Estimation of Complicated Profiles in Phase I, Clustering and S-estimation Approaches

Some quality characteristics are well defined when expressed as a function of an independent variable. This function is usually called a profile. If the functional form of the profile is known, parametric methods could be used to monitor the profile representing a process. However, some processes are complicated, and it is not suitable to use parametric models. In these cases, nonparametric methods may be used to monitor the profiles. One of the powerful nonparametric profile monitoring methods is to use wavelets. In this paper, the issue of estimating the complicated profiles in phase I is studied. In order to monitor the process using wavelets, it is required to estimate the vector of wavelet coefficients. Classical estimators are usually used to estimate the coefficients vector. These estimators should be used when the data do not contain outliers. However, it is possible that the data set is contaminated and includes some outliers. Thus, it is better to use robust estimators that are insensitive to the presence of outliers. In this paper, two robust estimators for estimating the complicated profiles using wavelets are proposed. In the first approach, the dimension of the coefficients vector is reduced by means of PCA incorporated into clustering. The second approach is based on the S‐estimation method. An extensive simulation study is performed using matlabscp>® software to evaluate the proposed methods and to compare the results with an existing classical method. The results show the well performance of the suggested methods in estimating the model parameters when the data set is not contaminated and in the presence of outliers.