Checking Correctness of a Symbolic Reliability Expression for a Capacitated Network
Omar Mutab Alsalami
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah, 21589, Saudi Arabia.
Ali Muhammad Ali Rushdi *
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah, 21589, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
Checking a symbolic reliability expression for a flow network is useful for detecting faults in hand derivations and for debugging computer programs. This checking can be achieved in a systematic way, though it may be a formidable task. Three exhaustive tests are given when a reliability system or network has a flow constraint. These tests apply to unreliability and reliability expressions for non-coherent as well as coherent systems, and to cases when both nodes and branches are unreliable. Further properties of reliability expressions derived through various methods are discussed. All the tests and other pertinent results are proved and illustrated by examples.
Keywords: Reliability expression, exhaustive test, success state, failure state, prime implicant, Bayes decomposition, capacitated (flow) network.