Comparisons of control schemes for monitoring the means of processes subject to drifts

• Published in: Metrika Vol. 70; no. 2; pp. 141 - 163
• Main Authors: Zou, Changliang, Liu, Yukun, Wang, Zhaojun
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.09.2009
• Subjects: Economic Theory/Quantitative Economics/Mathematical Methods; Mathematics and Statistics; Probability Theory and Stochastic Processes; Statistics; Generalized likelihood ratio chart; Drift; Cumulative sum control chart; Average run length; Generalized EWMA control chart; Exponentially weighted moving average control chart
• ISSN: 0026-1335; 1435-926X
• DOI: 10.1007/s00184-008-0183-6

Although statistical process control (SPC) techniques have been focused mostly on detecting step (constant) mean shift, drift which is a time-varying change frequently occurs in industrial applications. In this research, for monitoring drift change, the following five control schemes are compared: the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) charts which are recommended detecting drift change in the literature; the generalized EWMA (GEWMA) chart proposed by Han and Tsung (2004) and two generalized likelihood ratio based schemes, GLR-S and GLR-L charts which are respectively under the assumption of step and linear trend shifts. Both the asymptotic estimation and the numerical simulation of the average run length (ARL) are presented. We show that when the in-control (IC) ARL is large (goes to infinity), the GLR-L chart has the best overall performance among the considered charts in detecting linear trend shift. From the viewpoint of practical IC ARL, based on the simulation results, we show that besides the GLR-L chart, the GEWMA chart offers a good balanced protection against drifts of different size. Some computational issues are also addressed.