Reliability Analysis of a Multi-State Delivery Network through the Symbolic Derivation of a Probability-Ready Expression | Chapter 12 | Recent Advances in Mathematical Research and Computer Science Vol. 4

 The dependability of a multi-state delivery network (MSDN) with different suppliers, transfer stations, and marketplaces (depicted as vertices) connected by branches of multi-state capabilities, delivering a specific commodity or service between their end vertices is the subject of this chapter. We use a symbolic logic interpretation of network success to meet market demand while staying within budget and manufacturing capacity constraints, even while the network is deteriorating. This system success is a two-valued function described in terms of multi-valued component successes, and it has been derived in minimum form as the disjunction of prime implicants or minimal pathways of the relevant network in the literature. This chapter's key contribution is a systematic method for transforming this minimum expression into a probability-ready expression (PRE). The PRE notion has been effectively extrapolated from the two-valued logical domain to the multi-valued logical domain. This concept is crucial because it enables a one-to-one transformation of a random logical expression to its statistical expectation form by simply replacing all logic variables with their statistical expectations, as well as substituting arithmetic multiplication and addition for their logical counterparts (ANDing and ORing). This chapter's running example for showing PRE derivation is admittedly long and tiresome. The statistical expectation of the statement is that it will be equal to 1, and this is referred to as network dependability. The proposed method is demonstrated using a thorough symbolic example of a real-life case study, and it yields a more precise version of the identical numerical value obtained previously by another method. This chapter is part of a larger project to create educational materials for a variety of prospective methodologies for measuring multi-state reliability.

Author(S) Details

Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University, Faculty of Engineering, P. O. Box 80200, Jeddah 21589, Kingdom of 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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Karnaugh-Map Analysis of a Commodity-Supply Multi-State Reliability System | Chapter 3 | Theory and Practice of Mathematics and Computer Science Vol. 8

 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) Details

Ali 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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