Fuzzy Reliability of Weighted-((f / (r, s)), k)/ (m, n) G System

Abstract

In this chapter, the authors study a weighted-((f / (r, s)), k)/ (m, n): G system. The system consists of mn components arranged in a matrix form and the system works if all the sub matrices of order (r, s), the total weight of the working components is greater than f and the total weight of the working components in the system is at least k. This chapter deals with the evaluation of fuzzy reliability and fuzzy mean time to failure of the considered system with the application of fuzzy universal generating function and fuzzy Rayleigh distribution. In this study, the authors formed some prepositions to understand the behaviour of the considered system with respect to different varying parameters and also present an illustrative example to understand them.