Communications in Statistics—Simulation and Computation ® , 37: 1870–1880, 2008 Copyright © Taylor & Francis Group, LLC ISSN: 0361-0918 print/1532-4141 online DOI: 10.1080/03610910802296588 Quality Control A New Procedure to Monitor the Mean of a Quality Characteristic M. KIANI, J. PANARETOS, AND S. PSARAKIS Department of Statistics, Athens University of Economics and Business, Athens, Greece The Shewhart, Bonferroni-adjustment, and analysis of means (ANOM) control charts are typically applied to monitor the mean of a quality characteristic. The Shewhart and Bonferroni procedure are utilized to recognize special causes in production process, where the control limits are constructed by assuming normal distribution for known parameters (mean and standard deviation), and approximately normal distribution regarding to unknown parameters. The ANOM method is an alternative to the analysis of variance method. It can be used to establish the mean control charts by applying equicorrelated multivariate non central t distribution. In this article, we establish new control charts, in phases I and II monitoring, based on normal and t distributions having as a cause a known (or unknown) parameter (standard deviation). Our proposed methods are at least as effective as the classical Shewhart methods and have some advantages. Keywords Analysis of means; Average run length; Bonferroni-adjustment; False alarm probability; Shewhart. Mathematics Subject Classification 62P30; 62E15. 1. Introduction The Shewhart, the Bonferroni-adjustment, and the analysis of means control charts are common techniques for monitoring the process mean. Shewhart (1931) proposed a scheme for detecting out-of-control signals and shifts in the mean from its target value  0 . Ott (1975), Rocke (1989), Ryan (1989), Chen (1997), Quesenberry (1997), Smith (1998), Maravelakis et al. (2002), Woodall et al. (2004), Montgomery (2005), and several others modified and extended the Shewhart control charts. The Shewhart procedure usually is based on at least 20–25 sample group sizes k and at least 4–6 sample subgroup sizes n. This procedure with known mean and standard deviation parameters is based on a random variable that follows the normal distribution. When the mean and standard deviation are unknown, Received October 13, 2006; Accepted May 23, 2008 Address correspondence to J. Panaretos, Department of Statistics, Athens University of Economics and Business, 76 Patision St., Athens 104 34, Greece; E-mail: jpan@aueb.gr 1870 Downloaded By: [HEAL-Link Consortium] At: 11:14 3 December 2008