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Phase II Monitoring of Nonlinear Profile Variance Using Wavelet
Author(s) -
Nikoo Mehrdad,
Noorossana Rassoul
Publication year - 2013
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1460
Subject(s) - nonparametric regression , control chart , mathematics , estimator , statistics , wavelet , nonparametric statistics , nonlinear regression , variance function , parametric statistics , regression analysis , smoothing , computer science , artificial intelligence , process (computing) , operating system
In some statistical process control applications, the quality of a process or a product can be characterized by a nonlinear relationship between a response variable and one or more explanatory variables. Monitoring nonlinear profiles using nonlinear regression has been proposed by several researchers as a potential area for research. To avoid disadvantages of parameter estimation in nonlinear regression, we used nonparametric regression with wavelets for monitoring nonlinear profiles. In nonparametric regression framework, traditional variance estimator is not proper; other estimators should be used instead. Parametric or nonparametric control charts in phase II are proposed to monitor error term variance when nonparametric regression with wavelet is used. Multivariate control chart based on regression coefficients (approximate wavelet coefficients) is added to variance control chart to check stability in the process mean. It is well known that the performance of control schemes in detecting shifts in multivariate control charts deteriorates as the dimension of regression coefficient increases. To improve the performance of control schemes, we considered decomposition level as a smoothing parameter, which determines the form of regression function (size of approximate wavelet coefficients vector) in nonparametric regression with wavelet. A method based on an analysis of variance is proposed to determine the optimal decomposition level. The statistical performances of the proposed methods are evaluated using average run length criterion using vertical density profile data. Numerical results indicate that the proposed methods perform satisfactorily. Copyright © 2012 John Wiley & Sons, Ltd.