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A distribution-free multivariate CUSUM control chart using dynamic control limits

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  • Wenjuan Liang
  • Xiaolong Pu
  • Dongdong Xiang

Abstract

In modern quality control, it is becoming common to simultaneously monitor several quality characteristics of a process with rapid evolving data-acquisition technology. When the multivariate process distribution is unknown and only a set of in-control data is available, the bootstrap technique can be used to adjust the constant limit of the multivariate cumulative sum (MCUSUM) control chart. To further improve the performance of the control chart, we extend the constant control limit to a sequence of dynamic control limits which are determined by the conditional distribution of the charting statistics given the sprint length. Simulation results show that the novel control chart with dynamic control limits offers a better ARL performance, compared with the traditional MCUSUM control chart. Despite it, the proposed control chart is considerably computer-intensive. This leads to the development of a more flexible control chart which uses a continuous function of the sprint length as the control limit sequences. More importantly, the control chart is easy to implement and can reduce the computational time significantly. A white wine data illustrates that the novel control chart performs quite well in applications.

Suggested Citation

  • Wenjuan Liang & Xiaolong Pu & Dongdong Xiang, 2017. "A distribution-free multivariate CUSUM control chart using dynamic control limits," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2075-2093, August.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:11:p:2075-2093
    DOI: 10.1080/02664763.2016.1247784
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    References listed on IDEAS

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    1. Han, Dong & Tsung, Fugee, 2006. "A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 368-386, March.
    2. Xiaobei Shen & Changliang Zou & Wei Jiang & Fugee Tsung, 2013. "Monitoring poisson count data with probability control limits when sample sizes are time varying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 625-636, December.
    3. Margavio, Thomas M. & Conerly, Michael D. & Woodall, William H. & Drake, Laurel G., 1995. "Alarm rates for quality control charts," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 219-224, August.
    4. Qin Zhou & Changliang Zou & Zhaojun Wang & Wei Jiang, 2012. "Likelihood-Based EWMA Charts for Monitoring Poisson Count Data With Time-Varying Sample Sizes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1049-1062, September.
    5. Liu, Yafen & He, Zhen & Shu, Lianjie & Wu, Zhang, 2009. "Statistical computation and analyses for attribute events," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3412-3425, July.
    6. Bersimis, Sotiris & Psarakis, Stelios & Panaretos, John, 2006. "Multivariate Statistical Process Control Charts: An Overview," MPRA Paper 6399, University Library of Munich, Germany.
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