On a dynamic preventive maintenance policy for a system under inspection

The purpose of this article is to propose both state and time-dependent preventive maintenance policy for a multi-state deteriorating system, which is equipped with inspection equipment(s) connected to a computer center. After the system being identified as state x at nd through computation by the computer center after inspection (or measurement) via equipment(s), one maintenance action with the minimum expected total cost since nd till Nd (where N=n+K for a fixed integer 0<K<∞) will be chosen from the set Ax of alternatives also with the help of the computer center. In real case, the expected total costs since nd till Nd will be time-dependent and so is the maintenance action chosen at nd. A numerical example is given to illustrate such a maintenance policy for a Markovian deteriorating system to describe its state dependent aspect only for simplicity reason. Due to the fact that both equipment measurement and computer computation take time, the preventive maintenance policy for a sufficiently small d may be used in fact as the one under continuous inspection.