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Improved control chart for statistical process control using combined X and delayed EWMA statistics

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Abstract

In this paper, we propose a new combination of X and EWMA charts in which we intentionally delay the EWMA statistic one lag to make it independent of X. The intentional delay of EWMA induces a power loss in detecting abnormality. However, owing to the independence of two control statistics, the new chart is much easier to set the in-control average run length at the aimed level than the existing combinations. We numerically show how simple to design the new chart and also show that the new chart performs as well as the existing charts in out-control average run length. Finally, we apply it to the cyber-attack detection problem from the NSL-KDD dataset.

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Data availability

The data used in this study are openly available at https://www.unb.ca/cic/datasets/nsl.html.

References

  • Albin, S. L., Kang, L., & Shea, G. (1997). An X and EWMA chart for individual observations. Journal of Quality Technology, 29, 41–44.

    Article  Google Scholar 

  • Crowder, S. V. (1989). Design of exponentially weighted moving average schemes. Journal of Quality Technology, 21(2), 155–162.

    Article  Google Scholar 

  • Capizzi, G., & Masarotto, G. (2003). An adaptive exponentially weighted moving average control chart. Technometrics, 45, 199–207.

    Article  MathSciNet  Google Scholar 

  • Capizzi, G., & Masarotto, G. (2010). Evaluation of the run-length distribution for a combined Shewhart-EWMA control chart. Statistics and Computing, 20, 23–33.

    Article  MathSciNet  MATH  Google Scholar 

  • Duncan, A. J. (1956). The economic design of X charts used to maintain current control of a process. Journal of American Statistical Associations, 51, 228–242.

    MATH  Google Scholar 

  • Klein, M. (1996). Composite Shewhart-EWMA statistical control schemes. IIE Transactions, 28, 475–481.

    Article  Google Scholar 

  • Klein, M. (1997). Modified Shewhart-exponentially weighted moving average chart. IIE Transactions, 29, 1051–1056.

    Article  Google Scholar 

  • Li, Z., Zou, C., Gong, Z., & Wang, Z. (2014). The computation of average run length and average time to signal: an overview. Journal of Statistical Computation and Simulation, 84(8), 1779–1802.

    Article  MathSciNet  MATH  Google Scholar 

  • Liu, C. S., & Tien, F. C. (2011). A single-featured EWMA-X control chart for detecting shifts in process mean and standard deviation. Journal of Applied Statistics, 38(11), 2575–2596.

    Article  MathSciNet  MATH  Google Scholar 

  • Lucas, J. M. (1982). Combined Shewhart-CUSUM quality control schemes. Journal of Quality Technology, 14(2), 51–59.

    Article  Google Scholar 

  • Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: properties and enhancements. Technometrics, 32, 1–12.

    Article  MathSciNet  Google Scholar 

  • Montgomery, D. C. (2009). Introduction to Statistical Quality Control (6th ed.). New York: John Wiley & Sons.

    MATH  Google Scholar 

  • Qiu, P. (2014). Introduction to Statistical Process Control. CRC Press.

    Google Scholar 

  • Reynolds, M. R., Jr., & Stoumbos, Z. G. (2004). Should observations be grouped for effective process monitoring? Journal of Quality Technology, 36, 343–366.

    Article  Google Scholar 

  • Shamsuzzaman, M., Khoo, M. B. C., Haridy, S., & Alsyouf, I. (2016). An optimization design of the combined Shewhart-EWMA control chart. The International Journal of Advanced Manufacturing Technology, 86, 1627–1637.

    Article  Google Scholar 

  • Sklavounous, D., Leondakianakos, A., & Edoh, A. (2019). Statistical process control method for cyber intrusion detection (DDoS, U2R, R2L, Probe). International Journal of Cyber-Security and Digital Forensics, 8(1), 82–88.

    Article  Google Scholar 

  • Tolley, G. O., & English, J. R. (2001). Economic designs of constrained EWMA and combined EWMA-\({\bar{X}}\) control schemes. IIE Transactions, 33, 429–436.

    Article  Google Scholar 

  • Tavallaee, M., Bagheri, E., Lu, W. & Ghorbani, A. A. (2009). A detailed analysis of the KDD CUP 99 data set Proceedings of the 2009 IEEE Symposium on Computational Intelligence in Security and Defense Applications.

  • Woodall, W. H., & Mahmoud, M. A. (2005). The inertial properties of quality control charts. Technometrics, 47(4), 425–436.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We thank the two anonymous reviewers for their valuable comments improving the paper’s quality. This work was supported by National Research Foundation of Korea under Grant [No. NRF-2021R1A2C1010786, NRF-2019R1A2C1003257] and Samsung Electronics Co., Ltd. under Grant [No. IO201209-07860-01].

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Authors and Affiliations

  1. Department of Statistics, Seoul National University, Seoul, Korea

    Johan Lim

  2. Department of Statistics, Dankook University, Gyeonggi-do, Korea

    Sungim Lee

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  1. Johan Lim
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  2. Sungim Lee
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Correspondence to Sungim Lee.

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Lim, J., Lee, S. Improved control chart for statistical process control using combined X and delayed EWMA statistics. J. Korean Stat. Soc. 52, 944–959 (2023). https://doi.org/10.1007/s42952-023-00231-6

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