Multistate coherent systems

Abstract

The vast majority of reliability analyses assume that components and system are in either of two states: functioning or failed. The present paper develops basic theory for the study of systems of components in which any of a finite number of states may occur, representing at one extreme perfect functioning and at the other extreme complete failure. We lay down axioms extending the standard notion of a coherent system to the new notion of a multistate coherent system. For such systems we obtain deterministic and probabilistic properties for system performance which are analogous to well-known results for coherent system reliability.

Degradable systems:a survey of multistate system theory

“…As in the binary case, EPS [6], define a dual structure for each multistate structure. Equality holds in (i) ((ii)) for all x and y iff the system is parallel (series).…”

“…In this section we survey important relationships between the stochastic performance of a system in a given class and the stochastic performance of its components, which are often assumed to be independent, but in some cases assumed to be only associated (see The following theorem due to EPS [6] shows that h is strictly increasing in each pij j 0. This property generalizes the well known property of h in the binary case.…”

“…We first survey the treatments in which the state space S is taken to be the set (O,1,...,M), representing M+l levels of performance ranging from complete failure (0) to perfect functioning (M). The first class of multistate systems of this type is presented in EPS [6], where the structure function *:Sn -S is assumed to satisfy three conditions.…”

“…The following theorem in EPS [6] gives simple bounds on the performance of any structure function in their class.…”

On an Extension of Barlow-Wu Systems : Basic Properties

“…We present some properties of EBW systerns and c!arify the relationship arnong rnulti-state, EBW and binary coherent systems, As the main results ofthis paper, we show that any EBW systems are equiyalent to a class of binAry coherent systerns satisfying some conditions. Furtherrnore, vve [2], E.Nl-Newethi, F.?roschan and J.Sethuraman [3], W.S.Griffith [4], F.Ohi and T.Nishida [5,6,7] [2], which are called BIC (Barlow-Wu) systems.…”