Condition-Based Maintenance for Repairable Deteriorating Systems Subject to a Generalized Mixed Shock Model

Based on reliability analysis for a system subject to -dependent competing risks of internal degradation and external shocks, we propose a condition-based maintenance policy considering imperfect repair for complex systems. The internal degradation (e.g., crack growth, erosion, or corrosion) can be modeled using a stochastic deterioration process. External shocks arriving at random times are divided into two classes based on their impacts on the system: 1) fatal shocks that can cause the system to fail immediately, if a shock belongs to any of three classic shock models (i.e., extreme shock model, run shock model, and delta-shock model), or the generalized mixed shock model; and 2) non-fatal shocks that can damage the system by randomly increasing the degradation level. Using the proposed condition-based maintenance policy, the system is inspected at fixed time intervals, and a decision for an appropriate maintenance action (i.e.,no action, imperfect repair, preventive or corrective replacement) is made based on the actual health condition of the system detected through inspection. The imperfect repair restores the system by lowering the degradation amount to a certain level. The objective is to determine the optimal inspection interval that minimizes the expected long-run maintenance cost rate. A micro-electro-mechanical system example is used to evaluate the efficiency of the developed reliability and condition-based maintenance models.