联合监控均值和方差的累积和控制图优化设计

The Optimal Design of CUSUM Charts for Joint Monitoring Mean and Variance

为了提高监测均值和方差微小偏移的敏感度,围绕生产过程质量控制,建立同时监控均值和方差的累积和控制图。模型考虑均值和方差的变化,针对生产过程中的微小偏差,提出了一个新的累积和控制图,并给出了基于马尔可夫链理论的新控制图的平均链长计算方法。编程求解后对比文献中各控制图的平均链长数据以及更换变量数值改进控制图,通过计算变动比率得出新控制图的检测力度在不同偏移力度下都明显优于其他控制图方法。

A key challenge in designing control schemes is how to strengthen the sensitivity to detect inconspicuous shifts effeetively in the production process. By considering small shifts in the process mean and process variance simultaneously, a new control chart is developed based on the semi--circle control chart and cumulative sum chart. Markov chain method is used to analyze the average run length and optimal parameters of the proposed chart. The calculation of RARL shows that proposed CUSUM-SC chart has obviously better detecting power at different small shifts in the mean and standard deviation than the existing control charts.