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New EWMA control charts for monitoring the Weibull shape parameter.

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Title: New EWMA control charts for monitoring the Weibull shape parameter.
Authors: Huwang, Longcheen1 (AUTHOR) huwang@stat.nthu.edu.tw, Lin, Li‐Wei1 (AUTHOR)
Source: Quality & Reliability Engineering International. Oct2020, Vol. 36 Issue 6, p1872-1894. 23p.
Subjects: Quality control charts, Random variables, Weibull distribution, Maximum likelihood statistics, Point processes, Unbiased estimation (Statistics), Change-point problems
Abstract: In this article, we first propose a new exponentially weighted moving average (EWMA) chart for monitoring the shape parameter of the Weibull distribution. The proposed chart is developed based on the EWMA of the normal random variable, which is transformed from the easy‐to‐understand chi‐squared random variable. In contrast, the existing EWMA charts for monitoring the shape parameter use the sample range or the unbiased estimator of the shape parameter. Unfortunately, the EWMA chart generated from sample ranges is inefficient in detecting changes due to its lack of sufficiency, whereas the one produced using unbiased estimators of the shape parameter has a highly complicated distribution that is difficult to manipulate. Simulation studies are conducted to compare the effectiveness of the proposed EWMA chart and the two existing EWMA charts. Also, a maximum likelihood estimation method is employed to estimate the change point in the process for the proposed EWMA chart once an out‐of‐control (OC) signal has been triggered. Further, to reduce the time for detecting the OC signal, an EWMA chart with variable sampling intervals (VSIs) for monitoring the shape parameter is developed based on the proposed EWMA chart. This EWMA chart with VSIs is studied, and its performance is evaluated. Finally, an example to demonstrate the applicability and implementation of the proposed charts is provided. [ABSTRACT FROM AUTHOR]
Copyright of Quality & Reliability Engineering International is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 146200599
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  Data: New EWMA control charts for monitoring the Weibull shape parameter.
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  Data: <searchLink fieldCode="AR" term="%22Huwang%2C+Longcheen%22">Huwang, Longcheen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> huwang@stat.nthu.edu.tw</i><br /><searchLink fieldCode="AR" term="%22Lin%2C+Li‐Wei%22">Lin, Li‐Wei</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Quality+%26+Reliability+Engineering+International%22">Quality & Reliability Engineering International</searchLink>. Oct2020, Vol. 36 Issue 6, p1872-1894. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Quality+control+charts%22">Quality control charts</searchLink><br /><searchLink fieldCode="DE" term="%22Random+variables%22">Random variables</searchLink><br /><searchLink fieldCode="DE" term="%22Weibull+distribution%22">Weibull distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Point+processes%22">Point processes</searchLink><br /><searchLink fieldCode="DE" term="%22Unbiased+estimation+%28Statistics%29%22">Unbiased estimation (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Change-point+problems%22">Change-point problems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this article, we first propose a new exponentially weighted moving average (EWMA) chart for monitoring the shape parameter of the Weibull distribution. The proposed chart is developed based on the EWMA of the normal random variable, which is transformed from the easy‐to‐understand chi‐squared random variable. In contrast, the existing EWMA charts for monitoring the shape parameter use the sample range or the unbiased estimator of the shape parameter. Unfortunately, the EWMA chart generated from sample ranges is inefficient in detecting changes due to its lack of sufficiency, whereas the one produced using unbiased estimators of the shape parameter has a highly complicated distribution that is difficult to manipulate. Simulation studies are conducted to compare the effectiveness of the proposed EWMA chart and the two existing EWMA charts. Also, a maximum likelihood estimation method is employed to estimate the change point in the process for the proposed EWMA chart once an out‐of‐control (OC) signal has been triggered. Further, to reduce the time for detecting the OC signal, an EWMA chart with variable sampling intervals (VSIs) for monitoring the shape parameter is developed based on the proposed EWMA chart. This EWMA chart with VSIs is studied, and its performance is evaluated. Finally, an example to demonstrate the applicability and implementation of the proposed charts is provided. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Quality & Reliability Engineering International is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1002/qre.2663
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 23
        StartPage: 1872
    Subjects:
      – SubjectFull: Quality control charts
        Type: general
      – SubjectFull: Random variables
        Type: general
      – SubjectFull: Weibull distribution
        Type: general
      – SubjectFull: Maximum likelihood statistics
        Type: general
      – SubjectFull: Point processes
        Type: general
      – SubjectFull: Unbiased estimation (Statistics)
        Type: general
      – SubjectFull: Change-point problems
        Type: general
    Titles:
      – TitleFull: New EWMA control charts for monitoring the Weibull shape parameter.
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      – PersonEntity:
          Name:
            NameFull: Huwang, Longcheen
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          Name:
            NameFull: Lin, Li‐Wei
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          Dates:
            – D: 01
              M: 10
              Text: Oct2020
              Type: published
              Y: 2020
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              Value: 36
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              Value: 6
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            – TitleFull: Quality & Reliability Engineering International
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