Dominant multi-state systems

In this paper, we propose a definition of the dominant multi-state system. Under the proposed definition, multi-state systems are divided into two groups without reference to component relevancy conditions: dominant systems, and nondominant systems. Dominant systems can be further divided into two groups: with binary image, and without binary image. A multi-state system with binary image implies that its structure function can be expressed in terms of binary structure functions such that it can be treated as a binary system structure, and existing algorithms for reliability evaluation of binary systems can be applied for system performance evaluation. A technique is provided for establishing the bounds of performance distribution of dominant systems without binary image. The properties of dominant systems are studied. Examples are given to illustrate applications of the proposed definitions and methods.