角度平均方向合向量长度控制图

Mean direction-resultant length control charts for angle specifications in directional data

现行国际标准和等同采用该标准的中国国家标准中的计量值控制图不能直接用于圆周闭域(0,2π]上的角度统计过程控制。该文研究总体质量特性值服从V on M ises分布M(μ0,k)的角度质量控制问题。基于平均方向和合向量长度的抽样分布,研究反映角度过程集中程度的合向量长度控制图和反映角度过程集中位置的平均方向控制图。给出子组大小为4时不同的刻度参数所对应的控制图的控制界限,以及平均方向-合向量长度控制图的实施步骤。研究结果使得应用控制图方法解决角度质量控制问题成为可能。

International and Chinese standard control charts for the specification of angles in direction data can not be applied directly for statistical process control for angles in the range （0, 27π]. A quality control system was developed for angles with a Von Miaea distribution M（μ0, k）. Sampling distributions of mean direction and resultant length were used to develop control charts respectively reflecting the central tendencies and positions of the angle process. The control limits of the mean direction-resultant length control charts for different concentration parameters were given when sample size was chosen to be four. The results can be used to apply control charts for production quality control for angle data.