On alternative definitions of multistate coherent systems

Abstract

We investigate alternative definitions of multi-state coherency, and establish a chain of implication amongst these. The role of monotonicity within coherency is analysed by also considering the non-monotonic analogies of the various types of coherent systems, For coherent systems with a well defined binary image, we identify the structure of the minimal paths, and prove that the system must pass through all states. For a class of coherent systems within this group, but in turn containing the class of Bablow and Wu [5] (to which it is identical apart from those author's relevancy restrictions), we prove a decomposition for systems of identical components in terms of both binary-systems and multistate systems. Thin later result provides a, structural significance for the multistate k-out-of-n systems identified by El-Neweihi, Proschan and Sethubaman [14].

Keywords:

• Coherent systems
• multistate systems
• k-out-of n systems

AMS 1980 Subject Classification:

• Primary: 60K10