Statistical monitoring of nonlinear profiles by using piecewise linear approximation

Abstract

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.