Abstract: In phased mission system, the environment and system requirements may change at different stages, and the working elements may fail at any stage, which brings challenges to the reliability analysis and modeling of the system. In order to increase the reliability of the system, a common design method is to configure standby components. Standby methods include hot standby, cold standby and warm standby. In hot standby mode, two or more systems deployed on different devices run simultaneously, one of them is the main working process, the other is the active standby process. When the working process fails, the standby process can take over the tasks of the working process immediately without requiring a start-up time. In order to achieve rapid takeover, hot standby mode needs to copy the tasks in the working process to thestandby process in real time. Using this kind of hot standby technology to ensure the reliability of the system also brings problems such as excessive energy consumption. The main disadvantage of cold standby is that it takes a long time to start the standby process to take over the task. Warm standby is the intermediate state between cold standby and hot standby. In standby state, energy consumption is lower than hot standby, and switching speed is higher than cold standby. From the point of view of reliability model, warm standby can be regarded as the promotion of hot standby and cold standby. The reliability modeling method of warm standby system can also be used in cold standby or hot standby system.
Multi-valued decision graph is a directed acyclic graph, which can reflect the relationship between component state and system state. Most of the existing studies only consider the multi-state of the system and use multi-value decision diagram to analyze the reliability of the system. Few literatures have studied the application of multivalued decision maps in phased mission system reliability analysis.
On the basis of the existing research, the problem of system reliability modeling is presented for phased mission systemwith warm standby components. In the reliability analysis of phased mission system with warm standby components, the multi-valued decision graph method is used to construct the reliability calculation formulas of components in different state distributions, and the model is applied through two examples. Finally, the results of the solution are compared with the simulation values, and the validity and accuracy of the model are verified by the comparison results. The reliability model constructed has certain guiding significance in improving the reliability of aviation systems, military equipment systems and other engineering systems with phased mission requirements.

Key words: phased mission system (PMS), warm standby component, multi-valued decision graph, system reliability