带有辅助样本的X控制图经济设计

Economic design of Xcontrol chart with supplementary samples

针对异常因素产生时间服从指数分布的过程,采用带有辅助样本的X(SSX)控制图监控过程质量特性的均值和方差,研究了SSX控制图的经济性能。构建了SSX控制图监控生产过程的费用函数模型;采用模式搜索算法对费用函数模型进行寻优,得到SSX控制图的最优决策变量、平均调整时间及费用,并比较了SSX、均值极差和变采样间隔均值极差控制图的经济性能。仿真结果表明,SSX控制图比均值极差控制图能够明显缩短平均调整时间和减小控制图的监控费用,且在大部分的偏移大小下,SSX控制图的经济性能都要优于变采样间隔均值极差控制图;对参数的灵敏度进行分析,结果表明模型中参数变化对采样间隔、控制图的控制限系数都有一定影响。

Aiming at the occurrence time of assignable cause follows exponential distribution,a Supplementary Sample X(SSX)control chart was used to monitor the mean value and variance of process quality feature,and the economic performance of SSX control chart was researched.The cost function model for implementation of SSX control chart was constructed,and the pattern search algorithm was used to optimize this model.Thus the decision variables,Average Adjusted Time to Signal(AATS)and cost of SSX control chart were obtained,and the economic performance between SSX,XRand Variable Sampling Interval(VSI)XRcontrol chart was compared.The simulations revealed that the average adjustment time and monitoring costs of SSX chart were reduced obviously than XR,and SSX control chart was better than VSI XR under most cases of shifts.A sensitivity analysis of the model was performed,and the results showed that the sampling intervals and control limits of SSX control chart were affected by the parameters in the cost function.