Statistical monitoring of nonlinear profiles by using piecewise linear approximation

• Published in: Journal of process control 2011-09, Vol.21 (8), p.1217-1229
• Main Authors: Fan, Shu-Kai S., Yao, Ni-Chun, Chang, Yuan-Jung, Jen, Chih-Hung
• Format: Article
• Language: English
• Subjects: Akaike's information criterion (AIC); Change point; Nonlinear profile; Schwarz information criterion (SIC); Statistical process control (SPC)
• ISSN: 0959-1524; 1873-2771
• DOI: 10.1016/j.jprocont.2011.06.005

► We model the nonlinear profiles by using piecewise linear approximations. ► The proposed change-point model is designed based on the slope difference. ► The proposed change-point model shows great potential to identify outliers in phase I analysis of nonlinear profile monitoring. ► The proposed change-point model shows great performance to detect process changes in phase II analysis of nonlinear profiling monitoring. In many practical situations, the quality of a process, or product, is better characterized and summarized by the relationship between a response variable and one or more explanatory variables. Such a relationship between the response variable and explanatory variables is called a profile. Recently, profile monitoring has become a fertile research field in statistical process control (SPC). To handle the nonlinear profile data, the proposal considered in this paper is that the entire curve is broken into several segments of data points that exhibit a statistical fit to the linear model, and therefore each of them can be monitored separately by using existing linear profile SPC methods. A new method that determines the locations of change points based on the slop change is proposed. Two goodness-of-fit criteria are utilized for determining the best number of change points to avoid over-fitting. Two nonlinear profile examples taken from the literature are used to illustrate the proposed change-point model. Monitoring performances using the existing T 2 and EWMA-based approaches are presented when the nonlinear profile data is fitted by using the proposed change-point model.