This chapter addresses two important contributions that extend binary reliability techniques to multi-state reliability techniques: (a) the problem of complementation or inversion of the function of system success to that of system failure (or, equivalently, of deriving the logical minimal cutsets in terms of the logical minimal paths), and (b) the associated problem of hand-checking of a symbolic reliability expression, which relies on complete knowledge of the logical minimal paths. The research focuses on the resiliency of a multi-state distribution network with various suppliers and dwindling production capacity. It demonstrates two complementation techniques, one using multi-state De Morgan’s rules and the other using the multi-state Boole-Shannon expansion. The chapter also presents a way for testing the stability of a multi-state system in terms of its logical minimal paths and logical minimal cutsets, which is a common use case for this complementation.
Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University, Faculty of Engineering, P.O.Box 80200, Jeddah 21589, Saudi Arabia.
Motaz Hussain Amashah
Department of Computer Engineering and Networks, College of Computer Science and Engineering, University of Jeddah, P.O.Box 80327, Jeddah, Saudi Arabia.
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