Why and how to use vector autoregressive models for quality control: the guideline and procedures

While quality control on multivariate and serially correlated processes has attracted research attentions, a number of very detailed problems need to be overcome in order to construct practical control charts. We suggest guidelines for construction of control charts based on vector autoregressive (VAR) residuals. We discuss why VAR model is reasonable for real processes in nature, the use of VAR models to approximate multivariate serially correlated processes, residual estimation, selecting the number of variables, and selecting appropriate orders, among other issues. In addition, we illustrate an example employing VAR techniques to approximate a multivariate process previously examined and construct a control chart to monitor residuals. Last, we illustrate the potential development and use of the VAR residual chart to assist quality control and improvement.