ON AN EXTENSION OF BARLOW-WU SYSTEMS : BASIC PROPERTIES

Abstract

The present paper considers multi-state systems which are regarded as a generalization of binary systems, and generalizes the concepts of BW systems proposed by R. E. Barlow and Alexander S. Wu. Since the structure function of a BW system is defined by using the minimal path sets of a binary coherent system, the BW system has a strict restriction that the form of minimal path sets should be identical for any states of the system. In this paper we relax the strict condition and propose a class of multi-state systems which we call Extended BW systems (EBW systems). We present some properties of EBW systems and clarify the relationship among multi-state, EBW and binary coherent systems. As the main results of this paper, we show that any EBW systems are equivalent to a class of binary coherent systems satisfying some conditions. Furthermore, we provide the characterization that the class of EBW systems is the maximum class of the multi-state systems which can be transformed into binary coherent systems whose number is identical to the number of the states of the multi-state system.