Statistical monitoring of nonlinear product and process quality profiles

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile) is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T-2 control charts and other methods for monitoring the coefficients in a simple linear regression model of a profile. However, little work has been done to address the monitoring of profiles that can be represented by a parametric nonlinear regression model. Here we extend the use of the T-2 control chart to monitor the coefficients resulting from a parametric nonlinear regression model fit to profile data. We give three general approaches to the formulation of the T-2 statistics and determination of the associated upper control limits for Phase 1 applications. We also consider the use of non parametric regression methods and the use of metrics to measure deviations from a baseline profile. These approaches are illustrated using the vertical board density profile data presented in Walker and Wright