Residual Chart with Hidden Markov Model to Monitoring the Auto-Correlated Processes

Autocorrelations exist in real production extensively, and special statistical tools are needed for process monitoring. Residual charts based on autoregressive integrated moving average (ARIMA) models are typically used. However, ARIMA models need a quite amount of experience, which sometimes causes inconveniences in the implementation. With a good performance under less experience or even none, hidden Markov models (HMMs) were proposed. Since ARIMA models have many different performances in positive and negative autocorrelations, it is interesting and essential to study how HMMs affect the performances of residual charts in opposite autocorrelations, which has not been studied yet. Therefore, we extend HMMs to negatively auto-correlated observations. The cross-validation method is used to select the relatively optimal state number. The experiment results show that HMMs are more stable than Auto-Regressive of order one (AR(1) models) in both cases of positive and negative autocorrelations. For detecting abnormalities, the performance of HMMs approach is much better than AR(1) models under positive autocorrelations while under negative autocorrelations both methods have similar performances.