Steady-state bounds for multi-state systems' reliability via modular decompositions

A concept of modular decomposition plays a crucial role for theoretical and practical evaluation of reliability performances of systems, because real systems are usually composed of modules, and the components of the systems are arranged to form these modules. In this paper, we give stochastic bounds for multi‐state coherent systems by utilizing modular decompositions where the state spaces are assumed to be totally ordered sets. The presented bounds are shown to be better than those derived directly from the total systems and are extensions of the well‐known bounds for binary state systems to multi‐state cases. The results of this paper allows systems engineers or designers to have better stochastic approximations for the performance of a system by simply stacking stochastic bounds along with the hierarchy formed by the modules of the system. Copyright © 2014 John Wiley & Sons, Ltd.