基于延迟几何过程的可修劣化系统最优更换策略

摘要

A delayed geometric process is proposed after studying the general geometric process methods used in replacement policies modeling for degenerative repairable systems. A system is supposed to be returned to the "as good as former" state with probability p and returned to the "worse" state with probability q. The average cost rate of the system is given under policy N based on the delayed geometric process, and the optimal replacement policy is derived. Numerical examples are also used to validate the replacement policy after comparison with that under the general geometric process.%研究了可修劣化系统的更换策略,对劣化系统建模常用的几何过程加以改进,提出了延迟几何过程的概念,认为系统维修后以概率p恢复至前一修复状态,而以概率q发生劣化.选择系统的故障次数N为更换策略,利用延迟几何过程建立了系统长期运行的平均费用率模型,并给出了系统最优更换策略的解析表达.最后给出了数值算例并将结果和基于传统几何过程的更换策略进行了比较,验证了该方法的合理性.