Dynamically Optimal Replacement Policy for a Shock Model in a Markov Random Environment

We consider a system existing in a random environment. The environment is described by a Markov process called Markov environment process (MEP). The system is subject to a sequence of randomly occurring shocks, and each shock causes a random amount of damage which accumulates additively. The shock arrival and shock magnitude are influenced by changes of the environment. The damage process is assumed to be a piecewise semi-Markov process (PSMP) which is constructed by the shock process and the environment process. The optimal maintenance-replacement problem for the system is examined. A control-limit rule dependent on the MEP is driven.