Kiani, Mehdi and Panaretos, John and Psarakis, Stelios (2008): A New Procedure to Monitor the Mean of a Quality Characteristic. Forthcoming in: Communications in Statistics B, (Simulation and Computation)

PDF
MPRA_paper_9066.pdf Download (118kB)  Preview 
Abstract
The Shewhart, Bonferroniadjustment and analysis of means (ANOM) control chart 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 noncentral t distribution. In this paper, 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.
Item Type:  MPRA Paper 

Original Title:  A New Procedure to Monitor the Mean of a Quality Characteristic 
Language:  English 
Keywords:  Shewhart, Bonferroniadjustment, Analysis of means, Average run length, False alarm probability 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General 
Item ID:  9066 
Depositing User:  J Panaretos 
Date Deposited:  11. Jun 2008 07:23 
Last Modified:  11. Feb 2013 20:02 
References:  Budsaba, K., Smith, C. E., and Riviere, J. E. (2000). Compass Plots: A Combination of Star Plot and Analysis of Means to Visualize Significant Interactions In Complex Toxicology Studies. Toxicology Mechanisms and Methods, Vol. 10, No. 4, pp. 313332. Chen, G. (1997). The Mean and Standard Deviation of the Run Length Distribution of Xbar Charts with Control Limits Are Estimated. Statistica Sinica, Vol. 7, pp. 789798. Halperin, M., Greenhouse, S. W., Cornfield, J., and Zalokar, J. (1955). Tables of Percentage Points for the Studentized Maximum Absolute Deviation in Normal Samples. Journal of American Statistical Association, Vol. 50, pp. 185195. Hawkins, D. M., Qiu, P., and Kang, C. W. (2003). The Changepoint Model for Statistical Process Control. Journal of Quality Technology, Vol. 35, No. 4, pp. 355366. Jensen, W. A., JonesFarmer, L. A., Champ, C. W., and Woodall, W. H. (2006). Effects of Parameter Estimation on Control Chart Properties: A Literature Review. Journal of Quality Technology, Vol. 38, No. 4, pp. 349364. Kang, L., and Albin, S. L. (2000). OnLine Monitoring When the Process Yields a Linear Profile. Journal of Quality Technology, Vol. 32, No. 4, pp. 418426. Maravelakis, P. E., Panaretos, J., and Psarakis, S. (2002). Effect of Estimation of the Process Parameter on the Control Limits of the Univariate Control Charts for Process Dispersion. Communications in Statistics: Simulation and Computation. Vol. 31, No. 3, pp. 443461. Montgomery, D. C. (2005). Introduction to Statistical Quality Control, 5th edition. John Wiley, New York. Nedumaran, G., and Pignatiello, J. J. (2005). On Constructing Retrospective Xbar Control Chart Limits. Quality and Reliability Engineering International, Vol. 21, pp. 8189. Nelson, P. R. (1982). Exact Critical Points for the Analysis of Means. Communications in Statistics: Theory and Methods, Vol. 11, pp. 699709. Nelson, P. R. (1988). Testing for interactions Using the Analysis of Means. Technometrics, Vol. 30, pp. 5361. Nelson, P. R. (1993). Additional Using for the Analysis of Means and Extended Tables of Critical Values. Technometrics, Vol. 35, No. 1. pp. 6171. Ott, E. R. (1967). Analysis of MeansA Graphical Procedure. Industrial Quality Control, Vol. 24, pp. 101109. Ott, E. R. (1975). Process Quality Control. McGrawHill Book Company, New York. Quesenberry, C. P. (1997). SPC Methods for Quality Improvement. John Wiley & Sons. Ramig, P. F. (1983). Applications of the Analysis of Means. Journal of Quality Technology, Vol. 15, pp. 1925. Rao, C. V. (2005). Analysis of MeansA Review. Journal of Quality Technology, Vol. 37, No. 4, pp. 308315. Rocke, D. M. (1989). Robust Control Chars. Technometrics, Vol. 31, No. 2, pp. 173184. Ryan, T. P. (1989). Statistical Methods for Quality Improvement. John Wiley & Sons. Schilling, E. G. (1973). A Systematic Approach to the Analysis of Means. Part I. Analysis of Treatment effects. Journal of Quality Technology, Vol. 5, pp. 93108. Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product, D. van Nostrand Co., New York. Smith. G. M. (1998). Statistical Process Control and Quality Improvement. PrenticeHall, Inc. Tsai, T. R., Lin, J. J., Wu, S. J., and Lin, H. C. (2005). On estimating Control Limits of Xbar Chart When the Number of Subgroups Is Small. International Journal of Advanced Manufacturing Technology, Vol. 26, pp. 13121316. Woodall, W. H. (2000). Controversies and Contradictions in Statistical Process Control: with discussion. Journal of Quality Technology, Vol. 32, pp. 341378. Woodall, W. H., Spitzner, D. J., Montgomery, D. C., and Gupta, S. (2004). Using Control Charts to Monitor Process and Product Quality Profiles. Journal of Quality Technology, Vol. 36, No. 3, pp. 309320. Wludyka, P. S., and Nelson, P. R. (1997). An AnalysisofMeansType Test for Variance from Normal Population. Technometrics, Vol. 39, pp. 274285. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/9066 