基于随机系数增长模型的状态维修与EPQ联合优化

针对生产和维修计划共享生产设备的问题,建立了经济生产批量和设备状态监测维修的联合优化模型.运用随机系数增长模型描述设备的退化状态,每完成一个生产批量就对设备进行状态监测.监测到的设备状态由设备的实际状态和监测误差构成,当监测状态达到或超过预防性维修阈值时,需要对设备进行预防性维修并更新,当实际状态达到故障阈值时,设备故障停机,需对设备进行故障维修并更新.基于两种更新情况,建立了更新周期内的费用和周期长度模型,并进一步运用更新回报定理建立了单位时间期望费用模型,通过对模型进行优化,可得到预防性更新状态阈值和每个批量的生产时间两个决策变量的最优取值.最后,通过国内某钢厂轧钢设备的数据资料对模型进行了数值分析,分析结果和实际情况相符合.

Joint optimization of condition-based maintenance and EPQ based on the random coefficient growth model

A joint optimization model of economic production quantity and condition-based maintenance policy is proposed in this paper, considering the situation that the production plan and maintenance schedule share the same machine. Using the random coefficient growth model to describe the degenerated condition, the condition monitoring is carried out when a lot is finished. The observed condition composed of two parts, the actual deterioration condition and the random error, once the condition information observed is equal to or higher than the preventive maintenance level, or the actual condition is equal to the failure level, the machine should be renewed. The cost and the length model in the renewal cycle are proposed, then the expected cost per unit time is modeled based on the renewal reward theory. The optimal condition of preventive maintenance level and production time of one lot can be calculated by minimizing the expected cost per unit time. Numerical examples are presented based on the data collected from a steel mill, the results are consistent with the actual situation.