Analysis of a multi-component system with double threshold control policy

This paper investigates a multi-component repairable system with double threshold control policy. The system is composed of n identical and independent components which operate simultaneously at the beginning, and it is down when the number of operating components decreases to k - 1 (k <= n). When the number of failed components is less than the value L, the repairman repairs them with a low repair rate. The high repair rate is activated as soon as L failed components present, and continues until the number of failed components drops to the value N-1. Applying the matrix analytical method, the Laplace transform technique and the properties of the phase type distribution, various performance measures including the availability, the rate of occurrence of failures, and the reliability are derived in transient and stationary regimes. Further, numerical examples are reported to show the behaviour of the system.