Some research has been developed to handle aleatory and epistemic uncertainty in various engineering systems. But in this paper, we have established two methods, namely mass distribution and fuzzy reliability theory, to deal with these uncertainties in non-repairable k-out-ofn: G (F) systems, which has not been seen in the past. In the presented methodology, the failure rate (λ) is taken as a trapezoidal fuzzy number. Using the trapezoidal fuzzy number, expression for α-cut of fuzzy failure rate of every component and corresponding fuzzy reliability function has been calculated. Then, masses to the components are distributed with the help of these fuzzy reliability functions. By using these masses, reliability and MTTF of the considered systems have been computed. At last, a numerical example is taken to demonstrate the present approach.
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.
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