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Measurement Error Effect on the Power of Control Chart for the Ratio of Two Poisson Distributions

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  • Chakraborty Ashit B.

    (1St. Anthony's College, Shillong, Meghalaya, India)

  • Khurshid Anwer

    (2Department of Mathematical and Physical Sciences, College of Arts and Science, University of Nizwa, P.O. Box 33, PC 616, Birkat Al Mouz, Oman)

Abstract

It is widely recognized that measurement errors often exist in practice and may considerably affect the performance of control charts in some cases. Measurement error variability has uncertainty which may be originated from several sources. Recently, Chakraborty and Khurshid [3] studied the effects of measurement error on control charts for zero-truncated Poisson distribution. In this paper, we study the effect of the two sources of variability on the power characteristics of control charts and obtain the values of average run length (ARL) for the binomial distribution based on the ratio of two Poisson distributions as studied by Sahai and Khurshid [20]. Expression of the power of the control chart under the standardized normal variable for the binomial distribution is also derived when the underlying distribution is the ratio of two Poisson distributions.

Suggested Citation

  • Chakraborty Ashit B. & Khurshid Anwer, 2013. "Measurement Error Effect on the Power of Control Chart for the Ratio of Two Poisson Distributions," Stochastics and Quality Control, De Gruyter, vol. 28(1), pages 15-21, October.
    • Handle: RePEc:bpj:ecqcon:v:28:y:2013:i:1:p:15-21:n:3
    DOI: 10.1515/eqc-2013-0008
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    References listed on IDEAS

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    1. 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.
    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. Yang Su-Fen & Ho Han-Wei & Rahim M. A., 2007. "Effects of Measurement Error on Controlling Two Dependent Process Steps," Stochastics and Quality Control, De Gruyter, vol. 22(1), pages 127-139, January.
    4. Dietmar Stemann & Claus Weihs, 2001. "The EWMA-X-S-control chart and its performance in the case of precise and imprecise data," Statistical Papers, Springer, vol. 42(2), pages 207-223, April.
    5. 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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