This paper studies a system with n multi-state components, when the number of failed components reaches k, the system fails. During system operation, all non-failed components perform all missions simultaneously. A static mission allocation strategy and a partial mission abandonment strategy are explored. Among them, static mission allocation mainly refers to the allocation of system missions in a fixed proportion according to the performance of components, while partial mission abandonment represents the selection of an appropriate time to give up some missions for the mission system that can be classified according to the characteristics of importance. The study adopts the Markov process to deduce the system reliability and mission execution success probability, and explores the balance between them according to a cost-oriented partial mission abandonment strategy. A distributed computer system is taken as an example to show the feasibility of the model application, and an optimal strategy is provided for the optimization of partial mission abandonment strategy for a system characterized by missions can be graded in the analysis.