A New Procedure to Monitor the Mean of a Quality Characteristic

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.

[1]  Lan Kang,et al.  On-Line Monitoring When the Process Yields a Linear Profile , 2000 .

[2]  Jim E. Riviere,et al.  COMPASS PLOTS: A COMBINATION OF STAR PLOT AND ANALYSIS OF MEANS TO VISUALIZE SIGNIFICANT INTERACTIONS IN COMPLEX TOXICOLOGY STUDIES , 2000 .

[3]  J. Cornfield,et al.  Tables of Percentage Points for the Studentized Maximum Absolute Deviate in Normal Samples , 1955 .

[4]  Ronald D. Fricker.  Statistical Process Control and Quality Improvement , 2000, Technometrics.

[5]  C. Rao,et al.  Analysis of Means—A Review , 2005 .

[6]  Enrique del Castillo,et al.  SPC Methods for Quality Improvement , 1999, Technometrics.

[7]  Ellis R. Ott,et al.  Analysis of Means--A Graphical Procedure , 1983 .

[8]  William H. Woodall,et al.  Controversies and Contradictions in Statistical Process Control , 2000 .

[9]  Peter R. Nelson,et al.  Process Quality Control , 1991 .

[10]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[11]  Edward G. Schilling.  A Systematic Approach to the Analysis of Means, Part I. Analysis of Treatment Effects , 1973 .

[12]  Douglas M. Hawkins,et al.  The Changepoint Model for Statistical Process Control , 2003 .

[13]  Tzong-Ru Tsai,et al.  On estimating control limits of X ̄ chart when the number of subgroups is small , 2005 .

[14]  Douglas C. Montgomery,et al.  Using Control Charts to Monitor Process and Product Quality Profiles , 2004 .

[15]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[16]  Peter R. Nelson,et al.  Additional Uses for the Analysis of Means and Extended Tables of Critical Values , 1993 .

[17]  Peter R. Nelson,et al.  Exact critical points for the analysis of means , 1982 .

[18]  Joseph J. Pignatiello,et al.  On Constructing Retrospective ―X Control Chart Limits , 2005 .

[19]  S. Psarakis,et al.  EFFECT OF ESTIMATION OF THE PROCESS PARAMETERS ON THE CONTROL LIMITS OF THE UNIVARIATE CONTROL CHARTS FOR PROCESS DISPERSION , 2002 .

[20]  Charles W. Champ,et al.  Effects of Parameter Estimation on Control Chart Properties: A Literature Review , 2006 .

[21]  P. F. Ramig,et al.  Applications of the Analysis of Means , 1983 .

[22]  Lora S. Zimmer,et al.  Statistical Process Control and Quality Improvement , 2002, Technometrics.

[23]  Minitab.  Statistical Methods for Quality Improvement , 2001 .

[24]  Peter R. Nelson,et al.  An analysis-of-means-type test for variances from normal populations , 1997 .

[25]  Peter R. Nelson,et al.  Testing for interactions using the analysis of means , 1988 .

[26]  David M. Rocke.  Robust control charts , 1989 .

[27]  Edward G. Schilling,et al.  A Systematic Approach to the Analysis of Means, Part II. Analysis of Contrasts, Part III. Analysis of Non-Normal Data , 1973 .

[28]  William H. Woodall,et al.  Introduction to Statistical Quality Control, Fifth Edition , 2005 .