Keywords and phrases: quality control, multivariate analysis, monitoring process, covariance matrix.
Received: February 2, 2022; Accepted: March 5, 2022; Published: April 23, 2022
How to cite this article: M. S. Hamed, Comparison of Hotelling’s T2 and generalized variance | S | multivariate control charts procedures with industrial application, Advances and Applications in Statistics 76 (2022), 75-104. http://dx.doi.org/10.17654/0972361722037
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] F. B. Alt, Multivariate Quality Control, Encyclopedia of the Statistical Sciences, John Wiley & Sons, New York, 1985. [2] F. B. Alt and N. D. Smith, Multivariate process control, Handbook of Statistics, P. R. Krishnaiah and C. R. Rao, eds., Elsevier Science Publishers BV, North-Holland, Vol. 7, 1998, pp. 333-351. [3] F. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, 1958. [4] F. Aparisi, J. Jabaloyes and A. Carrion, Generalized variance chart design with adaptive sample size: the bivariate case, Commun. Statist. Simul. Comput. 30(4) (2001), 931-948. [5] F. Aparisi, J. Jabaloyes and A. Carrion, Statistical properties of the multivariate control chart, Commun. Statist. Theory Meth. 28(11) (1999), 2671-2686. [6] M. A. Djauhari, Improved monitoring of multivariate process variability, J. Quality Tech. 37(1) (2005), 32-39. [7] M. A. Djauhari, M. Mashury and D. E. Herwindiati, Multivariate process variability monitoring, Commun. Statist. Theory Methods 37(11) (2008), 1742-1754. [8] E. Dogu and I. D. Kocakoc, Estimation of change point in generalized variance control chart, Commun. Statist. Simul. Comput. 40 (2011), 345-363. [9] C. Fuchs and R. S. Kenett, Multivariate Quality Control Theory and Applications, Marcel Dekker, Inc., New York, 1998. [10] M. S. Hamed, Generalized variance chart for multivariate quality control process procedure with application, Appl. Math. Sci. 163(8) (2018), 8137- 8151. [11] H. Hotelling, Multivariate Quality Control in Techniques of Statistical Analysis, McGraw Hill, New York, 1947, pp. 111-184. [12] A. A. Houshmand and A. Javaheri, Multivariate ridge residual charts, Ph.D. Dissertation, University of Cincinnati, 1998. [13] J. E. Jackson, Multivariate quality control, Commun. Statist. Theory Methods 11 (1988), 2657-2688. [14] J. E. Jackson and R. H. Morris, An application of multivariate quality control to photographic processing, J. Amer. Statist. Assoc. 52 (1957), 186-199. [15] B. P. Korin, On the distribution of a statistic used for testing a covariance matrix, Biometrika 55(1) (1968), 171-178. [16] K. W. Linna, W. H. Woodal and K. L. Busby, The performance of multivariate control charts in the presence of measurement error, Journal of Quality Technology 33 (2001), 349-355. [17] C. A. Lowry and D. C. Montgomery, A review of multivariate control charts, IEEE Transactions 27 (1995), 800-810. [18] J. F. MacGregor and T. Kourti, Statistical process control of multivariate process, Control Eng. Practice 3(3) (1995), 403-414. [19] R. L. Mason, C. W. Champ, N. D. Tracy, S. T. Wierda and J. C. Young, Assessment of multivariate process control techniques: a discussion on statistically-based process monitoring and control, Journal of Quality Technology 29 (1997), 140-143. [20] R. L. Mason, N. D. Tracy and J. C. Young, Multivariate statistical process control with industrial application, American Statistical Association and Society for Industrial and Applied Mathematics, 2002, pp. 197-215. [21] D. C. Montgomery, Introduction to Statistical Quality Control, 4th ed., John Wiley & Sons, New York, NY, 2001. [22] Gerald I. Onwuka, Hotelling’s T-square and principal component analysis approaches to quality control sustainability, International Journal of Computational Engineering Research 2 (2012), 211-217. [23] T. P. Ryan, Statistical Methods for Quality Improvement, John Wiley, New York, 1989. [24] G. A. F. Seber, Multivariate Observations, Wiley, New York, 2018. [25] H. M. Shehata, Statistical study of multivariate quality control procedures and its applications, M.Sc. Thesis, Benha University, 2020. [26] H. N. Timm, Multivariate quality control using finite intersection tests, Journal of Quality Technology 28 (1996), 233-243. [27] N. D. Tracy, J. C. Young and R. L. Mason, Multivariate control charts for individual observations, Journal of Quality Technology 24 (1992), 88-95. [28] J. A. Vargas, Robust estimation in multivariate control chart for individual observations, Journal of Quality Technology 35(4) (2003), 367-376. [29] S. J. Wierda, Multivariate statistical process control - recent results and directions for future research, Statistica Neerlandica 48 (1994), 147-168. [30] S. S. Wilks, Certain generalizations in the analysis of variance, Biometrika 24 (1932), 471-494. [31] J. D. Williams, W. H. Woodall, J. B. Birch and J. E. Sullivan, Distribution of Hotelling’s statistic based on the successive differences estimator, Journal of Quality Technology 38(3) (2006), 217-229. [32] W. H. Woodall, D. J. Spitzner, D. C. Montgomery and S. Gupta, Using control charts to monitor process and product quality profiles, Journal of Quality Technology 36 (2004), 309-320.
|