On some multivariate control charts

[摘要] To maintain the quality of a product or to improve the reliability of a process, all industries need to monitor several parameters about their production process. Control charts are some visualization tools for monitoring processes statistically. In this work, we propose a few control charting schemes to monitor several characteristics of a process at the same time and to detect when it goes out of control. Our objective is to reduce the false alarms (the scheme detects a problem when actually there is none) as well as to quickly detect the correct out-of-control situation. The novelty of the proposed schemes are that they do not depend on commonly assumed Normal distribution of the process variables and is applicable for a much wider range of data distributions. At first, we make a detailed literature review of some univariate and multivariate control charts. We perform a comparison study of the commonly used multivariate control charts when the underlying distribution is not normal and show that they perform poorly giving a very high false alarm rate. Next we propose some nonparametric multivariate control charts based on the lengths of the multivariate rank vectors. The ideas are similar to the ones proposed by Liu (1995), however, we show that our proposed methods are computationally simpler in any dimension. We propose some more multivariate versions of Shewhert type, CUSUM and EWMA control charts based on spatial sign vectors and signed rank vectors. We also discuss several design parameters in the construction of these charts. None of the proposed charts depend on the assumption of underlying distribution or estimation of distributional parameters.

[发布机构] University:University of Birmingham;Department:School of Mathematics

[关键词] Q Science;QA Mathematics;QA75 Electronic computers. Computer science