Nonparametric Profile Monitoring by Mixed Effects Modeling

In some applications, quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. Profile monitoring is for checking the stability of this relationship over time. Control charts for monitoring nonparametric profiles are useful when the relationship is too complicated to be described parametrically. Most existing control charts in the literature are for monitoring parametric profiles. They require the assumption that within-profile measurements are independent of each other, which is often invalid in practice. This paper focuses on nonparametric profile monitoring when within-profile data are correlated. A novel control chart is suggested, which incorporates local linear kernel smoothing into the exponentially weighted moving average (EWMA) control scheme. In this method, within-profile correlation is described by a nonparametric mixed-effects model. Our proposed control chart is fast to compute and convenient to use. Numerical examples show that it works well in various cases. Some technical details are provided in an appendix available online as supplemental materials.