A Robust Self‐Starting Bayesian Approach for Multivariate Phase II Monitoring

Traditional multivariate control charts require in‐control (IC) parameter estimates to be known or estimated from a large set of uncontaminated, historical Phase I observations. However, some processes need to be monitored when little Phase I data are available, and self‐starting approaches, including Bayesian methods, have proven useful. Self‐starting methods are sensitive to early outliers and degrade quickly in their presence. Even when a large Phase I data set is available, contamination, such as outliers, can result in poor chart performance. For these cases, control charts based on robust estimators of IC parameters are often used to obtain satisfactory fault detection performance. However, few methods exist to handle situations wherein Phase I data are both limited and contaminated. Therefore, we propose a robust self‐starting Bayesian approach to detect faults in multivariate Phase II data using parameters that are estimated from limited and contaminated Phase I data. In simulations assessing model performance in several Phase II fault scenarios, the proposed approach often substantially outperforms existing methods that are either purely robust or self‐starting. Finally, the method is applied to data from a water treatment process.