A Reliability Problem with Spares and Multiple Repair Facilities

Abstract

A single unit system with (N−1) spares and c repair facilities is considered. It is assumed that the failure time distribution of each unit is negative exponential with parameter λ and repair time distribution of each repair facility is again a negative exponential with parameter μ. The Time-to-System Failure Period (TSFP) process has been investigated solving the difference-differential equation through the compensating function technique. The general process probabilities are obtained through renewal arguments from TSFP process and System Down Time (SDT) process, and their ergodic properties are discussed. The long-run availability of the system and the cost implication has been illustrated by a numerical example.