Monitoring Nonlinear Profiles Using Wavelets

Abstract

In many manufacturing processes, the quality of a product is characterized by a non-linear relationship between a dependent variable and one or more independent variables. Using nonlinear regression for monitoring nonlinear profiles have been proposed in the literature of profile monitoring which is faced with two problems 1) the distribution of regression coefficients in small samples is unknown and 2) with the increasing complexity of process, regression parameters will increase and thereby the efficiency of control charts decreases. In this paper, wavelet transform is used in Phase II for monitoring nonlinear profiles. In wavelets transform, two parameters specify the smoothing level, the first one is threshold and the second one is decomposition level of regression function form. First, using the adjusted coefficient of determination, decomposition level is specified and then process performance is monitored using the mean of wavelet coefficients and profile variance. The efficiency of the proposed control charts based on the average run length (ARL) criterion for real data is compared with the existing control charts for monitoring nonlinear profiles in Phase II

Keywords

• Nonlinear profiles
• Discrete wavelet transform
• Decomposition level
• Adjusted coefficient of determination
• Nonlinear regression