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Process monitoring of exponentially distributed characteristics through an optimal normalizing transformation

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  • Zhenlin Yang
  • Min Xie

Abstract

Many process characteristics follow an exponential distribution, and control charts based on such a distribution have attracted a lot of attention. However, traditional control limits may be not appropriate because of the lack of symmetry. In this paper, process monitoring through a normalizing power transformation is studied. The traditional individual measurement control charts can be used based on the transformed data. The properties of this control chart are investigated. A comparison with the chart when using probability limits is also carried out for cases of known and estimated parameters. Without losing much accuracy, even compared with the exact probability limits, the power transformation approach can easily be used to produce charts that can be interpreted when the normality assumption is valid.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:8:p:1051-1063
    DOI: 10.1080/02664760050173373
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    References listed on IDEAS

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    1. Linguo Gong & Wushong Jwo & Kwei Tang, 1997. "Using On-Line Sensors in Statistical Process Control," Management Science, INFORMS, vol. 43(7), pages 1017-1028, July.
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    Cited by:

    1. Shih-Chou Kao & Chuanching Ho, 2007. "Monitoring a Process of Exponentially Distributed Characteristics through Minimizing the Sum of the Squared Differences," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(1), pages 137-149, February.
    2. Fatimah Alshahrani & Ibrahim M. Almanjahie & Majid Khan & Syed M. Anwar & Zahid Rasheed & Ammara N. Cheema, 2023. "On Designing of Bayesian Shewhart-Type Control Charts for Maxwell Distributed Processes with Application of Boring Machine," Mathematics, MDPI, vol. 11(5), pages 1-20, February.
    3. 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.
    4. 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.
    5. Nandini Das, 2011. "Control Charts Based on the g-and-h Distribution," Stochastics and Quality Control, De Gruyter, vol. 26(1), pages 3-14, January.

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