Development of a stochastic model for maintenance planning in a multi-stage process

A stochastic mathematical model is developed for a two-stage process. Each stage of the process has two operational states including an in-control state and an out-of-control state. It is assumed that two assignable causes may affect the process so that each stage shifts from the in-control state to the out-of-control state due to the occurrence of assignable causes. The time of occurrence for each cause is assumed as a random variable that follows a general continues distribution function. The model determines an optimal time point for conduction maintenance actions such that the expected cost per time unite be minimized.