random shocks and degradation with two kinds of path function, including additive and multiplicative. Two numerical examples with sensitivity analysis for additive and multiplicative degradation path are discussed separately to illustrate this combination model. Based on the definition of the cumulative damage system, the imperfect preventive maintenance policy (N*, T*) with a common improvement factor is obtained to minimize the expected maintenance cost rate. The uncertainty of the reliability estimation and maintenance optimization is considered in the problem modeling. Also some extensions for this combination model are suggested for further research.