Fuzzy reliability of a turbines structure system using the right triangular fuzzy number

PurposeThe purpose of this paper is to investigate the performance of a turbine structure of the oil and gas Egyptian company in terms of reliability, mean time to failure (MTTF), mean time to repair (MTTR) and mean time between failures (MTBF) under fuzzy environment and working criteria. This paper examines the impact of the failure of various components on the complete turbine structure of the oil and gas system.Design/methodology/approachTo overcome the problem of uncertain behavior of available data for various components, the right triangular generalized fuzzy number (RTrGFN) is proposed to be taken into the account to express the uncertainty which attains some tolerance in data. Furthermore, reliability indices are calculated with the help of the Lambda Tau method and the arithmetic operations on right generalized triangular fuzzy numbers (RTrGFN).FindingsThis paper explores the reliability of a repairable 3 out of 4 structure of turbines and along with the other parameters namely MTTF, MTTR and MTBF; under a fuzzy environment. Failure rates and repair times are expected to be exponential. The ranking of components of the structure is being found to decide the priority for maintenance.Originality/valueThis paper investigates the performance of the system with different spread/tolerance like 15%, 25% and 50% of crisp data. It helps to predict realistic results in the range value. To enhance the system's performance, the most important item of the system requires greater attention. For this, the authors find the sensitive part by ranking. For ranking, an extended approach has been developed to find the sensitive unit of the system by using the right triangular generalized fuzzy number. This paper explores the most and least sensitive component of the system, which helps the maintenance department to plan the maintenance action.

Ranking parametric form of fuzzy numbers by defuzzification based on centroids value and ambiguity

This paper proposes a new method to rank the parametric form of fuzzy numbers based on defuzzification. The defuzzification process use centroids, value, ambiguity and decision levels on fuzzy number developed from the parametric form of a generalized fuzzy number. The proposed method avoids reducing function to remove lower alpha levels and can overcome the shortcomings in some of the existing fuzzy ranking methods. The proposed method can effectively rank symmetric fuzzy numbers with the same core and different heights, fuzzy numbers with the same support and different cores, crisp numbers, crisp numbers having the same support and different heights, and fuzzy numbers having compensation of areas. A demonstration of the proposed method through examples and a comparative study with other methods in the literature shows that the proposed method gives effective results.

Lebesgue Decomposition Theorem and Weak Radon-Nikodým Theorem for Generalized Fuzzy Number Measures

The Lebesgue type decomposition theorem and weak Radon-Nikodým theorem for fuzzy valued measures in separable Banach spaces are established.