A fuzzy approach to reliability analysis

Abstract

Most of the existing approaches for fuzzy reliability analysis are based on fuzzy probability. The aim of this paper is to describe fuzzy reliability using fuzzy differential equation. The reliability of a system in real world applications is affected by some uncertain parameters. Fuzzy reliability is a way to present the reliability function uncertainly using fuzzy parameters. In the proposed fuzzy differential equation for reliability, two types of fuzzy derivative: Hukuhara derivative and generalized differentiability are used. It is proved that the Hukuhara differentiability is not adequate for fuzzy reliability analysis. Finally, using the fuzzy integration, the concept of fuzzy mean time to failure (FMTTF) will be introduced. Some numerical simulations are presented to show the applicability and validity of generalized differentiability, in comparison with the Hukuhara differentiability results for fuzzy reliability analysis.