On Boolean reliability algebra

TL;DR

This paper introduces the concept of reliability algebra, an algebraic structure for systems of binary components, and proves it forms a Boolean algebra, providing a foundation for defining fuzziness measures with reliability values.

Contribution

It defines the reliability algebra and proves it is a Boolean algebra, establishing a new algebraic framework for reliability analysis.

Findings

Reliability algebra is a Boolean algebra.

Provides a foundation for fuzziness measures with reliability values.

Establishes algebraic properties of systems with binary components.

Abstract

In this paper we consider systems which consist of binary components with known reliabilities. We discuss their algebraic properties and define the corresponding algebraic structure, which we call the reliability algebra. We prove that the reliability algebra is a Boolean algebra. The reliability algebra seems an appropriate context for defining fuzziness measure i.e. membership function with reliability values.