A two-step method for monitoring normally distributed multi-stream processes in high dimensions

Abstract

This paper proposes a two-step method for monitoring high-dimensional normally distributed multi-stream processes. The first step consists of a single Hotelling chi-square chart, while the second includes a Shewhart chart for each stream to diagnose off-target streams. The second step is needed only if an alarm triggered in the first step. The required control limits and performance measures such as statistical power and ARLs are computed exactly and efficiently for both cases of independent and dependent streams. The new method performs well in detecting small shifts and has a competitive statistical performance relative to a recent method.

Keywords:

• Statistical process control
• control charts
• multi-stream processes
• multivariate processes
• high-dimensional data streams

Notes

1 This code can be used only for non-commercial purposes provided that the source is properly cited.

2 This code can be used only for non-commercial purposes provided that the source is properly cited.

3 This code can be used only for non-commercial purposes provided that the source is properly cited.

Additional information

Notes on contributors

Amir Ahmadi-Javid

Amir Ahmadi-Javid is an Associate Professor of Operations Management and Business Analytics at Amirkabir University of Technology (Tehran Polytechnic). He has published numerous research articles on different planning aspects of supply chains and service systems, risk analysis, project management, and financial engineering. He is a professional expert in developing efficient mathematical solutions and analytics for complex management problems based on optimization, game theory, stochastic analysis, statistics, and data analysis. He can be contacted at [email protected].

Mohsen Ebadi

Mohsen Ebadi is currently a postdoc fellow at the department of Statistics & Actuarial Science, University of Waterloo. He 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. He can be contacted at [email protected].