8 Switching-algebraic symbolic analysis of the reliability of non-repairable coherent multistate systems
Ali Muhammad Ali Rushdi, Fares Ahmad Muhammad Ghaleb · 2021
This chapter presents a switching-algebraic analysis of non-repairable coherent multistate systems (MSSs) with independent non-identical multistate components. We adapt various switching-algebraic binary concepts and tools such as probabilityready expressions (PREs), Boolean quotients, the Boole-Shannon expansion, and the Karnaugh map to the multistate case. This chapter analyzes a multistate reliability system without explicit utilization of the algebraic techniques of multiple-valued logic or those of multivalued discrete-function theory. The analysis required is achieved via the evaluation of each of the multiple non-zero levels of the system output as a binary or propositional function of the system multivalued inputs. The formula of each of these levels is then written as a PRE, thereby allowing its immediate conversion, on a one-toone basis, into a probability value. The symbolic reliability analysis of two small coherent MSSs is completed successfully herein, yielding results that have been checked symbolically, and can also be shown to agree numerically with those obtained earlier. The algebraic techniques used are supplemented by illustrative visualization via multivalued Karnaugh maps. Emphasis is placed on the generalization of concepts of coherent binary systems to those of coherent multistate ones, rather than innovating new unfamiliar stand-alone concepts for these latter systems.