基于可用度的预防维修和均值控制图联合优化模型

For production systems with high availability requirements (i.e., repairable systems, hereinafter referred to as the system), a joint optimization model of preventive maintenance and mean control charts is proposed, with the unit time cost as a constraint and the maximization of availability as the goal. Firstly, considering that there are two states of the system operation, namely, in control and out of control, as well as the probabilities of two types of errors (missing alarm and false alarm) of the mean control chart, under the assumption of perfect maintenance, four system operation (renewal) scenarios (S1 - S4) are constructed. Then, the availability and economic models for each renewal scenario are established, and on this basis, the availability objective function and the economic constraint function of the system are established to achieve the goal of maximizing the system availability through the joint optimization of preventive maintenance and mean control charts under the constraint of unit time cost. For the established joint optimization model, the effectiveness of the model is verified through example comparison, and the decision variables are optimized using a genetic algorithm. The example optimization results show that this model can effectively improve the system availability and reduce the system cost. Finally, the sensitivity analysis of the model parameters is carried out through methods such as orthogonal experiments and regression analysis.

针对高可用度要求的生产系统(即可修复系统,以下简称系统),提出一种以单位时间成本为约束,可用度最大化为目标的预防维修和均值控制图联合优化模型。首先,考虑到系统运行存在受控、失控两种状态以及均值控制图两类错误(漏报警和误报警)发生的概率,在完美维修假设前提下,构建了4种系统运行(更新)情景(S1~S4)。然后,建立了每种更新情景的可用度和经济模型,并在此基础上建立了系统的可用度目标函数和经济约束函数,以实现单位时间成本约束条件下预防维修和均值控制图联合优化的系统可用度最大化目标。针对所建立的联合优化模型,通过实例对比验证了模型的有效性,并利用遗传算法对决策变量进行优化,实例优化结果表明,该模型能够有效提高系统可用度,并能降低系统成本。最后,通过正交试验、回归分析等方法对模型进行了参数的灵敏度分析。