Statistica Sinica 19 (2009), 1337-1357

NONPARAMETRIC CONTROL CHART FOR MONITORING

PROFILES USING CHANGE POINT

FORMULATION AND ADAPTIVE SMOOTHING

Changliang Zou$^1$, Peihua Qiu$^2$ and Douglas Hawkins$^2$

$^1$Nankai University and $^2$University of Minnesota

Abstract: In many applications, quality of a process is best characterized by a functional relationship between a response variable and one or more explanatory variables. Profile monitoring is used for checking the stability of this relationship over time. Control charts based on nonparametric regression are particularly useful when the in-control (IC) or out-of-control (OC) relationship is too complicated to be specified parametrically. This paper proposes a novel nonparametric control chart, using a sequential change-point formulation with generalized likelihood ratio tests. Its control limits are determined by a bootstrap procedure. This chart can be implemented without any knowledge about the error distributions, as long as a few IC profiles are available beforehand. Moreover, benefiting from certain good properties of the dynamic change-point approach and of the proposed charting statistic, the proposed control chart not only offers a balanced protection against shifts of different magnitudes, but also adapts to the smoothness of the difference between IC and OC regression functions. Consequently, it has a nearly optimal performance for various OC conditions.

Key words and phrases: Adaptive smoothing, bandwidth selection, change point, generalized likelihood ratio test, local linear kernel smoothing, profile monitoring, statistical process control.