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Bivariate control charts with double sampling

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  • A. F. B. Costa
  • M. A. G. Machado

Abstract

In this article, we consider the T2 chart with double sampling to control bivariate processes (BDS chart). During the first stage of the sampling, n1 items of the sample are inspected and two quality characteristics (x; y) are measured. If the Hotelling statistic [image omitted] for the mean vector of (x; y) is less than w, the sampling is interrupted. If the Hotelling statistic [image omitted] is greater than CL1, where CL1>w, the control chart signals an out-of-control condition. If [image omitted] , the sampling goes on to the second stage, where the remaining n2 items of the sample are inspected and [image omitted] for the mean vector of the whole sample is computed. During the second stage of the sampling, the control chart signals an out-of-control condition when the statistic [image omitted] is larger than CL2. A comparative study shows that the BDS chart detects process disturbances faster than the standard bivariate T2 chart and the adaptive bivariate T2 charts with variable sample size and/or variable sampling interval.

Suggested Citation

  • A. F. B. Costa & M. A. G. Machado, 2008. "Bivariate control charts with double sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 809-822.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:7:p:809-822
    DOI: 10.1080/02664760802061939
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    References listed on IDEAS

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    1. He, David & Grigoryan, Arsen, 2006. "Joint statistical design of double sampling and s charts," European Journal of Operational Research, Elsevier, vol. 168(1), pages 122-142, January.
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    4. De Magalhaes, Maysa S. & B. Costa, Antonio F. & Moura Neto, Francisco D., 2006. "Adaptive control charts: A Markovian approach for processes subject to independent disturbances," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 236-246, February.
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    6. Costa, A.F.B. & Rahim, M.A., 2006. "The non-central chi-square chart with two-stage samplings," European Journal of Operational Research, Elsevier, vol. 171(1), pages 64-73, May.
    7. Chao-Yu Chou & Chung-Ho Chen & Hui-Rong Liu, 2006. "Economic Design of EWMA Charts with Variable Sampling Intervals," Quality & Quantity: International Journal of Methodology, Springer, vol. 40(6), pages 879-896, December.
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    1. A. F.B. Costa & M. A.G. Machado, 2011. "A control chart based on sample ranges for monitoring the covariance matrix of the multivariate processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 233-245, September.

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