Reliability Analysis of a Multi-State Truly-Threshold System Using a Multi-Valued Karnaugh Map

TL;DR

This paper presents a Boolean-based method for analyzing multistate systems using multi-valued Karnaugh maps, enabling efficient reliability evaluation of complex non-binary systems.

Contribution

It introduces a novel approach to represent and analyze multistate systems with Boolean expressions and multi-valued Karnaugh maps, extending traditional binary reliability methods.

Findings

Boolean expressions for system states derived

Multi-valued Karnaugh maps facilitate analysis

Applicable to non-repairable multistate systems

Abstract

This paper deals with the Boolean-based analysis of a prominent class of non-repairable coherent multistate systems with independent nonidentical multistate components. This class of systems is represented by a multistate coherent truly threshold system of several states, which is not necessarily binary-imaged. The paper represents such a system via Boolean expressions of system success or system failure at each non-zero level, which are in the form of minimal sop formulas, or disjoint sop formulas. These are expressions that are directly convertible to expected values. Several map representations are also offered, including a single multi-value Karnaugh map.