Methodol Comput Appl Probab (2006) 8: 409–426 DOI 10.1007/s11009-006-9754-z Improving the Performance of the Chi-square Control Chart via Runs Rules Markos V. Koutras · Sotirios Bersimis · Demetrios L. Antzoulakos Received: 7 February 2005 / Revised: 8 August 2005 / Accepted: 13 September 2005 © Springer Science + Business Media, LLC 2006 Abstract The most popular multivariate process monitoring and control procedure used in the industry is the chi-square control chart. As with most Shewhart-type control charts, the major disadvantage of the chi-square control chart, is that it only uses the information contained in the most recently inspected sample; as a consequence, it is not very efficient in detecting gradual or small shifts in the process mean vector. During the last decades, the performance improvement of the chi- square control chart has attracted continuous research interest. In this paper we introduce a simple modification of the chi-square control chart which makes use of the notion of runs to improve the sensitivity of the chart in the case of small and moderate process mean vector shifts. Keywords Multivariate statistical quality control · Chi-square control chart · Average run length · Runs rules AMS 2000 Subject Classification 62N10 1 Introduction Process-monitoring pertaining to the simultaneous control of two or more dependent variables (quality characteristics) is usually referred in the literature as multivariate M. V. Koutras (B ) · S. Bersimis · D. L. Antzoulakos Department of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, Greece e-mail: mkoutras@unipi.gr S. Bersimis e-mail: sbersim@unipi.gr D. L. Antzoulakos e-mail: dantz@unipi.gr