Monitoring of Multiple Binary Data Streams using a Hierarchical Model Structure

摘要

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 (c) 2015 John Wiley & Sons, Ltd.