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HEWMA Control Chart Using Auxiliary Information

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Abstract

A type of hybrid exponential weighted moving average (HEWMA) control chart is presented by using two-parametric ratio estimator to strengthen the performance of control chart for detecting shift in process mean at phase-II. Auxiliary information is incorporated by assuming the bivariate normal distribution for study variable Y and auxiliary variable X. Monte Carlo simulation method is used to calculate the average run length of the proposed control chart. In order to detect the small and moderate shift, the proposed control chart performed better than existing HEWMA control chart.

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Acknowledgment

The authors are grateful to the reviewers for their suggestions which helped in improving substantially, the earlier version of this article.

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Authors and Affiliations

  1. COMSATS Institute of Information Technology, Lahore, Pakistan

    Muhammad Noor-ul-Amin, Shahana Khan & Aamir Sanaullah

Authors
  1. Muhammad Noor-ul-Amin
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  2. Shahana Khan
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  3. Aamir Sanaullah
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Corresponding author

Correspondence to Muhammad Noor-ul-Amin.

Appendix

Appendix

Following tables show the ARLs of the MdHEWMA control chart at different correlations using α = 0.1414 (coefficient of variation) and β = 1.126 (mean deviation) (Tables 12, 13, and 14).

Table 12 ARLs (SDRL) of the proposed MdHEWMA control chart with time varying limits, ρXY = 0.05 and ARL0 = 500
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Table 13 ARLs (SDRL) of the proposed MdHEWMA control chart with time varying limits, ρXY = 0.5 and ARL0 = 500
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Table 14 ARLs (SDRL) of the proposed MdHEWMA control chart with time varying limits, ρXY = 0.8 and ARL0 = 500
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Following tables show the ARLs of the MdHEWMA control chart at different correlations using α = 0.135 (coefficient of quartile deviation) and β = 0.9537 (quartile deviation) (Tables 15, 16, and 17).

Table 15 ARLs (SDRL) of the proposed MdHEWMA control chart with time varying limits, ρXY = 0.05 and ARL0 = 500
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Table 16 ARLs (SDRL) of the proposed MdHEWMA control chart with time varying limits, ρXY = 0.5 and ARL0 = 500
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Table 17 ARLs (SDRL) of the proposed MdHEWMA control chart with time varying limits, ρXY = 0.8 and ARL0 = 500
Full size table

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Noor-ul-Amin, M., Khan, S. & Sanaullah, A. HEWMA Control Chart Using Auxiliary Information. Iran J Sci Technol Trans Sci 43, 891–903 (2019). https://doi.org/10.1007/s40995-018-0585-x

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  • DOI: https://doi.org/10.1007/s40995-018-0585-x

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