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Using one EWMA chart to jointly monitor the process mean and variance

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Abstract

Two control charts are usually used to monitor the process mean and variance separately. The mean is monitored using the \({\bar{{X}}}\) chart while the variance using either the standard deviation, S chart, or the range, R chart. Recently, numerous single variable charts are proposed to jointly monitor the mean and variance. Most approaches transform the sample mean and sample variance into two statistics, each having a standard scale, and either plotting them on the same chart or combining them into a single statistic to be plotted on a chart. The R chart is more widely used than the S chart but no attempt is made to combine the \({\bar{{X}}}\) and R charts in the construction of a single variable chart and to study its properties and performance. In this paper, we transform the \({\bar{{X}}}\) and R statistics into two standard normal random variables, used in the computation of two corresponding exponentially weighted moving average (EWMA) statistics, which are then merged into a single plotting statistic for the proposed chart, called the EWMA \({\bar{{X}}-R}\) chart.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Minden, Penang, Malaysia

    Michael Boon Chong Khoo & Kah Wai Yeong

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Nanyang, 639798, Singapore

    Zhang Wu

  3. Department of Management and Information Technology, Southern Taiwan University, 1 Nan-Tai Street, Yung-Kang City, Tainan, 710, Taiwan

    Chung-Ho Chen

Authors
  1. Michael Boon Chong Khoo
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  2. Zhang Wu
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  3. Chung-Ho Chen
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  4. Kah Wai Yeong
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Correspondence to Michael Boon Chong Khoo.

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Khoo, M.B.C., Wu, Z., Chen, CH. et al. Using one EWMA chart to jointly monitor the process mean and variance. Comput Stat 25, 299–316 (2010). https://doi.org/10.1007/s00180-009-0177-5

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  • DOI: https://doi.org/10.1007/s00180-009-0177-5

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