Measuring the Performance of an Eigenvalue Control Chart for Monitoring Multivariate Process Variability
Keywords:Statistical Process Control, Multivariate Dispersion, Covariance Matrix, Generalized Variance, Vector Variance,
AbstractIn manufacturing process, it is very important to control and monitor the stability of a process such that a high quality product will be produced. The most common statistical tool used for monitoring the stability of a process is the control chart. In recent applications of control charting methods, there is a need to construct a control chart that is able to represent the behaviour of a multivariate process since in many manufacturing processes; quality of a product is determined by the joint-level of several quality characteristics. For this reason, in this paper, a new control chart is introduced for monitoring the stability of multivariate process in terms of the process variability. The proposed method is based on charting each of the eigenvalues of a covariance matrix. To show the efficiency of the proposed method, we conduct a simulation study and compare the performance of the proposed method with the existing method. A real example will be presented to illustrate the advantage of our proposed method.
F. B. Alt, ESS, John Wiley & Sons, New York, 5(1985), 110-119.
F. B. Alt and N. D. Smith, Handbook of Statis., Elsevier Science Publisher, North Holland, 7(1988), 333-351.
D. C. Montgomery, Introduction to Statistical Quality Control, John Wiley & Sons, New York, 2009.
F. Aparisi, J. Jabaloyes and A. Carrion, Comm. Statist. Theory Methods, 28(1999), 2671–2686.
W. H. Woodall, J. Qual. Techno., 32(2000), 341-350.
N. J. A. Vargas and C. J. Lagos, Qual. Eng., 19(2007), 191-196.
A. Grigoryan and D. He, Int. J. Prod. Res., 43(2005), 715-730.
S. S. Wilks, Biometrika, 24(1932), 471-494.
M. A. Djauhari, M. Mashuri and D. E. Herwindiati, Comm. Statist. Theory Methods, 37(2008), 1742-1754.
M. A. Djauhari, MATEMATIKA, 27(2011), 51-57.
M. A. Djauhari, IEEE Xplore, (2011), 620-625.
R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, Prentice Hall, New Jersey, 2007.
M. A. Djauhari and M. Ismail, S. Afr. J. Ind.Eng., 21(2010), 207-215.
K. V. Mardia, J. T. Kent and J. M. Bibby, Multivariate Analysis, Academic Press, New York, 1979.