Reliability Analysis of Uncertain Weighted $k$ -Out-of-$n$ Systems

The uncertain variable is used to model a quantity under human uncertainty, and the weighted k-out-of-n system is used to model a system of n components, which functions if and only if the total weights of functioning components is greater than k. Considering the human uncertainty in operating the system, this paper introduces the uncertain variable to the weighted k-out-of-n system, and proposes a concept of uncertain weighted k-out-of-n system. Some formulas are derived to calculate the reliability index of such a system. As a generalization, this paper also studies an uncertain weighted k-out-of-n system whose weights are estimated by experts and modeled by uncertain variables instead of crisp numbers. In addition, this paper analyzes the importance measure of the components in the uncertain weighted k-out-of-n systems.