Monitoring of Multiple Binary Data Streams using a Hierarchical Model Structure

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.