A Novel Weakest t-norm based Fuzzy Fault Tree Analysis Through Qualitative Data Processing and Its Application in System Reliability Evaluation

Abstract

The quantification of the fuzzy fault tree analysis (FFTA) is based on fuzzy arithmetic operations. It is well known that the weakest t-norm (Tw)-based fuzzy arithmetic operations have some advantages. The Tw-based fuzzy arithmetic operations provide fuzzy results with less fuzziness and preserve the shape of fuzzy numbers. The purpose of this study is to develop a Tw-based fuzzy fault tree analysis (TBFFTA) to assess system reliability when only qualitative data such as expert opinions or decisions are available and described in linguistic terms. The developed TBFFTA applies Tw-based fuzzy arithmetic operations to evaluate the lower bound, best estimate, and upper bound top event probability of a system fault tree, where occurrence possibilities of basic events are characterized by triangular fuzzy membership functions. To demonstrate the applicability and feasibility of TBFFTA, a case study has been performed. The computed results have been compared with results analyzed by existing fuzzy approach. The comparative study concludes that TBFFTA reduces fuzzy spreads (uncertainty interval) and provides more exact fuzzy results.

Keywords

• fuzzy failure possibility
• fault tree analysis
• weakest t-norm
• fuzzy number