A multi‐criteria optimal replacement policy for a system subject to shocks

A system is subject to shocks that arrive according to a non‐homogeneous Poisson process. As these shocks occur, the system experiences one of two types of failures: a type‐I failure (minor), rectified by a minimal repair; or a type‐II failure (catastrophic) that calls for a replacement. In this study, we consider a multi‐criteria replacement policy based on system age, nature of failure, and entire repair‐cost history. Under such a policy, the system is replaced at planned life time T, or at the nth type‐I failure, or at the kth type‐I failure (k < n) at which the accumulated repair cost exceeds the pre‐determined limit, or at the first type‐II failure, whichever occurs first. An optimal policy over the control parameters is studied analytically by showing its existence, uniqueness, and structural properties. This model is a generalization of several existing models in the literature. Some numerical examples are presented to show several useful insights.