IJPAM: Volume 37, No. 3 (2007)


Willem Albers$^1$, Wilbert C.M. Kallenberg$^2$
$^{1,2}$Department of Applied Mathematics
Faculty of Electrical Engineering, Mathematics and Computer Science
University of Twente
P.O. Box 217, AE Enschede, 7500, THE NETHERLANDS
$^1$e-mail: w.albers@math.utwente.nl
$^2$e-mail: w.c.m.kallenberg@math.utwente.nl

Abstract.Classical control charts for monitoring the mean are based on the assumption of normality. When normality fails, these control charts are no longer valid and serious errors often arise. Data driven control charts, which choose between the normal chart, a parametric one and a nonparametric chart, have recently been proposed to solve the problem. They also correct for estimation errors due to estimation of the parameters involved or, in the nonparametric chart, for estimation of the appropriate quantiles of the distribution. In many cases these data driven control charts are performing very well. However, when the data point towards the nonparametric chart no satisfactory solution is obtained unless the number of Phase I observations is very large. The problem is that accurate estimation of an extreme quantile in a nonparametric way needs a huge number of observations. Replacing the nonparametric individual chart by a nonparametric chart for grouped observations does the job. These improved data driven control charts are presented here. Ready-made formulas are given, which make implementation of the charts quite straightforward. An application on real data clearly shows the improvement: estimation of extreme quantiles is replaced by estimation of ordinary quantiles, which can be done in an accurate way for common sample sizes.

Received: April 4, 2007

AMS Subject Classification: 62P30, 62G32, 62G30

Key Words and Phrases: statistical process control, Phase II control limits, order statistics, unbiasedness, exceedance probability, nonparametric, model selection, minimum control chart

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 3