Optimisation of a set of or principal components control charts using genetic algorithms

Abstract

When a multivariate process is to be monitored, there are the options of employing a set of univariate control charts or a single multivariate chart. This paper shows how to effectively design a multivariate control scheme consisting of two or three X charts, using genetic algorithms to optimise the charts parameters. The procedure is implemented using software tools, which we designed. A complete performance comparison of the scheme with the Hotelling's T ² control chart can be made in order to help the user in choosing the most adequate option for the process under consideration. Also, if the user prefers to employ charts based on principal components rather than on the original variables, the software can be used in the same way to optimise a set of two or three control charts based on these components, and to compare their performance with the performance of the T ² chart on the principal components.

Keywords:

• control chart
• optimisation
• multiple
• genetic algorithms

Acknowledgments

This work has been supported by the Ministry of Education and Science of Spain, research project number DPI2006-06124, including European FEDER funding, and the support of the ITESM-Foundation Carolina agreement, and also by CNPq (the Brazilian Council for Scientific and Technological Development), project number 201811/2007-3.