In this paper, we review different definitions that multi-state k-out-of-n systems have received along the literature and study them in a unified way using the algebra of monomial ideals. We thus obtain formulas and algorithms to compute their reliability and bounds for it. We provide formulas and computer experiments for simple and generalized multi-state k-out-of-n systems and for binary k-out-of-n systems with multi-state components.

中文翻译：

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多状态k个out-of - n系统的代数可靠性—勘误

在本文中，我们回顾了文献中收到的多态k out of of n系统的不同定义，并使用单项理想代数以统一的方式对其进行了研究。因此，我们获得了公式和算法来计算其可靠性和界限。我们为简单和广义的多状态k个out-of- n系统以及具有多状态分量的二进制k个out-of- n系统提供公式和计算机实验。