Optimal degradation processes control by two-level policies

Two-level control policies are applied to various types of Markov processes describing degrading parameters of system units. To estimate the system operation cost an expectation of losses per unit time is evaluated. It is assumed that the degradation process is observable, and a monitoring system can signal about future failures. Firstly, semi-Markov processes are considered. A death process is proposed for a unit subjected to corrosion. A Markov chain are used for the problem of fatigue crack growth. The control problem is studied mainly in a steady-state regime for units of multiple use when the cost function is performed as the ratio of expectations. The cost function as the expectation of losses per unit time for single units is also studied, and the majorizing property of this cost function is shown.