Nowadays, networks (systems) appear in many areas of science and technology. One of the most important strategies to reduce the likelihood of the failure of an operating network is preventive maintenance (PM). In this article, we propose some optimal PM models for a network consisting of n, n ≥ 1, links (components). The criteria of interest are the “cost function” of renewing the network and “stationary availability” of the network during its mission. In the first part of the article, we consider the case that the network is formed of identical components while in the second part, we deal with the case that the network is built up from several nonidentical groups of components. In both parts, we utilize the PM under some partial information about the status of the network at a time t. The results of the article are developed using the notions of signature and survival signature. To interpret the proposed models, the results are illustrated numerically and graphically for two networks.

中文翻译：

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可修复网络的最佳预防性维护

如今，网络（系统）出现在许多科技领域。降低运行网络故障可能性的最重要策略之一是预防性维护 (PM)。在本文中，我们为由n , n  ≥ 1 链接（组件）组成的网络提出了一些最佳 PM 模型。感兴趣的标准是更新网络的“成本函数”和网络在其任务期间的“固定可用性”。在文章的第一部分，我们考虑网络由相同的组件组成的情况，而在第二部分，我们处理网络是由几个不同的组件组构成的情况。在这两个部分中，我们一次使用了一些关于网络状态的部分信息下的 PM吨。本文的结果是使用签名和生存签名的概念开发的。为了解释所提出的模型，结果以数字和图形方式说明了两个网络。