Practical Design of Generalized Likelihood Ratio Control Charts for Autocorrelated Data

Control charts based on generalized likelihood ratio (GLR) tests are attractive from both theoretical and practical points of view. In particular, in the case of an autocorrelated process, the GLR test uses the information contained in the time-varying response after a change and, as shown by Apley and Shi, is able to outperfom traditional control charts applied to residuals. In addition, a GLR chart provides estimates of the magnitude and the time of occurrence of the change. In this article we present a practical approach to implementating GLR charts for monitoring an autoregressive moving average process assuming that only a phase I sample is available. The proposed approach, based on automatic time series identification, estimates the GLR control limits through stochastic approximation using bootstrap resampling and thus is able to take into account the uncertainty about the underlying model. A Monte Carlo study shows that our methodology can be used to design, in a semiautomatic fashion, a GLR chart with a prescribed rate of false alarms when as few as 50 phase I observations are available. A real example is used to illustrate the designing procedure.