Multivariate Process Control Chart for Controlling the False Discovery Rate

  • Park, Jang-Ho (Department of Industrial and Management Engineering, POSTECH) ;
  • Jun, Chi-Hyuck (Department of Industrial and Management Engineering, POSTECH)
  • Received : 2012.11.19
  • Accepted : 2012.11.22
  • Published : 2012.12.30


With the development of computer storage and the rapidly growing ability to process large amounts of data, the multivariate control charts have received an increasing attention. The existing univariate and multivariate control charts are a single hypothesis testing approach to process mean or variance by using a single statistic plot. This paper proposes a multiple hypothesis approach to developing a new multivariate control scheme. Plotted Hotelling's $T^2$ statistics are used for computing the corresponding p-values and the procedure for controlling the false discovery rate in multiple hypothesis testing is applied to the proposed control scheme. Some numerical simulations were carried out to compare the performance of the proposed control scheme with the ordinary multivariate Shewhart chart in terms of the average run length. The results show that the proposed control scheme outperforms the existing multivariate Shewhart chart for all mean shifts.


Supported by : National Research Foundation of Korea


  1. Anderson, T. W. (1958), An Introduction to Multivariate Statistical Analysis, Wiley, New York, NY.
  2. Benjamini, Y. and Hochberg, Y. (1995), Controlling the false discovery rate: a practical and powerful approach to multiple testing, Journal of the Royal Statistical Society B Methodological, 57(1), 289- 300.
  3. Benjamini, Y. and Kling, Y. (1999), A look at statistical process control through the p-values, Research Paper: RP-SOR-99-08, Tel Aviv University, School of Mathematical Science, Israel.
  4. Hotelling, H. (1947), Multivariate quality control, illustrated by the air testing of sample bombsights. In: Eisenhart, C. (ed.), Selected Techniques of Statistical Analysis for Scientific and Industrial Research, and Production and Management Engineering, Mc- Graw-Hill Books, New York, NY.
  5. Lee, S. H. and Jun, C. H. (2010), A new control scheme always better than X-bar chart, Communications in Statistics-Theory and Methods, 39(19), 3492-3503.
  6. Lee, S. H. and Jun, C. H. (2012), A process monitoring scheme controlling false discovery rate, Communications in Statistics-Simulation and Computation, 41(10), 1912-1920.
  7. Li, Z., Qiu, P., Chatterjee, S., and Wang, Z. (2012), Using p values to design statistical process control charts, Statistical Papers, 1-17.
  8. MacGregor, J. F. and Kourti, T. (1995), Statistical process control of multivariate processes, Control Engineering Practice, 3(3), 403-414.
  9. Miller, R. G. (1981), Simultaneous Statistical Inference, Springer-Verlag, New York, NY.
  10. Montgomery, D. C. (2007), Introduction to Statistical Quality Control, Academic Internet Publishers, Ventura, CA.