When at least km components are in state m or above for all m such that 1 m j, a multi-state k-out-of-n: G device has a multi-valued success greater than or equal to a certain value j (lying between 1 (the lowest non-zero output level) and M (the highest output level) This paper examines a commodity-supply scheme that serves as a gold standard for a non-repairable multi-state k-out-of-n: G system with non-identical independent components. Every instance of the multi-state system output is expressed as an explicit function of the system's multi-valued inputs. Our analysis yields a Multi-Valued Karnaugh Map (MVKM), which is a normal, special, and comprehensive representation of the multi-state system. We use “binary” entities to connect each instance of the output to the multi-valued inputs in order to construct this MVKM. These binary entities are represented by an eight-variable Conventional Karnaugh Map (CKM) that has been modified to a map with four four-valued variables each. Despite the fact that the maps used are relatively broad, they are still very useful due to their normal structure. There was no attempt to draw loops on the maps or find minimal formulas. The maps were merely useful tools. for combinatorial representation and jointly executing ANDing, ORing, and complementation operations The MVKM obtained can be used for symbolic analysis, yielding results that are numerically consistent with those previously obtained. The map is a valuable resource for computing a variety of Importance Measures for the system's components, as well as a useful tool for visualising several system resources.
Author(s) DetailsAli Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah, 21589, Saudi Arabia.
Abdulghani Bakur Alsayegh
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O.Box 80200, Jeddah, 21589, Saudi Arabia.
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