Phase II Nonparametric Profile Monitoring and Decision Making on Process Quality via a Mixed Model

In many statistical process control applications, the quality of a process is characterized by a profile. A profile is a function in terms of one or more explanatory variables. In profile monitoring, one is interested to monitor the performance of a process or product using this functional relationship. Control charts for monitoring nonparametric profiles are useful when the relationship is too complex to be described parametrically. Most of the existing control charts in the literature are suitable for monitoring parametric profiles. This article focuses on nonparametric profile monitoring when within-profile autocorrelation is present. Our proposed phase II control chart considers mixed-effect model and uses the framework of a general smoothing spline analysis of variance (SS-ANOVA) along with Hoteling T2 control scheme. The proposed method is especially suitable for categorical data. Numerical results show that the proposed method is capable of detecting profile shifts and identifying the exact location of problematic segments.