This work deals with the hesitant fuzzy number and averaging operator and fuzzy reliability with the help of Weibull lifetime distribution. Fuzzy reliability function and triangular hesitant fuzzy number also computed with α-cut set of the proposed reliability function. After applying the averaging operator of hesitant theory, the results are better than simple fuzzy. Also at last, a numerical example has been shown that how the hesitant fuzzy and α-cut work in case of reliability theory.
In this study, we have proposed a model of the sliding window coherent system in case of multiple failures. The considered model consists of G linearly required multi-state elements and G number of parallel elements in A-within-B-from-D/G for each multi-state. The system fails if at least A group elements out of B consecutive of D consecutive multi-state elements have performance lower than the weight w. We have evaluated the signature reliability, expected value and system sensitivity on the basis of the extended universal generating function of the considered system.
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