The Research On Multiple Change Points Detection Method To Detect Local Changes In Nonlinear High-dimensional Profile

In the modern industrial production, quality can play an important role in the success and prosperity of many manufacturing and service organizations. Without quality, any organizations can success. Statistical process control(SPC) is the primary method for q uality control of the enterprise. However, with the development of science and technology, the quality characteristics of the product developed from single factor to multi- factors, which means that there is a function between corresponding values and response variable, such as such as linear or non- linear functions. While the term “profile” refers to the functional relationship between a response variable and one or more explanatory variables. And the detection of the change in profile is named as “profile monitoring”.Linear profile monitoring problem has been widely discussed. However, the complexity of the regression of nonlinear profile makes it hard to monitor the estimated parameters. So, authors has come up with various methods, and the dimensionality reduction method has drawn our attention. This method has a great advantage in monitoring high dimensional nonlinear profiles. With the complexity and precision increasing, profile monitoring has developed from linear profiles to complex nonlinear profiles, and the local changes has causes more attentions at the same time. Also, a large number of linear and nonlinear dimensionality reduction methods have been widely proposed and applied. Linear dimensional reduction methods such as PC A have been widely applied to various fields, while nonlinear dimensional reduction methods such as LLE has a great advantage as LLE's local properties. Through dimensionality reduction, complex nonlinear high dimensional profiles can be reduced to very low dimensional, this makes it easier to analyze the lower-dimensional data.For the case of local change in high dimensional complex nonlinear profile, I propose a dimensionality reduction method based on LLE. Through dimension reduction, I can extract key information, and detect the change points by Sullivan(2002)' change point identification method CPD. Finally, I can estimate the performance of change point through cluster analysis: rand indicators. Simulation and case analysis show that the procedure I proposed in this paper is a very effective high-dimensional nonlinear complex profiles local change point identification tool.