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.

中文翻译：

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不确定加权 $k$ -Out-of- $n$ 系统的可靠性分析


不确定变量用于对人类不确定性下的量进行建模，加权 k-out-of-n 系统用于对 n 个组件的系统进行建模，当且仅当功能组件的总权重大于 k 时，该系统才起作用。考虑到人为操作系统的不确定性，将不确定变量引入到加权k-out-of-n系统中，提出不确定加权k-out-of-n系统的概念。推导了一些公式来计算此类系统的可靠性指标。作为概括，本文还研究了一个不确定的加权 k-out-of-n 系统，其权重由专家估计，并通过不确定变量而不是清晰的数字进行建模。此外，本文还分析了不确定加权k-out-of-n系统中各组成部分的重要性测度。