VSS EWMA均值控制图和预防维修联合经济设计模型

Joint economic design model for VSS EWMA mean chart and planned maintenance

针对生产过程质量特性均值漂移由设备异常导致的可修系统,提出一种可变样本容量指数加权移动平均均值控制图和预防维修联合经济设计模型。在该模型中,系统被界定存在控制图误报警、正确报警、预防维修点到达3种更新情景;针对样本可变情况,分析得到了控制图两类错误期望概率;为避免平均失控运行长度带来的计算复杂等问题,以抽样间隔为基本分析单元代替传统方法的失、受控两阶段分析模式,建立了各更新事件期望周期成本和时长的函数表达式,进而构建了单位时间期望成本最小化决策模型,并与蒙特卡罗仿真方法进行了对比分析。应用实例分析结果表明,该模型能够较真实地反映生产系统实际运行状况,并可为系统优化分析提供支持。最后,对模型参数进行了灵敏度分析。

For the repairable system of process mean shift which caused by, failure, a joint economic design model for Variable Sampling Size Exponentially Weighted Moving Average （VSS EWMA） mean chart and Planned Mainte- nance （PM） was developed. In this model, three renewal-scenarios which were in-control alert signal, out-of-control alert signal and no alert signal were considered. The expected probability of Type- I error and Type- U error of VSS EWMA mean chart was obtained by Markov Process. To avoid computational difficulties and other issues resulting from the average runs length during out-of-control process, each scenario＇s cycle cost and cycle time were established by the anaiysis of each sampling interval process, instead of in-control process and out-of-control process in previous models. Furthermore, a mathematical model was given to minimize the expected cost per unit time. A Monte Carlo simulation experiment was conducted as comparison to ensure the analysis of the presented model. The results of a case indicated that the model had a satisfactory application performance and could optimize system＇s cost. A sensitiv- ity analysis was performed to demonstrate the effects of model parameters.