Practical Design of Generalized Likelihood Ratio Control Charts for Autocorrelated Data

Abstract

Control charts based on Generalized Likelihood Ratio (GLR) tests are attractive from both a theoretical and practical point 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 paper, we present a practical approach to the implementation of GLR charts for monitoring an autoregressive and 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 via stochastic approximation using bootstrap resampling. Thus, it 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 semi-automatic 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.

A Change-Point Approach for Phase-I Analysis in Multivariate Profile Monitoring and Diagnosis

“…An extension of the proposed MFPCA-based method to the non-normal or autocorrelated case could be a worthwhile and necessary future contribution to the existing multivariate Phase I methods (Capizzi and Masarotto 2008;Bell et al 2014). …”

An Enhanced Control Chart for Start-Up Processes and Short Runs

“…We found that an efficient approach for the computation of consists in using the Polyak-Ruppert stochastic approximation algorithm [16,20]. In particular, our implementation is based on the recommendations given by Capizzi and Masarotto [3]. …”

“…In this context, three alternative approaches can be used to address the design issue: i) modifying decision intervals: control limits of classical control charts are widened to account for the variability in the sampling distribution of the estimates; see for example Jones [13] and Capizzi and Masarotto [3] for independent and autocorrelated data, respectively;…”

An enhanced residual MEWMA control chart for monitoring autocorrelated data

“…Observe, however, that when there is a nonnegligible uncertainty on the system matrices, the suggested detection algorithm may be designed using the bootstrap based methodology described in Capizzi & Masarotto [13], [14].…”