Publication Cover
Journal of Quality Technology
A Quarterly Journal of Methods, Applications and Related Topics
Volume 55, 2023 - Issue 4
192
Views
0
CrossRef citations to date
0
Altmetric
Article

Phase I analysis of high-dimensional processes in the presence of outliers

ORCID Icon, &

References

  • Abdella, G. M., K. N. Al-Khalifa, S. Kim, M. K. Jeong, E. A. Elsayed, and A. M. Hamouda. 2017. Variable selection-based multivariate cumulative sum control chart. Quality and Reliability Engineering International 33 (3):565–78. doi: 10.1002/qre.2041.
  • Ahmadi-Javid, A., and M. Ebadi. 2021. A two-step method for monitoring normally distributed multi-stream processes in high dimensions. Quality Engineering 33 (1):143–55. doi: 10.1080/08982112.2020.1786118.
  • Bai, Z., and H. Saranadasa. 1996. Effect of high dimension: By an example of a two sample problem. Statistica Sinica 6:311–29.
  • Bersimis, S., S. Psarakis, and J. Panaretos. 2007. Multivariate statistical process control charts: An overview. Quality and Reliability Engineering International 23 (5):517–43. doi: 10.1002/qre.829.
  • Capizzi, G., and G. Masarotto. 2011. A least angle regression control chart for multidimensional data. Technometrics 53 (3):285–96. doi: 10.1198/TECH.2011.10027.
  • Capizzi, G., and G. Masarotto. 2015. Comparison of phase II control charts based on variable selection methods. Frontiers in Statistical Quality Control 11:151–62. Springer International Publishing.
  • Chenouri, S. E., S. H. Steiner, and A. M. Variyath. 2009. A multivariate robust control chart for individual observations. Journal of Quality Technology 41 (3):259–71. doi: 10.1080/00224065.2009.11917781.
  • Croux, C., and G. Haesbroeck. 1999. Influence function and efficiency of the minimum covariance determinant scatter matrix estimator. Journal of Multivariate Analysis 71 (2):161–90. doi: 10.1006/jmva.1999.1839.
  • Ebadi, M., S. Chenouri, D. K. Lin, and S. H. Steiner. 2022. Statistical monitoring of the covariance matrix in multivariate processes: A literature review. Journal of Quality Technology 54 (3):269–89. doi: 10.1080/00224065.2021.1889419.
  • Ebadi, M., S. Chenouri, and S. H. Steiner. 2021. On monitoring high-dimensional multivariate processes with individual observations. Arxiv Preprint. doi: 10.48550/arXiv.2110.13696.
  • Ebadi, M., and H. Shahriari. 2014. Robust estimation of parameters in simple linear profiles using M-estimators. Communications in Statistics – Theory and Methods 43 (20):4308–23. doi: 10.1080/03610926.2012.721914.
  • Ebadi, M., H. Shahriari, M. R. Abdollahzadeh, and A. Bahrini. 2011, September. Robust estimation of parameters in multivariate processes. In 2011 IEEE International Conference on Quality and Reliability, 585–9. IEEE.
  • Fan, J., L. Shu, A. Yang, and Y. Li. 2021. Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues. Journal of Quality Technology 53 (4):333–46. doi: 10.1080/00224065.2020.1746212.
  • Hotelling, H. 1947. Multivariate quality control, illustrated by the air testing of sample bombsights. Techniques of Statistical Analysis, 111–84. New York: McGraw Hill.
  • Jiang, W., K. Wang, and F. Tsung. 2012. A variable-selection-based multivariate EWMA chart for process monitoring and diagnosis. Journal of Quality Technology 44 (3):209–30. doi: 10.1080/00224065.2012.11917896.
  • Lehmann, E. L., and J. P. Romano. 2006. Testing statistical hypotheses. New York: Springer Science & Business Media.
  • Li, W., D. Xiang, F. Tsung, and X. Pu. 2020. A diagnostic procedure for high-dimensional data streams via missed discovery rate control. Technometrics 62 (1):84–100. doi: 10.1080/00401706.2019.1575284.
  • Martinez, W. G., M. L. Weese, and L. A. Jones-Farmer. 2020. A one -class peeling method for multivariate outlier detection with applications in phase I SPC. Quality and Reliability Engineering International 36 (4):1272–95. doi: 10.1002/qre.2629.
  • Nassar, S. H., and A. S. G. Abdel-Salam. 2021. Semiparametric MEWMA for Phase II profile monitoring. Quality and Reliability Engineering International 37 (5):1832–46. doi: 10.1002/qre.2829.
  • Pison, G., S. Van Aelst, and G. Willems. 2002. Small sample corrections for LTS and MCD. Metrika 55 (1–2):111–23. doi: 10.1007/s001840200191.
  • Ro, K., C. Zou, Z. Wang, and G. Yin. 2015. Outlier detection for high-dimensional data. Biometrika 102 (3):589–99. doi: 10.1093/biomet/asv021.
  • Rousseeuw, P. J., and K. Van Driessen. 1999. A fast algorithm for the minimum covariance determinant estimator. Technometrics 41 (3):212–23. doi: 10.1080/00401706.1999.10485670.
  • Satterthwaite, F. E. 1941. Synthesis of variance. Psychometrika 6 (5):309–16. doi: 10.1007/BF02288586.
  • Satterthwaite, F. E. 1946. An approximate distribution of estimates of variance components. Biometrics 2 (6):110–4.
  • Srivastava, M. S. 2005. Some tests concerning the covariance matrix in high dimensional data. Journal of the Japan Statistical SOCIETY 35 (2):251–72. doi: 10.14490/jjss.35.251.
  • Srivastava, M. S. 2009. A test for the mean vector with fewer observations than the dimension under non-normality. Journal of Multivariate Analysis 100 (3):518–32. doi: 10.1016/j.jmva.2008.06.006.
  • Srivastava, M. S., and M. Du. 2008. A test for the mean vector with fewer observations than the dimension. Journal of Multivariate Analysis 99 (3):386–402. doi: 10.1016/j.jmva.2006.11.002.
  • Srivastava, M. S., and H. Yanagihara. 2010. Testing the equality of several covariance matrices with fewer observations than the dimension. Journal of Multivariate Analysis 101 (6):1319–29. doi: 10.1016/j.jmva.2009.12.010.
  • Variyath, A. M., and J. Vattathoor. 2014. Robust control charts for monitoring process mean of phase-i multivariate individual observations. Quality and Reliability Engineering International 30 (6):795–812. doi: 10.1002/qre.1559.
  • Vargas, N. J. A. 2003. Robust estimation in multivariate control charts for individual observations. Journal of Quality Technology 35 (4):367–76. doi: 10.1080/00224065.2003.11980234.
  • Walker, E., and S. P. Wright. 2002. Comparing curves using additive models. Journal of Quality Technology 34 (1):118–29. doi: 10.1080/00224065.2002.11980134.
  • Wang, K., and W. Jiang. 2009. High-dimensional process monitoring and fault isolation via variable selection. Journal of Quality Technology 41 (3):247–58. doi: 10.1080/00224065.2009.11917780.
  • Welch, B. L. 1951. On the comparison of several mean values: An alternative approach. Biometrika 38 (3-4):330–6. doi: 10.2307/2332579.
  • Willems, G., G. Pison, P. J. Rousseeuw, and S. Van Aelst. 2002. A robust hotelling test. Metrika 55 (1-2):125–38. doi: 10.1007/s001840200192.
  • Williams, J. D., W. H. Woodall, and J. B. Birch. 2003. Phase I monitoring of nonlinear profiles. In quality and productivity research conference. New York: Yorktown Heights.
  • Williams, J. D., W. H. Woodall, and J. B. Birch. 2007. Statistical monitoring of nonlinear product and process quality profiles. Quality and Reliability Engineering International 23 (8):925–41. doi: 10.1002/qre.858.
  • Williams, J. D., W. H. Woodall, J. B. Birch, and J. H. Sullivan. 2006. Distribution of Hotelling’s T2 statistic based on the successive differences estimator. Journal of Quality Technology 38:217–29.
  • Woodall, W. H. 2000. Controversies and contradictions in statistical process control (with discussion). Journal of Quality Technology 32 (4):341–50. doi: 10.1080/00224065.2000.11980013.
  • Woodall, W. H., and D. C. Montgomery. 2014. Some current directions in the theory and application of statistical process monitoring. Journal of Quality Technology 46 (1):78–94. doi: 10.1080/00224065.2014.11917955.
  • Woodall, W. H., D. J. Spitzner, D. C. Montgomery, and S. Gupta. 2004. Using control charts to monitor process and product quality profiles. Journal of Quality Technology 36 (3):309–20. doi: 10.1080/00224065.2004.11980276.
  • Zhang, H., and S. Albin. 2009. Detecting outliers in complex profiles using a χ2 control chart method. IIE Transactions 41:335–45.
  • Zhang, L., T. Zhu, and J. T. Zhang. 2020. A simple scale-invariant two-sample test for high-dimensional data. Econometrics and Statistics 14:131–44. doi: 10.1016/j.ecosta.2019.12.002.
  • Zou, C., and P. Qiu. 2009. Multivariate statistical process control using LASSO. Journal of the American Statistical Association 104 (488):1586–96. doi: 10.1198/jasa.2009.tm08128.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.