Statistica Sinica 20 (2010), 1077-1096

A NONLINEAR FILTER CONTROL CHART

FOR DETECTING DYNAMIC CHANGES

Dong Han$^{1}$, Fugee Tsung$^{2}$, Yanting Li$^{1}$ and Kaibo Wang$^{3}$

$^{1}$Shanghai Jiao Tong University,

$^{2}$Hong Kong University of Science and Technology and

$^{3}$Tsinghua University

Abstract: All conventional control charts can be viewed as charting the output of a linear filter applied to the process data. In this paper, we present a nonlinear filter control chart (NFC) in which the control statistic consists of a nonlinear combination of a data process. We also present a theorem on an estimation of the average run length for the NFC chart, and we theoretically compare the detection power of any two such control charts. A criterion is provided for selecting an optimal NFC chart. In particular, we discuss some special nonlinear filter control charts for detecting dynamic changes in process mean that can be viewed as extensions of the conventional CUSUM control charts.

Key words and phrases: Average run length, change point detection, dynamic changes, statistical process control.