修理工单重定期休假可修系统更换模型研究  

Research on Replacement Model for Repairable System Considering its Repairman Having Single Regular Vacations

作　　者：贾积身[1] 巴玉强[2] 张清叶[3] 

机构地区：[1]河南机电高等专科学校科研处,河南新乡453002 [2]郑州职业技术学院基础教育处,河南郑州450121 [3]河南机电高等专科学校基础部,河南新乡453002

出　　处：《数学的实践与认识》2014年第19期207-215,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(70473037);河南省自然科学基金(0611054400)

摘　　要：针对修理工带有单重休假的单部件可修系统,提出了一种新的维修更换模型.假定系统是可修的,逐次故障后的维修时间构成随机递增的几何过程,系统工作时间构成随机递增的几何过程,在修理工休假时间为定长的情况下,分别选取系统的总工作时间T和故障维修次数N为更换策略,以长期运行单位时间内的期望效益为目标函数,通过更新过程和几何过程理论建立数学模型,导出了目标函数的解析表达式,通过最大化目标函数来获取系统最优的更换策略T*和N*.并在一定条件下给出了策略N比策略T优的充分条件.最后,通过数值例子验证了方法的有效性.To study one unit repairable system with single repairman vacation, this paper proposes a kind of new maintenance and replacement model. Supposing that the system is repairable, the successive survival time of the system constitute a decreasing geometric process stochastically, while the consecutive repair time of the system constitute an increasing geometric process, under the conditions that the repairman vacation time is constant, we consider respectively replacement policy based on the working age Tand the failure number Nfor the system and choose the long--run expected profit per unit time as objective function, and establish mathematic models by using renewal process and geometric process theory, the explicit expressions of the objective function is derived, the optimal replacement policyT＊and. N＊ are obtained by maximizing the objective function. Under the conditions, we can derive that the policy N is better than the policy T. Finally, one numerical example is given to validate the effectiveness of the method.

关 键 词：可修系统 定期休假 总工作时间 故障次数 期望效益 几何过程 

分 类 号：N945.17[自然科学总论—系统科学]