An Axiomatic Characterization of Multistate Coherent Structures

Mathematical models for multistate reliability systems of multistate components have been proposed by Barlow and Wu (Barlow, R. E., A. S. Wu. 1978. Coherent systems with multistate components. Math. Oper. Res.3 275–281.), El-Neweihi et al. (El-Neweihi, E., F. Proschan, J. Sethuraman. 1978. Multistate coherent systems. J. Appl. Probab.15 675–688.) and Griffith (Griffith, W. S. 1980. Multistate reliability models. J. Appl. Probab.17 735–744.). Unlike the approach used by Barlow and Wu, the other authors preferred to establish their classes of models through sets of axioms extending the early binary notions and containing as special cases the class of models suggested by Barlow and Wu. Since the Barlow and Wu approach is set theoretic and the model definition is essentially qualitative, a question of interest concerns its axiomatic characterization among larger classes of models. In this paper such a characterization is established that relates the Barlow and Wu models to the other classes of models introduced later.