A definition of generalizedk— out— of— n multistate systems and their structural and probabilistic properties

Abstract

Recently several authors have treated multistate systems, which assume intermediate states between failure and normal states. Systems which assume failure and normal states are called binary-state systems. Almost all the discussion on multistate systems is how to extend the several concepts with respect to binary-state systems. Especially a definition ofk-out-of-n systems is presented only by Barlow and Wu [2], which is a straight extension of binary-state case and have some restrictions, e.g., all the state space of units and the system composed of them are the same, the structure functions of the systems have particular form, and so on. In this paper we present a definition ofk-out-of-n multistate systems under more general situation that all the state spaces of units and the system composed of them are not necessarily the same, and explain the order structure of them, probabilistic properties of which are also presented. The probabilistic properties suggests that we may apply thek-out-of-n systems to the problem of how to construct the optimal safety monitoring systems.