Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth–death process

Abstract

A general repairable k-out-of-n:G system with non-identical components, which is a common form of redundancy, is considered in this paper. The number of repairmen is assumed to be r (1≤ r≤ n− k+1) while components can have similar or different repair priorities. The objective of this work is to address the problem of efficient evaluation of the system's availability in a way that steady state solutions can be obtained systematically in a reasonable computational time. This problem is modeled as a finite state-dependent non-homogeneous quasi-birth–death (QBD) process. An algorithm is introduced to systematically generate the system state vectors and transition rate matrix and then an iterative method based on the Block Gauss–Seidel method is employed to determine the steady state probabilities. These are the novel contributions made in this paper. An analog Monte Carlo simulation is presented to demonstrate the correctness and the efficiency of the proposed method.