Extended maintenance and inspection models for a parallel system

This paper discusses an optimal maintenance policy for a parallel system with periodic inspection. The system is composed of several units which have an independent and identical distribution. When the number of failed unit exceeds a threshold level, the system incurs a loss cost per unit of time from a failure to the next inspection. When the next inspection finds the failure, the system is overhauled, and the system becomes like new. Further, the system is overhauled at planned time in spite of the state of the system. Introducing the loss cost for an inspection and overhaul, the expected cost is obtained and an optimal number of inspections which minimizes the expected cost rate is derived analytically. Numerical examples are given when the failure distribution of each unit is exponential.