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.
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.