An Individuals Generalized Likelihood Ratio Control Chart for Monitoring Linear Profiles

Abstract

This paper investigates a generalized likelihood ratio (GLR) control chart for detecting sustained changes in the parameters of linear profiles when individual observations are sampled. The control charts usually used for monitoring linear profiles are based on taking a sample of n observations at each sampling time point, where n is large enough that a regression model can be fitted at each sampling point using these n observations. For this sampling scenario, it has been shown that a GLR control chart has many advantages over other control chart schemes in terms of convenience of design, fast detection of process changes, and useful diagnostic aids. However, in many applications, it may not be convenient or possible to take a sample larger than n = 1. Therefore, it is desirable to develop some control chart to monitor profile data with individual observations (n = 1) at each sampling point. In this paper, we consider a GLR control chart based on individual observations and show that it has certain advantages compared with the GLR chart based on groups of observations. An important advantage of GLR control charts is that the only design parameter that needs to be specified in order to use a GLR chart is the control limit, and here, control limits for linear profiles up to eight regression coefficients are provided for convenient use by practitioners. Copyright © 2013 John Wiley & Sons, Ltd.