On an extension of Barlow-Wu systems-Basic properties

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. The paper relaxes the strict condition and proposes a class of multi-state systems which it calls Extended BW systems (EBW systems). It presents some properties of EBW systems and clarifies the relationship among multi-state, EBW and binary coherent systems. As its main results the paper shows that any EBW systems are equivalent to a class of binary coherent systems satisfying some conditions. Furthermore, it provides 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.