监测均值变动的多重控制图方法

本文证明了当受控平均运行长度充分大时, 多重控制图有两个优点: 一是相比较GLR (广义似然比) 和GEWMA (广义指数权重移动平均)控制图它可以大大降低运算的复杂性; 二是能够较快地监测均值变化的大小. 数值模拟也表明: 多重控制图不仅优于其构成的单个控制图, 而且在监测未知的均值变动方面也优于单个的CUSUM, EWMA, 多重EWMA和GLR控制图.

A Multi-Chart Approach for Mean Shift Detection

In this paper we consider a multi-chart for detecting a unknown shift in the mean of an identically distributed process. It is shown that the multi-chart has usually two advantages: one is in that it can much reduce computational complexity compared to the GLR (generalized likelihood ratio) and GEWMA (generalized exponentially weighted moving average) control charts when the in-control ARL (average run length) is large; the other is that it can quickly detect the size of the mean shift. Moreover, the numerical simulations show that the multi-chart can not only perform better than its constituent charts which consist of the multi-chart in the sense that the average of the ARLs of the constituent charts is large than that of the multi-chart, but also be superior on the whole to a single CUSUM, EWMA, EWMA multi-chart and GLR control charts in detecting the various mean shifts when the in-control ARL is not large.