Phase I analysis of high-dimensional processes in the presence of outliers

Abstract

One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of high-dimensional processes with individual observations when the available number of samples collected over time is limited. Using a new charting statistic, we propose a robust procedure for parameter estimation in Phase I. This robust procedure is efficient in parameter estimation in the presence of outliers or contamination in the data. A consistent estimator is proposed for parameter estimation and a finite sample correction coefficient is derived and evaluated through simulation. We assess the statistical performance of the proposed method in Phase I. This assessment is carried out in the absence and presence of outliers. We show that, in both cases, the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Besides, we present two real-world examples to illustrate the applicability of our proposed method.

Keywords:

• high-dimensional multivariate process
• Phase I analysis
• robust estimation
• statistical process monitoring

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Mohsen Ebadi

Mohsen Ebadi received his BS, MS, and PhD degrees in Industrial Engineering from Iran University of Science and Technology, Khajeh Nasir University of Technology, and Amirkabir University of Technology (Tehran Polytechnic), respectively. His research interests are in the areas of statistical process monitoring, applied statistics, and data analytics.

Shoja’eddin Chenouri

Dr. Shojaeddin Chenouri is a Professor of Statistics at the Department of Statistics and Actuarial Science, University of Waterloo. His research focuses on developing nonparametric and robust statistical procedures to analyze data structures from various disciplines such as engineering, health, environmental studies, and humanities. He has extensive consulting experience and publishes on a wide range of statistical and data science topics.

Stefan H. Steiner

Stefan Steiner is a Professor in the Department of Statistics and Actuarial Science at the University of Waterloo. His primary research interests include quality improvement, process monitoring, experimental design and measurement system assessment. He is a Fellow of the American Statistical Association and the American Society for Quality.