Identifying control charts concurrent patterns using Hidden Markov Models

Hidden Markov Models (HMMs) is a powerful probabilistic tool with many potential uses, but its application in quality control has not yet been completely explored. In this study, we develop an HMMs-base methodology to identify (concurrent) patterns in Shewhart control charts. The proposed model integrates Hidden Markov Models and hierarchical clustering method to effectively group observations based on their statistical similarities, which allows, identifying the number of distributions observations are generated from. To improve the performance and robustness of the proposed approach, we modify the Baum-Welch algorithm based on the concepts of Bayesian Information Criterion (BIC). The proposed mechanism will provide an effective and efficient tool to identify different type of patterns in the process. Simulations studies are conducted to evaluate the performance of the proposed method under various scenarios. In addition, the model has been applied in a healthcare setting to identify various trajectories of chronic diseases over time.