Boolean-based symbolic analysis for the reliability of coherent multi-state systems of heterogeneous components

Abstract EN

This paper is devoted to the Boolean-based analysis of non-repairable coherent multi-state systems with independent non-identical multi-state components.

We adapt several binary concepts and tools such as probability-ready expressions, Boolean quotients, the Boole-Shannon expansion, and the Karnaugh map to the multi-state case.

The paper utilizes algebraic techniques of multiple- valued logic to evaluate each of the multiple levels of the system output as a binary or propositional function of the system multi-valued inputs.

The formula of each of these levels is then written as a probability–ready expression, thereby allowing its immediate conversion, on a one-to-one basis, into a probability or expected value.

The symbolic reliability analysis of two small systems (which serve as standard gold examples of coherent multi-state systems) is completed successfully herein, yielding results that have been checked symbolically, and are also shown to agree numerically with those obtained earlier.

The algebraic techniques used are supplemented by illustrative visualization via multi-valued Karnaugh maps.

Emphasis is placed on the generalization of concepts of coherent binary systems to those of coherent multi-state ones, rather than innovating new unfamiliar stand- alone concepts for these latter systems.