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- Title
A Distribution-Free Multivariate Control Chart for Phase I Applications.
- Authors
Cheng, Ching‐Ren; Shiau, Jyh‐Jen Horng
- Abstract
The purpose of this paper is to provide a novel distribution-free control chart for monitoring the location parameter vector of a multivariate process in phase I analysis. To be robust to the process distribution, the spatial sign statistic that defines the multivariate direction of an observation is used to construct a Shewhart-type control chart for detecting out-of-control observations in historical phase I data. The proposed control chart is distribution free in the sense that the false-positive rate (or false alarm rate), the proportion of wrongly classified in-control samples, can be controlled at the specified value for elliptical-direction distributions. In addition, we demonstrate through simulation studies that the false-positive rate of the proposed chart is robust to the shift size of the out-of-control condition if we only delete the most extreme out-of-control observation at each iteration of phase I analysis. Compared with the traditional Hotelling's T2 control chart and some of its robust versions, the proposed chart is generally more powerful in detecting out-of-control observations and more robust to the normality assumption. Copyright © 2014 John Wiley & Sons, Ltd.
- Subjects
NONPARAMETRIC statistics; MULTIVARIATE analysis; QUALITY control charts; MATHEMATICAL statistics; FALSE positive error
- Publication
Quality & Reliability Engineering International, 2015, Vol 31, Issue 1, p97
- ISSN
0748-8017
- Publication type
Article
- DOI
10.1002/qre.1751