二项分布下VSI EWMA控制图的经济设计  

Economic design of variable sampling intervals EWMA control chart under binomial distributions

作　　者：薛丽 何桢[1] Xue Li;He Zhen(College of Management and Economics,Tianjin University,Tianjin 300072,China;School of Management Engineering,Zhengzhou University of Aeronautics,Zhengzhou 450046,China)

机构地区：[1]天津大学管理与经济学部,天津300072 [2]郑州航空工业管理学院管理工程学院,河南郑州450046

出　　处：《系统工程学报》2020年第5期711-720,共10页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(71701188,U1204702,71661147003,71672209,71871204);河南省高校科技创新人才支持计划资助项目(19HASTIT032);航空科学基金资助项目(2016ZG55021);中国博士后科学基金资助项目(2016M601266);河南省科技攻关计划资助项目(202102310638).

摘　　要：为了降低过程控制成本,同时提高监控不合格品数的效率,研究二项分布下可变抽样区间(VSI)指数加权移动平均(EWMA)控制图的经济设计问题.首先基于质量损失函数和预防维修策略,构建VSI二项EWMA控制图的联合经济模型;其次以期望损失函数最小为目标,运用遗传算法确定控制图设计参数的最优值;然后对所建立的联合经济模型进行灵敏度分析,得出期望损失函数随着单元抽样费用、过程波动和产品不合格时的损失的增大而增大.通过最优性分析得出基于联合经济模型设计的VSI二项EWMA控制图具有较小的单位时间期望损失成本,优于统计方法设计的VSI二项EWMA控制图.To reduce the costs for process control and improve the efficiency of monitoring unqualified products,the economic design of exponential weighted moving average(EWMA)control chart with variable sampling intervals(VSI)for monitoring binomial distribution is discussed in this paper.Firstly,an integrated economic model of VSI EWMA control chart based on the quality loss function and preventive maintenance is developed.Secondly,the optimal values of the parameters are determined such that the expected loss function is minimized,and genetic algorithms are used to search for the optimal values of the parameters.Further,sensitivity analysis is presented to illustrate the model,and the result shows that the fixed cost per sample,process shift and loss caused by nonconforming product significantly and positively affect the expected loss function.Finally,through a comparative study,it is concluded that the VSI EWMA control chart designed by the joint economic decision model has less unit time expected loss,and is superior to VSI EWMA control chart designed by traditional methods.

关 键 词：可变抽样区间 EWMA控制图 经济设计 质量损失函数 预防维修 

分 类 号：O213.1[理学—概率论与数理统计]