Threshold recovery policy for the machine interference repair problem with server vacations

Abstract

Abstract In this paper, we consider the threshold recovery policy for the machine interference problem (MIP) with server vacations, having a non-dependable server which operates a threshold recovery policy, i.e., service starts after a fixed threshold level q ≥ 1. In the threshold recovery policy, M machines of similar nature are subject to fail or break down with a single server responsible for maintaining or repairing the failed machines. When the server is working, it is subject to breakdown with exponential distribution rate α; it is not possible to repair any server until the number of failed computers exceeds a predetermined threshold, q where 1 ≤ q ≤ M. The repaired rate is exponentially distributed with rate β. The server breaks down with a constant failure rate. The repair and vacation time of server is exponentially distributed. We developed the difference differential equations for the transient state probabilities for the system. We calculate the threshold recovery strategy for the MIP with server vacation using the ODE45 (Runge-Kutta method for solving ordinary differential equations) in the MATLAB computer language. We develop a variety of operational quality metrics for the system.