In system design process, standby redundancy is a widely used technique to improve system reliability and availability. Typical standby techniques involve cold standby, hot standby, and warm standby. In this article, we investigate the repairable K-out-of-N system with mixed standby strategy containing both warm and cold standby. In the proposed system, each component can be in failure, cold, warm, and active states and the components are assumed to be repairable. The systems are modeled by continuous time Markov chain and the system long-run availability is derived. Furthermore, the optimal configuration of standby components in the system is studied considering both system availability and system running cost. Illustrative examples are presented to show the applications of the proposed model.

在系统设计过程中，备用冗余是提高系统可靠性和可用性的一种广泛使用的技术。典型的待机技术包括冷待机，热待机和热待机。在本文中，我们研究了可修复的K -of- N具有混合待机策略的系统，同时包含热待机和冷待机。在提出的系统中，每个组件都可以处于故障，冷，热和活动状态，并且假定这些组件是可修复的。通过连续时间马尔可夫链对系统进行建模，得出系统的长期可用性。此外，还考虑了系统可用性和系统运行成本，研究了系统中备用组件的最佳配置。给出了说明性示例以说明所提出模型的应用。