基于变点模型的非参数控制图设计与应用

Dseign and Application of Nonparametric Control Chart Based on Change-point Model

在传统控制图的设计原理中,往往假定过程观测数据来自某一标准分布,而实际中,过程分布有可能未知或者很难获取。针对这种情况,文章提出了基于变点模型的非参数控制图(简称为SW-控制图):首先推导证明了Wilcoxon秩和统计量的数学性质;其次设计了非参数控制图,并利用蒙特卡洛抽样法进行计算机模拟,结果显示SW-控制图与标准化的次序秩控制图(简称为SR-控制图)相比,SW-控制图不仅提高了对小漂移的检测效率,而且比SR-控制图更稳健;最后,结合实例来说明SW-控制图在实际中的应用。

In the design principle of traditional control charts, it is often assumed that the process observation data comes from a standard distribution, but in practice, the process distribution may be unknown or difficult to obtain. In view of this, this paper proposes a nonparametric control chart(SW-control chart for short) based on change-point model. Firstly, the paper deduces and proves the mathematical properties of Wilcoxon rank-sum statistics, and then designs a nonparametric control diagram. Finally, the paper uses Monte Carlo sampling method for computer simulation. The results show that compared with the standardized order rank control chart(SR-control chart for short), the SW-control chart not only improves the detection efficiency of small drift, but is more robust. Finally, an example is given to illustrate the application of SW-control chart in practice.