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      Univariate X̄ control charts for individual characteristics in a multinormal model

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      Author
      Serel, D. A.
      Moskowitz, H.
      Tang, J.
      Date
      2000
      Source Title
      IIE Transactions
      Print ISSN
      0740-817X
      Electronic ISSN
      1545-8830
      Publisher
      Taylor & Francis
      Volume
      32
      Issue
      12
      Pages
      1115 - 1125
      Language
      English
      Type
      Article
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      Abstract
      The early work on multivariate statistical process control was built upon Hotelling's T2 control chart which was developed to simultaneously monitor the means of correlated quality variables. This chart, however, has a drawback, namely, the problem of identifying the responsible variable(s) when an out-of-control signal occurs. One alternative is to use a separate X̄ control chart for each individual characteristic with equal risks, based on Bonferroni inequality. In this study, we show that, from an economic perspective, it may be desirable to have unequal type I risks for the individual charts, because of different inspection and restoration costs associated with each variable. We obtain their risk ratios, which are measures of relative importance of the variables monitored. Then, based on these risk ratios, we develop computer algorithms for finding the exact control limits for individual variables from a multinormal distribution, in the sense that the overall type I risk of the charts is equal to the desired value. Numerical studies show that the proposed methods give optimal or near-optimal results from an economic as well as statistical point of view.
      Keywords
      Algorithms
      Cost effectiveness
      Inspection
      Mathematical models
      Probability distributions
      Quality control
      Statistical methods
      Bonferroni inequality
      Control charts
      Multinormal distribution
      Univariate Shewhart charts
      Statistical process control
      Permalink
      http://hdl.handle.net/11693/24950
      Published Version (Please cite this version)
      http://dx.doi.org/10.1023/A:1007640732394
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