Reliability Bounds for Multistate Systems with Multistate Components

Abstract

The reliability literature has recently introduced several multistate models. This paper discusses reliability bounds in the most general of these models. It presents inclusion-exclusion bounds and compares them with disjoint subset bounds. The later bounds are based on a generalization of Abraham's recursive disjoint products.

Customer-driven reliability models for multistate coherent systems

“…Barlow and Wu [1978], El-Neweihi et al [1978], and Ross [1979] developed dynamic models for multistate coherent systems. Hudson [1981] extended the development of dynamic models for a general MCS.…”

System reliability maximization for a computer network by finding the optimal two-class allocation subject to budget

“…Such a probability can be obtained particularly via inclusion-exclusion principle [5,22] or state-space decomposition [1,4]. Although inclusion-exclusion principle is an easier method to be understood, state-space decomposition has better computational efficiency.…”

Multistate components assignment problem with optimal network reliability subject to assignment budget

“…Such a probability can be calculated by inclusion-exclusion principle [14,18,35] or state-space decomposition [2,16]. State-space decomposition proposed by Doullize and Jamoulle [6] adopted the Ford and Fulkerson [7] labeling scheme to decompose the state space into a set of acceptable state vectors, a set of unacceptable state vectors, and disjoint & unspecified sets of state vectors.…”