基于游程检验的多元非参控制图

本文提出了一个新的基于游程检验的多元非参控制图。首先，运用Kruskal算法的思想，将观测值排列成最短汉密尔顿路径；其次，基于最短汉密尔顿路径中的游程数设计带有滑动窗口的EWMA结构控制图，记为HAMEWMA控制图。通过蒙特卡洛随机方法对HAMEWMA控制图在不同条件(维度的高低，均值漂移的程度，受控数据量大小以及观测数据遵循的分布)下的控制效果进行研究，并与其他多元非参控制图(DFEWMA、SREWMA、SSEWMA、RTC)进行比较。结果表明：当均值漂移较大时，HAMEWMA控制图有更优秀的监控性能；当数据分布为非正态时，HAMEWMA控制图同样表现良好甚至优于数据分布为正态时；HAMEWMA控制图更适用于高维度的监控环境。

A Distribution Free Multivariate Control Chart Based on Run Test

A new distrbution free multivariate control chart based on run test is proposed. First, the shortest Hamilton path of the observations is determined by means of Kruskal algorithm, a new EWMA control chart with sliding window (HAMEWMA) is based on the number of runs of the above shortest Hamilton path. Monte Carlo simulation is used to study the control effect of HAMEWMA control chart under different conditions (dimensions, mean shift, controlled sample size and distributions of observations). Compared with some non-parametric multivariate control charts (DFEWMA, SREWMA, SSEWMA, RTC), HAMEWMA has a superior performance. The results show that: when mean shift is large, HAMEWMA has a better monitoring performance. When distributions are non-normal, HAMEWMA also performs well, even better than when the distribution is normal. Last but not the least, the HAMEWMA chart is more suitable for monitoring in high-dimensional situations