The reliability study of k-out-of-n systems is of interest both from theoretical and practical points of view. Applications of such models can be seen in many real-world phenomena, including telecommunication, transmission, transportation, manufacturing, and services. A probabilistic study of a real-world k-out-of-n system often helps to develop an optimal strategy for maintaining high system-level reliability. There are many investigations devoted to the reliability-centric analysis of such systems. We consider a mathematical model of a repairable k-out-of-n system that works until k of its n components have failed. During the system's life cycle, its components are repaired with the help of a single repair facility. It is supposed that the components' lifetimes have an exponential distribution and their repair times have a general distribution. The proposed model is intended to be applied to the description of operation of unmanned rotorcraft high-altitude platforms and to be validated with the help of an experimental prototype. For the considered system, we propose an algorithm for calculation of the reliability function, and for special cases, k = 2 and k = 3, its closed-form representation is given. A numerical investigation is performed for special cases. The obtained results are a first step toward the sensitivity analysis of reliability characteristics of k-out-of-n systems to the shape of the repair time distributions of their components.

中文翻译：

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具有一般维修时间分布的 K-OUT-OF-N 系统的可靠性函数

可靠性研究ķ-在......之外-n从理论和实践的角度来看，系统都是令人感兴趣的。这种模型的应用可以在许多现实世界的现象中看到，包括电信、传输、运输、制造和服务。对现实世界的概率研究ķ-在......之外-n系统通常有助于制定最佳策略，以保持高系统级可靠性。有许多研究致力于对此类系统进行以可靠性为中心的分析。我们考虑一个可修复的数学模型ķ-在......之外-n一直有效的系统ķ它的n组件发生故障。在系统的生命周期中，其组件在单一维修设施的帮助下进行维修。假设组件的寿命具有指数分布，并且它们的修复时间具有一般分布。所提出的模型旨在应用于无人驾驶旋翼机高空平台的操作描述，并在实验原型的帮助下进行验证。对于所考虑的系统，我们提出了一种计算可靠性函数的算法，对于特殊情况，ķ= 2 和ķ= 3，给出了它的闭式表示。针对特殊情况进行数值调查。获得的结果是对可靠性特性进行敏感性分析的第一步ķ-在......之外-n系统对其组件的修复时间分布的形状。