Abstract
Many problems in industrial quality control involve n measurements on p process variables X n,p . Generally, we need to know how the quality characteristics of a product behavior as process variables change. Nevertheless, there may be two problems: the linear hypothesis is not always respected and q quality variables Y n,q are not measured frequently because of high costs. B-spline transformation remove nonlinear hypothesis while principal component analysis with linear constraints (CPCA) onto subspace spanned by column X matrix. Linking Y n,q q and X n,p variables gives us information on the Y n,q without expensive measurements and off-line analysis. Finally, there are few uncorrelated latent variables which contain the information about the Y n,q and may be monitored by multivariate control charts. The purpose of this paper is to show how the conjoint employment of different statistical methods, such as B-splines, Constrained PCA and multivariate control charts allow a better control on product or service quality by monitoring directly the process variables. The proposed approach is illustrated by the discussion of a real problem in an industrial process.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
ABECASSIS, J., DURAND, J.F., MEOT, J.M., and VASSEUR, P. (1992): Etude non linéaire de l’influence des conditions de séchage sur la qualité des pâtes alimentaires par l’analysis en composantes principales par rapport à des variables instrumentales. Agro-Industrie et Methodes Statistiques, 3èmes Journees Europeennes.
D’AMBRA, L., and LAURO, N. (1982): Analisi in componenti principali in rapporto ad un sottospazio di riferimento. Italian Journal of Applied Statistics, 1.
DAUDIN, J.J., DUBY, C., and TRECOURT, P. (1988): Stability of stability of principal com-ponent analysis studied by bootstrap method. Statistics , 19, 2.
DE BOOR, C. (1978): A practical guide to splines. Springer, N.Y.
DURAND, J.F. (1993): Generalized principal component analysis with respect to instrumental variables via univariate spline trasformations. Computational Statistics Data Analysis, 16,423-440.
EUBANK, R.L. (1988): Smoothing splines and non parametric regression. Markel Dekker and Bosel, N.Y.
GIFI, A. (1990): Nonlinear Multivariate Analysis. Wiley, Chichester, England.
GROVE, D.M., WOODS, D.C., and LEWIS, S.M. (2004): Multifactor B-Spline Mixed Mod-els in Designed Experiments for the Engine Mapping Problem. Journal of Quality Tech-nology, 36, 4, 380-391.
IZERNMAN, A.J. (1975): Reduced-rank regression for the multivariate linear model. Journal of Multivariate Analysis, 5.
HUBERT, M., ROUSSEEUW, P.J., and BRANDEN, K.V. (2005): ROBPCA: A New Ap-proach to Robust Principal Component Analysis. Technometrics, 47, 1.
MACGREGOR, J.F. and KOURTI, T. (1995): Statistical Process Control of Multivariate Pro-cesses. Control Engineering Practice, 3, 3, 403-414.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gallo, M., D’Ambra, L. (2008). Nonlinear Constrained Principal Component Analysis in the Quality Control Framework. In: Preisach, C., Burkhardt, H., Schmidt-Thieme, L., Decker, R. (eds) Data Analysis, Machine Learning and Applications. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78246-9_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-78246-9_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78239-1
Online ISBN: 978-3-540-78246-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)