Optimal Preventive Maintenance Rate for Best Availability With Hypo-Exponential Failure Distribution

The optimal rate of periodic preventive maintenance to achieve the best availability is studied for Markov systems with multiple degraded operational stages, where the time-to-failure has a hypo-exponential distribution. An analytical expression is developed for the availability of such systems having n operational stages, and a necessary and sufficient condition is derived for a non-trivial optimal rate of periodic maintenance to exist. Numerical procedures for finding the optimal rate of periodic maintenance are given, and examples are presented.