On the Charting Procedures: MEWMA Chart and DD-Diagram
Author(s)
Mekki Hajlaoui
Affiliation(s)
Faculté des Sciences Economiques et de Gestion de Mahdia, Université de Monastir, Mahdia, Tunisia.
Faculté des Sciences Economiques et de Gestion de Mahdia, Université de Monastir, Mahdia, Tunisia.
ABSTRACT
In light of rapid development of customer requirements, control procedures of quality concept use multivariate analysis. This is because of recent advances in information technology and in recording. The charting procedures are based on Mahalanobis distance but their performance needs normality and a type-I error rate choice. The DD-diagram is an alternative scheme that uses data depth to avoid these conditions rarely met in practice. For a given error-free sample, the performance of DD-diagram and that of multivariate EWMA control procedures are compared through a real example on individual observations taken from a multivariate quality process.
In light of rapid development of customer requirements, control procedures of quality concept use multivariate analysis. This is because of recent advances in information technology and in recording. The charting procedures are based on Mahalanobis distance but their performance needs normality and a type-I error rate choice. The DD-diagram is an alternative scheme that uses data depth to avoid these conditions rarely met in practice. For a given error-free sample, the performance of DD-diagram and that of multivariate EWMA control procedures are compared through a real example on individual observations taken from a multivariate quality process.
KEYWORDS
Multivariate Data, Quality Control, Mahalanobis Distance, MEWMA Chart, Data Depth, DD-Diagram
Multivariate Data, Quality Control, Mahalanobis Distance, MEWMA Chart, Data Depth, DD-Diagram
Cite this paper
Hajlaoui, M. (2015) On the Charting Procedures: MEWMA Chart and DD-Diagram. Open Journal of Statistics, 5, 373-381. doi: 10.4236/ojs.2015.55039.
Hajlaoui, M. (2015) On the Charting Procedures: MEWMA Chart and DD-Diagram. Open Journal of Statistics, 5, 373-381. doi: 10.4236/ojs.2015.55039.
References
[1] Alloway Jr., J.A. (1995) Visual Evaluation of Multivariate Control Chart Assumptions. Proceedings of the American Statistical Association, the Section on Quality and Productivity, 49-54. [2] Liu, R.Y., Parelius, J.M. and Singh, K. (1999) Multivariate Analysis by Data Depth: Descriptive Statistics, Graphics and Inference. The Annals of Statistics, 27, 783-858.
http://dx.doi.org/10.1214/aos/1018031259 [3] Li, J. and Liu, R.Y. (2004) New Nonparametric Tests of Multivariate Locations and Scales Using Data Depth. Statistical Science, 19, 686-696.
http://dx.doi.org/10.1214/088342304000000594 [4] Huh, I. (2010) Multivariate EWMA Control Chart and Application to a Semiconductor Manufacturing Process. A Thesis for Master of Science Degree, McMaster University, Ontario. [5] Lowry, C.A., Woodall, W.H., Champ, C.W. and Rigdon, S.E. (1992) A Multivariate Exponentially Weighted Moving Average Control Chart. Technometrics, 34, 46-53.
http://dx.doi.org/10.2307/1269551 [6] Liu, R.Y. (1990) On a Notion of Data Depth Based on Random Simplices. The Annals of Statistics, 18, 405-414.
http://dx.doi.org/10.1214/aos/1176347507 [7] Ghosh, A.K. and Chaudhuri, P. (2005) On Maximum Depth and Related Classifiers. Scandinavian Journal of Statistics, 32, 327-350. [8] Hajlaoui, M. (2010) A Graphical Quality Control Procedure Using Data Depth. Advances & Applications in Statistics, 19, 97-111. [9] Hajlaoui, M. (2011) On the Charting Procedures: T2 Chart and DD-Diagram. International Journal of Quality, Statistics, and Reliability, 2011, Article ID: 830764.
http://dx.doi.org/10.1155/2011/830764
[1] Alloway Jr., J.A. (1995) Visual Evaluation of Multivariate Control Chart Assumptions. Proceedings of the American Statistical Association, the Section on Quality and Productivity, 49-54. [2] Liu, R.Y., Parelius, J.M. and Singh, K. (1999) Multivariate Analysis by Data Depth: Descriptive Statistics, Graphics and Inference. The Annals of Statistics, 27, 783-858.
http://dx.doi.org/10.1214/aos/1018031259 [3] Li, J. and Liu, R.Y. (2004) New Nonparametric Tests of Multivariate Locations and Scales Using Data Depth. Statistical Science, 19, 686-696.
http://dx.doi.org/10.1214/088342304000000594 [4] Huh, I. (2010) Multivariate EWMA Control Chart and Application to a Semiconductor Manufacturing Process. A Thesis for Master of Science Degree, McMaster University, Ontario. [5] Lowry, C.A., Woodall, W.H., Champ, C.W. and Rigdon, S.E. (1992) A Multivariate Exponentially Weighted Moving Average Control Chart. Technometrics, 34, 46-53.
http://dx.doi.org/10.2307/1269551 [6] Liu, R.Y. (1990) On a Notion of Data Depth Based on Random Simplices. The Annals of Statistics, 18, 405-414.
http://dx.doi.org/10.1214/aos/1176347507 [7] Ghosh, A.K. and Chaudhuri, P. (2005) On Maximum Depth and Related Classifiers. Scandinavian Journal of Statistics, 32, 327-350. [8] Hajlaoui, M. (2010) A Graphical Quality Control Procedure Using Data Depth. Advances & Applications in Statistics, 19, 97-111. [9] Hajlaoui, M. (2011) On the Charting Procedures: T2 Chart and DD-Diagram. International Journal of Quality, Statistics, and Reliability, 2011, Article ID: 830764.
http://dx.doi.org/10.1155/2011/830764