Reliability analysis of generalized multi-state k-out-of-n systems

Abstract

The recently proposed generalized multi-state k-out-of- n system model provides more flexibility in describing practical systems. In this model, there are n components in the system where each component and the system can be in one of M + 1 possible states: 0, 1, 2, …, M. The system is in below state j if there exists an integer value l, (1  ≤ i ≤ j) such that at least kl components are in states below l. Although the model has several practical applications, existing methods for computing either the exact or approximate reliability of these systems are computationally inefficient and limited to very small systems. This paper proposes an efficient method and a detailed algorithm to compute the exact reliability of multi-state k-out-of- n systems with independent and identically distributed components. The method is based on conditional probabilities and is applicable for all cases of multi-state k-out-of- n systems with respect to the recent definitions of this system.