Monitoring of Multiple Binary Data Streams using a Hierarchical Model Structure |
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| Authors: | Devashish Das Yong Chen Shiyu Zhou Crispian Sievenpiper |
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| Affiliation: | 1. Department of Industrial and Systems Engineering, University of Wisconsin Madison, Madison, WI, USA;2. Department of Mechanical and Industrial Engineering, College of Engineering, The University of Iowa, Iowa City, IA, USA;3. GE Healthcare, Milwaukee, WI, USA |
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| Abstract: | Multiple streams of binary data occur commonly in practice. In this paper, we propose a hierarchical statistical model to describe multi‐stream binary data that demonstrate over‐dispersion. In such a model, a group of binary streams in a multi‐stream dataset is modeled by a beta‐binominal hierarchical mixture distribution. Using this hierarchical model structure, a cumulative sum (CUSUM) chart based on the log‐likelihood ratio is developed to monitor all the data streams simultaneously. The performance of the CUSUM chart is investigated and compared to conventional monitoring schemes through numerical studies and a real‐world dataset. It is shown that the CUSUM method using the hierarchical model is effective and advantageous over the conventional methods. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | attribute control chart multi‐stream process monitoring over‐dispersed binary data monitoring |
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