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：

---

多态 k-out-of-n 系统的代数可靠性

在本文中，我们回顾了多状态的不同定义ķ-在......之外-n系统已经收到了文献，并使用单项式理想的代数以统一的方式对其进行了研究。因此，我们获得了计算其可靠性和界限的公式和算法。我们为简单和广义的多态提供公式和计算机实验ķ-在......之外-n系统和二进制ķ-在......之外-n具有多状态组件的系统。