Open AccessDerivation of Minimal Cutsets from Minimal Pathsets for a Multi-State System and Utilization of Both Sets in Checking Reliability Expressions
Author(s) -
Ali Muhammad Ali Rushdi,
Motaz Hussain Amashah
Publication year - 2021
Publication title -
journal of engineering research and reports
Language(s) - English
Resource type - Journals
ISSN - 2582-2926
DOI - 10.9734/jerr/2021/v20i817354
Subject(s) - reliability (semiconductor) , state (computer science) , computer science , binary decision diagram , binary number , mathematics , algorithm , reliability engineering , theoretical computer science , arithmetic , engineering , power (physics) , physics , quantum mechanics
This paper addresses two important useful extensions of binary reliability techniques to multi-state reliability techniques, namely: (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. The paper deals specifically with the reliability of a multi-state delivery network. It presents two complementation procedures, one via the application of multi-state De Morgan’s rules, and the other via the multi-state Boole-Shannon expansion. The paper also illustrates one case in which this complementation is needed, as it outlines a method for checking the reliability of the multi-state system in terms of its logical minimal paths and logical minimal cutsets.