Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2011, Article ID 830764, 8 pages
http://dx.doi.org/10.1155/2011/830764
Research Article

On the Charting Procedures: Chart and DD-Diagram

Faculté des Sciences Economiques et de Gestion de Mahdia, Sidi Messoud, 5111 Mahdia, Tunisia

Received 6 August 2011; Revised 23 November 2011; Accepted 23 December 2011

Academic Editor: Shuen L. Jeng

Copyright © 2011 Mekki Hajlaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Multivariate analysis is increasingly used to include all dimensions of quality concept, in light of rapid development of customer requirements. With the recent advances in information technology and in recording, large amounts of multivariate data are now needed to be analyzed. Many charting procedures are based on Mahalanobis distance, but their applicability relies heavily on the requirement of normality and their performance is related to the choice of a type I error rate. An alternative charting scheme based on data depth is pursued and its performance is assessed through a real example. This performance and that of a chart for individual observations are discussed. Using the centre-outward ranking, this new method named DD-diagram is used to detect any multivariate quality datum that one of its components exceeds its limiting variation interval. For a given error-free sample, the DD-diagram can be used to signal out any point of another observed sample taken from a multivariate quality process. This new scheme based on data depth uses a properly chosen limiting variation line or in order to evaluate the outlyingness of every point in the observed sample in all directions of the considered -variates of quality process.