On Multistate System Analysis

Abstract

Discrete function theory, which extends switching function theory and multiple-valued logic function theory, is introduced into multistate system analysis. Some theoretical conclusions and algorithms which play key roles in multistate system analysis are presented. The concepts of s-coherence and duality in binary-state system analysis are generalized. The set of minimal upper (maximum lower) vectors for level j, which play the role of min path (cut) set, is introduced to represent the states of a monotonic multistate system. Two approaches to computing state probability of multistate systems are given, one is based on inclusion-exclusion, the other is based on enumeration. Binary-state fault-tree is extended to multistate fault-tree. A computer code (MSTA1) has been programmed and is used to evaluate a multistate fault-tree. Multistate fault-tree and the computer code have been applied to paper-making industry; the results are consistent with the field data.