Analysis of Coherent Multistate Systems

Abstract

The structure and reliability of homogeneous s-coherent multistate systems is studied. Homogeneous systems have two properties: 1) their components can be rearranged internally in any arbitrary way without affecting the mapping of the component states onto the system state; 2) all components, all subsystems composed of them, and the system have the same set of states. Because of the s-coherence and homogeneity properties, mapping of the component states onto the system state, as well as calculating probabilities of system states from those of the component states, become very simple. In homogeneous systems, states can be ranked according to their relative dominance, and the state ranking completely determines the structure of such a system. Any homogeneous s-coherent system belongs to one of four categories which differ in whether the identity property is satisfied or not, or on details of the state ranking. As an application, the high pressure injection system of a pressurized water reactor is modeled as a multistate system composed of homogeneous s-coherent multistate subsystems.