可变抽样区间几何 EWMA 控制图的经济设计

摘要

为了降低生产过程周期成本，本文对单位缺陷数服从几何分布时，可变抽样区间的指数加权移动平均（EWMA）控制图进行经济设计。首先建立可变抽样区间几何EWMA控制图的经济模型，使单位时间期望费用最小来确定参数的最优值；其次用遗传算法来寻找经济模型的最优解；最后对可变抽样区间几何EWMA控制图的经济模型进行灵敏度分析和最优性分析。研究结果表明单位时间期望费用分别随着异常原因发生的频率、过程失控时单位时间的质量费用、发现异常原因的时间期望值和纠正过程的时间期望值的增大而增大。%To reduce the production process cycle cost , the economic design of exponential weighted moving aver-age(EWMA)control chart with variable sampling intervals (VSI)under geometric distribution is discussed in this paper.First, the economic model of VSI EWMA control chart under geometric distribution is developed , the optimal values of the parameters will be determined such that the expected total cost is minimized .Further , the genetic algorithms will be used to search for the optimal values of the parameters of the VSI EWMA control chart under geometric distribution .Finally, the sensitivity analysis and optimality analysis of this model is done .The result of sensitivity analysis shows that the occurrences frequency of the assignable cause , the average quality cost per hour while producing out of control , expected time to discover the assignable cause and expected time to cor-rect the process significantly affect the average total cost .The larger the four model parameters respectively , the larger the average total cost .The economic design method which proposed in this paper can be applied to other VSI control charts .