A robust wavelet based profile monitoring and change point detection using S-estimator and clustering

Some quality characteristics are well defined when treated as response variables and are related to some independent variables. This relationship is called a profile. Parametric models, such as linear models, may be used to model profiles. However, in practical applications due to the complexity of many processes it is not usually possible to model a process using parametric models.In these cases, non-parametric methods are used to model the processes. One important and applicable non- parametric method used to model complicated profiles is wavelet transformation. Use of wavelet transformation requires estimation of the in control profile in phase I. Classical estimators are usually used in phase I to estimate the in control profile, using wavelet transformation. However,the presence of outliers in data in phase I may affects classical estimators.In this research a robust estimator of the in control profile based on clustering is proposed which is insensitive to the presence of outliers. As well as estimating the in control profile in phase I it is of interest to determine the change point of the process in phase II. In this work a procedure for estimating the change point of complicated profiles in phase II is also introduced. This suggested method does not require normality assumption of the error terms. Aggregation of the proposed robust estimator with the change point detection method results a procedure for detecting the change point. Simulation studies show that the proposed method is robust in presence of outliers compare to the classical methods of profile monitoring and change point detection.