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Transforming the exponential by minimizing the sum of the absolute differences

Author

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  • Shih-Chou Kao
  • Chuan-Ching Ho
  • Ying-Chin Ho

Abstract

This work presents an optimal value to be used in the power transformation to transform the exponential to normality for statistical process control (SPC) applications. The optimal value is found by minimizing the sum of absolute differences between two distinct cumulative probability functions. Based on this criterion, a numerical search yields a proposed value of 3.5142, so the transformed distribution is well approximated by the normal distribution. Two examples are presented to demonstrate the effectiveness of using the transformation method and its applications in SPC. The transformed data are almost normally distributed and the performance of the individual charts is satisfactory. Compared to charts that use the original exponential data and probability control limits, the individual charts constructed using the transformed distribution are superior in appearance, ease of interpretation and implementation by practitioners.

Suggested Citation

  • Shih-Chou Kao & Chuan-Ching Ho & Ying-Chin Ho, 2006. "Transforming the exponential by minimizing the sum of the absolute differences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(7), pages 691-702.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:7:p:691-702
    DOI: 10.1080/02664760600708780
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    References listed on IDEAS

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    1. Zhenlin Yang & Min Xie, 2000. "Process monitoring of exponentially distributed characteristics through an optimal normalizing transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(8), pages 1051-1063.
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    Cited by:

    1. Bah, El-hadj M. & Ward, Jeremy, 2011. "Effectiveness of foreign aid in Small Island Developing States," MPRA Paper 32062, University Library of Munich, Germany.
    2. Maksim Belitski & Julia Korosteleva, 2011. "Entrepreneurship and Cities: Evidence from the Post-communist World," WIFO Working Papers 397, WIFO.
    3. Shih-Chou Kao, 2010. "Normalization of the origin-shifted exponential distribution for control chart construction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1067-1087.

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