A fuzzy universal generating function-based method for the reliability evaluation of series systems with performance sharing between adjacent units under parametric uncertainty

This paper considers fuzzy multi-state systems (MSSs) with performance sharing between adjacent units, in which each fuzzy multi-state unit has a random performance and a random demand. If the performance of a unit exceeds its individual demand (performance > demand), its surplus performance can be transmitted to its adjacent unit that experiences performance deficiency (performance < demand). The performance/demand of a unit is represented by the performance/demand levels and the corresponding state probabilities. It is usually difficult to estimate the precise state probabilities due to the inaccuracy and insufficiency of data, therefore, fuzzy state probabilities are given instead of precise state probabilities. This paper proposes a fuzzy universal generating function (FUGF)-based method to evaluate the fuzzy reliability of series systems with performance sharing between adjacent units considering the parametric uncertainty related to the state probabilities of the performance/demand levels of units. The originality of this work lies in two aspects: i) the surplus performance of a unit can only be shared with its adjacent units which experience deficiency; ii) the parametric uncertainty related to the state probabilities is considered. An illustrative example is provided to validate the proposed method.