Abstract Multivariate control charts have a wide range of applications in the field of quality management. This paper proposes a new multivariate non-parametric control chart based on run test. First, the shortest Hamiltonian path of the observations is determined by means of Kruskal algorithm. Then an EWMA control chart with sliding window based on the number of runs of the shortest Hamiltonian path is proposed. The selection of the design parameters and the determination of control limit are discussed in detail. The effect of different dimensions, shift magnitude, reference data size and the underlying distribution are investigated via Monte Carlo simulation. Compared with three recent non-parametric multivariate control charts, the newly proposed chart has superior performance when mean shift magnitude is large and the underlying distribution is non-normal. Also, the chart proposed is more suitable for monitoring in high-dimensional situations. A real case study is also presented to show the implementation procedures of the chart.

中文翻译：

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基于运行检验的多元非参数控制图

摘要 多元控制图在质量管理领域有着广泛的应用。本文提出了一种新的基于运行检验的多元非参数控制图。首先，观测的最短哈密顿路径是通过 Kruskal 算法确定的。然后提出了一种基于最短哈密顿路径运行次数的带滑动窗口的EWMA控制图。详细讨论了设计参数的选择和控制极限的确定。通过蒙特卡罗模拟研究了不同维度、位移幅度、参考数据大小和基础分布的影响。与最近的三个非参数多元控制图相比，当均值偏移幅度较大且基础分布为非正态时，新提出的图表具有优越的性能。此外，所提出的图表更适合在高维情况下进行监控。还提供了一个真实的案例研究，以显示图表的实施程序。