The effect of autocorrelation on the diagnostic procedures

Apart from quick detection of abnormal changes in a multivariate process, it is also critical to accurately identify the factors of abnormal changes after an out-of-control signal in multivariate statistical process control. Some diagnostic methods for fault identification were proposed by scholars on which one of the basic assumptions is that the process data are independent. The independent assumption is reasonable for many applications. However, with the development of industrial automation, the process data usually meet the phenomenon of autocorrelation. As it is well known, the autocorrelation affects detection ability of control chart. It is a natural question that is whether the autocorrelation affects the diagnostic performance of the diagnostic procedures. In the article, we propose the method adopted the analogy residual sequences and compare it with the performance of existing diagnostic methods for different shift sizes and various autocorrelation and cross-correlation structures. To limit the complexity, our discussion employs a first-order vector autoregressive process and focuses mainly on bivariate data in this article. The results of the simulation show the performances of diagnostic procedures were affected by autocorrelation and the impacts become greater as autocorrelation increases. On the other hand, the proposed method in the article can be free from the impacts of autocorrelation. Finally, a real example is also presented to demonstrate the implementation of the proposed method.