Abstract

This article considers an one-unit multi-state system with a general α-series process and an order-replacement policy. It is supposed that the working times of the system after repair become shorter and shorter, while the repair times of the system become longer and longer. Further, an ordering policy N − 1 and a replacement policy N is adopted. After the Nth repair, the system is replaced by an identical new one, and the unit for replacement is immediately ordered at the end of the $(N-1)$ th repair. Some important properties of the system are derived by using the probability theory and the stochastic process theory. In addition, the explicit expression for the long-run expected cost function is developed to search the optimal order-replacement policy.

摘要

本文考虑了具有一般α系列过程和订单替换策略的单单元多状态系统。可以认为，维修后系统的工作时间越来越短，而系统的维修时间越来越长。此外，排序策略ñ  - 1和替代政策ñ被采用。第N次维修后，用相同的新系统替换该系统，并在维修结束时立即订购要更换的单元。$（ñ-\mathrm{1个}）$修理。利用概率论和随机过程理论推导了系统的一些重要性质。此外，还开发了长期预期成本函数的显式表达式，以搜索最佳订单替换策略。