Nonlinear Profile Monitoring of Reflow Process Data Based on the Sum of Sine Functions


Correspondence to: Shu-Kai S. Fan, Department of Industrial Engineering and Management, National Taipei University of Technology, Taipei City, Taiwan.



In most statistical process control (SPC) applications, it is often assumed that the quality of a process or product can be adequately represented by the distribution of a univariate quality characteristic. However, in some particular situations, the quality-related response of interest is not a single variable but a function of some independent variables. Such a functional relationship is called a profile. Recently, profile monitoring has drawn considerable attention in the statistical process control literature. This article proposes a new approach for the reflow process data, which applies the sum of sine functions to model the nonlinear profiles and then the vector of parameter estimates is monitored using the Hotelling T2 and metric control charts. Through an actual data set of the reflow process, the proposed approach is compared with the polynomial regression approach in phase I and phase II analyses. The experimental results show that the proposed approach demonstrates good abilities to detect outlying profiles in phase I and provides better out-of-control average run length performances than the polynomial regression approach in phase II. Copyright © 2012 John Wiley & Sons, Ltd.