Improved data driven control charts

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

Research output: Book/ReportReportProfessional

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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 When normality fails, these control charts are no longer valid and serious errors often arise.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
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages10
Publication statusPublished - 2006

Publication series

NameApplied Mathematics Memoranda
PublisherDepartment of Applied Mathematics, University of Twente
No.1791
ISSN (Print)0169-2690

Keywords

  • IR-65596
  • EWI-2690
  • MSC-62G32
  • MSC-62G30
  • MSC-62P30
  • METIS-230991

Cite this

Albers, WW., & Kallenberg, W. C. M. (2006). Improved data driven control charts. (Applied Mathematics Memoranda; No. 1791). Enschede: University of Twente, Department of Applied Mathematics.
Albers, Willem/Wim ; Kallenberg, W.C.M. / Improved data driven control charts. Enschede : University of Twente, Department of Applied Mathematics, 2006. 10 p. (Applied Mathematics Memoranda; 1791).
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author = "Willem/Wim Albers and W.C.M. Kallenberg",
year = "2006",
language = "Undefined",
series = "Applied Mathematics Memoranda",
publisher = "University of Twente, Department of Applied Mathematics",
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Albers, WW & Kallenberg, WCM 2006, Improved data driven control charts. Applied Mathematics Memoranda, no. 1791, University of Twente, Department of Applied Mathematics, Enschede.

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

Enschede : University of Twente, Department of Applied Mathematics, 2006. 10 p. (Applied Mathematics Memoranda; No. 1791).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Improved data driven control charts

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

PY - 2006

Y1 - 2006

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 - MSC-62P30

KW - METIS-230991

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BT - Improved data driven control charts

PB - University of Twente, Department of Applied Mathematics

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Albers WW, Kallenberg WCM. Improved data driven control charts. Enschede: University of Twente, Department of Applied Mathematics, 2006. 10 p. (Applied Mathematics Memoranda; 1791).