Bayesian multivariate control charts for multivariate profiles monitoring

In many topical applications, the product's quality can be well described in terms of statistical regression relationships between one or more response and a set of explanatory variables. In the literature, various types of regression models have been proposed for profile monitoring applications, and each of those regression models can be implemented and applied in its standard frequentist's and its Bayesian variant. We formulate two popular Phase II multivariate cumulative sum control charts for monitoring multivariate linear profiles in terms of Bayesian regression models, and we show empirically that the resulting new Bayesian control charts perform better than the corresponding non-Bayesian control charts. For the comparative evaluation of the control charts we employ the average run length criterion. Moreover, we propose a new Bayesian approach, which we refer to as the informative prior generation method. The key idea of this method is to make use of historical datasets to generate informative prior distributions. The advantage of this method is that we do not ignore the historical data from Phase I. Instead we re-use it to construct informative prior distributions for Phase II monitoring. The applicability and the superiority of the proposed Bayesian control charts are illustrated through extensive simulation studies.