随机工作时长下并联系统替换策略

Replacement First and Last for a Parallel System within a Random Working Cycle

为了分析一个有随机工作时长要求的n个单元并联系统的最优替换策略,假设系统要求的随机工作时长Y服从一定的分布,如果系统崩溃,则立即进行事后替换,否则在固定的时点T进行预防替换。考虑两种预防替换策略:F-替换和L-替换,其中F-替换即随机工作时长任务完成与时点T先到达的时点替换,L-替换即随机工作时长任务完成与时点T后到达的时点替换,分别得到单位时间期望费用率和使期望费用率达到最低的最佳固定时长T*。同时,对F-替换和L-替换策略进行比较,可以发现:随着CT/CF的增加,L-替换递略可以节省更多的替换成本。

This paper observes optimal replacement times for a parallel system with n units when it is operating for successive jobs with a random working cycle. The classical ″whichever occurs first″ and the newly proposed ″whichever occurs last″ are respectively employed for replacements scheduled at time T and working cycle Y,whose policies are called F-replacement and L-replacement. F-replacement is the first replacement time that the long task completion of the random work and the point of time T. L-replacement is the last replacement time that the long task completion of the random work and the point of time L. We obtain their expected replacement cost rates and the optimal fixed length T＊ for the expected cost rate to the lowest minimum. Further,comparison of F-replacement and L-replacement are described： L-replacement can save more replacement cost.