A Multistate System under an Inspection and Repair Policy

This paper presents a multistate system under a certain inspection and repair policy over an infinite time span. A complete failure state of the system is detected at once, but other states can be identified only by inspection; so the system is periodically inspected. Two types of repairs are considered; the repair type depends upon the detected state of the system. These repairs are imperfect, ie, after any repair the system goes to the normal state with a certain probability. In order to analyse this system, state probabilities are determined, and then the inspection time interval is evaluated which maximizes average profit rate of the system. The problem is solved by using Laplace transforms.