Monitoring autocorrelated processes using the hidden Markov model

The hidden Markov model (HMM) is an unsupervised statistical learning method capable of modeling sequential data by varying the number of hidden states.This paper investigates an HMM-based monitoring procedure for autocorrelated processes, focusing on how the number of hidden states influences its performance.The performance is evaluated using the average run length (ARL) and the relative mean index (RMI).The proposed approach is also benchmarked against a deep learning-based RNN residual chart.The results indicate that the optimal number of HMM states depends on both the autocorrelation structure of the process and the type of process change.Notably, for autoregressive (AR) models with strong first-order autocorrelation, the HMM-based procedure demonstrated superior overall performance compared to the RNN-based procedure.