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The performance of the Shewhart-RZ control chart in the presence of measurement error

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  • K.P. Tran
  • P. Castagliola
  • G. Celano

Abstract

Recent literature about quality control has investigated the continuous surveillance of the ratio of two normal random variables under the assumption of no measurement error. However, in practice, measurement errors always exist in quality control applications and may considerably affect the performance of control charts. In this paper, the performance of the Shewhart-RZ control chart is investigated in the presence of a measurement error and modelled by a linear covariate error model. Several figures and tables are generated and commented to show the statistical performance of the Shewhart-RZ control chart for different sources of the measurement error. Two examples illustrate the use of this chart on a quality control problem simulated from the food industry and a real industrial case from a plant treating batteries for recyclement.

Suggested Citation

  • K.P. Tran & P. Castagliola & G. Celano, 2016. "The performance of the Shewhart-RZ control chart in the presence of measurement error," International Journal of Production Research, Taylor & Francis Journals, vol. 54(24), pages 7504-7522, December.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:24:p:7504-7522
    DOI: 10.1080/00207543.2016.1198507
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    References listed on IDEAS

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    1. Jack Hayya & Donald Armstrong & Nicolas Gressis, 1975. "A Note on the Ratio of Two Normally Distributed Variables," Management Science, INFORMS, vol. 21(11), pages 1338-1341, July.
    2. Petros Maravelakis & John Panaretos & Stelios Psarakis, 2004. "EWMA Chart and Measurement Error," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(4), pages 445-455.
    3. Antonio F. B. Costa & Philippe Castagliola, 2011. "Effect of measurement error and autocorrelation on the X¯ chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 661-673, December.
    4. Petros E. Maravelakis, 2012. "Measurement error effect on the CUSUM control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 323-336, May.
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    Cited by:

    1. Nguyen, H.D. & Tran, K.P. & Tran, K.D., 2021. "The effect of measurement errors on the performance of the Exponentially Weighted Moving Average control charts for the Ratio of Two Normally Distributed Variables," European Journal of Operational Research, Elsevier, vol. 293(1), pages 203-218.
    2. Wenhui Liu & Zhonghua Li & Zhaojun Wang, 2022. "Monitoring of Linear Profiles Using Linear Mixed Model in the Presence of Measurement Errors," Mathematics, MDPI, vol. 10(24), pages 1-17, December.

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