Some properties of a linear combination CUSUM statistic for controlling a multivariate mean vector
- 作者：Ruojia Li ; Richard A. Johnson ; Sang-Hoon Cho
- 关键词：Average run length (ARL) ; Multivariate statistical process control
- 刊名：Journal of Statistical Planning and Inference
- 出版年：2007
- 期刊代码：36_03783758
- 类别：mt
- 出版时间：1 November 2007
- 卷：137
- 期：11
- 页码：3591-3600
- 文件大小：183 K
摘要
We develop a class of new multivariate procedures for monitoring quality by detecting a change in the level of a multivariate process. Following the ideas of S.N. Roy, we first consider a linear combination statistic which results from projecting the multivariate observations onto a unit vector and then maximizing a selected univariate statistic over all directions.
An application to a sheet metal assembly process is discussed in Section 3. Comparisons are made between one of our new procedures and other major multivariate quality monitoring schemes in Section 4. A small simulation study compares the average run lengths of the different procedures both when the process is in-control and after a shift has occurred. Some large sample properties are discussed in Section 5 and some computational details in Section 6.