Bayesian control limits for statistical process monitoring

This paper presents a Bayesian approach, based on infinite Gaussian mixtures, for the calculation of control limits for a multivariate statistical process control scheme. Traditional approaches to calculating control limits have been based on the assumption that the process data follows a Gaussian distribution. However this assumption is not necessarily satisfied in complex dynamic processes. A novel probability density estimation method, the infinite Gaussian mixture model (GMM), is proposed to address the limitations of the existing approaches. The infinite GMM is introduced as an extension to the finite GMM under a Bayesian framework, and it can be efficiently implemented using the Markov chain Monte Carlo method. Based on probability density estimation, control limits can be calculated using the bootstrap algorithm. The proposed approach is demonstrated through its use for the monitoring of a simulated continuous chemical process.