Title: System reliability estimation based on fuzzy Weibull distribution incorporating hexagonal fuzzy number

Authors: Jaya Bhadauria; Deepak Kumar

Addresses: Department of Mathematics, Kumaun University (D.S.B. Campus), Nainital, Uttarakhand, India ' Department of Mathematics, Kumaun University (D.S.B. Campus), Nainital, Uttarakhand, India

Abstract: In this study, we used fuzzy Weibull distribution in a hexagonal fuzzy environment to assess the fuzzy reliability function, fuzzy hazard function and fuzzy mean time to failure of distinct configurations and systems. Firstly, we evaluated the system reliability, where the lifetime of components is represented by a Weibull distribution with fuzzy parameters in the form of hexagonal fuzzy number and secondly, this research focuses on fuzzy reliability evaluation for linear and circular consecutive k-out-of-n: F systems as well as series and parallel systems. Additionally, numerical examples are also given to show how fuzzy survival function and fuzzy hazard function vary with respect to time along with the tables and graphs. This research also presents a novel approach to determine system reliability by utilising a fuzzy number with six parameters.

Keywords: fuzzy Weibull distribution; series and parallel configuration; linear and circular consecutive (k-out-of-n: F) system; fuzzy reliability function; fuzzy hazard function; fuzzy mean time to failure.

DOI: 10.1504/IJRS.2025.145527

International Journal of Reliability and Safety, 2025 Vol.19 No.2, pp.174 - 197

Received: 20 Apr 2024
Accepted: 15 Oct 2024
Published online: 02 Apr 2025 *

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