Evaluation of Phase I analysis scenarios on Phase II performance of control charts for autocorrelated observations

ABSTRACT

Phase I analysis of a control chart implementation comprises parameter estimation, chart design, and outlier filtering, which are performed iteratively until reliable control limits are obtained. These control limits are then used in Phase II for online monitoring and prospective analyses of the process to detect out-of-control states. Although a Phase I study is required only when the true values of the parameters of a process are unknown, this is the case in many practical applications. In the literature, research on the effects of parameter estimation (a component of Phase I analysis) on the control chart performance has gained importance recently. However, these studies consider availability of complete and clean data sets, without outliers and missing observations, for estimation. In this article, we consider AutoRegressive models of order 1 and study the effects of two extreme cases for Phase I analysis; the case where all outliers are filtered from the data set (parameter estimation from incomplete but clean data) and the case where all outliers remain in the data set during estimation. Performance of the maximum likelihood and conditional sum of squares estimators are evaluated and effects on the Phase II use are investigated. Results indicate that the effect of not detecting outliers in Phase I can be severe on the Phase II application of a control chart. A real-world example is provided to illustrate the importance of an appropriate Phase I analysis.

KEYWORDS:

• autocorrelation
• conditional sum of squares estimator
• control charts
• maximum likelihood estimator
• outliers
• Phase I analysis
• statistical process control

About the authors

Erdi Dasdemir is a research assistant in the Department of Industrial Engineering at Hacettepe University. He received his B.S. (2013) and M.S. (2015) degrees in Industrial Engineering from Hacettepe University, Turkey.

Christian Weiß is a Professor at the Department of Mathematics and Statistics at the Helmut Schmidt University in Hamburg, Germany. His research areas include time series analysis, statistical quality control, and computational statistics.

Murat Caner Testik is a Professor of Industrial Engineering at Hacettepe University in Ankara, Turkey. He serves as an Associate Editor of IIE Transactions on Healthcare Systems Engineering and on the editorial review board of Quality and Reliability Engineering International. He is the editor of Quality Engineering. His research interests include statistical process control, quality engineering, and applications of datamining.

Sven Knoth is a Professor at the Department of Mathematics and Statistics at the Helmut Schmidt University in Hamburg, Germany. His research areas include statistical process control, computational statistics, and engineering statistics.

Acknowledgments

The authors are grateful to the anonymous reviewers for their valuable comments which helped to improve this article. We also would like to thank Professor Dr. Roland Fried (TU Dortmund, Germany) for very helpful advice concerning the robust estimation of the AR(1) parameters.

Notes

1 In the i.i.d. case(φ = 0)), the ARL₀ value of 370.4 corresponds to the choice CL=3. If φ=0, we have to choose CL>3 to obtain ARL₀ = 370.4 (Schmid 1995, 119).