聯合多維管制圖

Abstract

本文提出一種新的聯合多維管制圖，只要隨機變數的聯合機率密度函數已知即可應用此管制圖。這解決了當今現存的多維管制圖普遍都只應用在多維常態分配上的不足。此管制圖與2005年 Chen, Cheng and Xie 提出的二維常態分配平均移動管制圖具有相當的競爭性。當隨機變數的聯合機率密度函數為未知時，可利用模擬方法建造近似聯合多維管制圖。本文也提出有關於這兩個聯合多維管制圖的平均連串長度之研究。

A new combined control chart for multivariate distribution is proposed. This control chart may be applied on any distribution that its joint probability density function in terms of a random sample is known its distribution while the existed multivariate control charts are generally designed only for multivariate normal distribution. A comparison of this chart with a moving average control chart by Chen, Cheng and Xie (2005) for bivariate normal distribution shows that it is very competitive. When the joint probability density function is not known in its distribution, an approximate combined chart is proposed. Studies of ARLs for these two charts are performed and displayed.