Improved data driven control charts

Willem/Wim Albers, W.C.M. Kallenberg

Research output: Contribution to journalArticleAcademicpeer-review

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 When normality fails, these control charts are no longer valid and serious errors often arise.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.
Original languageUndefined
Pages (from-to)423-439
Number of pages17
JournalInternational journal of pure and applied mathematics
Volume37
Issue number3
Publication statusPublished - 2007

Keywords

  • EWI-10752
  • MSC-62G30
  • MSC-62G32
  • MSC-62P30
  • METIS-241774
  • IR-61842
  • unbiasedness
  • Minimum control chart
  • Model selection
  • Nonparametric
  • Statistical Process Control
  • Phase II control limits
  • Order statistics
  • Exceedance probability

Cite this

Albers, WW., & Kallenberg, W. C. M. (2007). Improved data driven control charts. International journal of pure and applied mathematics, 37(3), 423-439.
Albers, Willem/Wim ; Kallenberg, W.C.M. / Improved data driven control charts. In: International journal of pure and applied mathematics. 2007 ; Vol. 37, No. 3. pp. 423-439.
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Albers, WW & Kallenberg, WCM 2007, 'Improved data driven control charts' International journal of pure and applied mathematics, vol. 37, no. 3, pp. 423-439.

Improved data driven control charts. / Albers, Willem/Wim; Kallenberg, W.C.M.

In: International journal of pure and applied mathematics, Vol. 37, No. 3, 2007, p. 423-439.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Improved data driven control charts

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

N1 - eemcs-eprint-10752

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

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KW - Nonparametric

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KW - Phase II control limits

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