Monitoring Multivariate Processes Using an Adaptive T2 Chart

In recent years, there has been an increasing demand for quality control of multivariate dynamic systems. Conventional directionally invariant charts fail to make use of versatile shift patterns in a multivariate process and are sensitive to general failures only. Directionally variant charts, however, are designed for specific and constant shifts and are not suitable for processes with dynamic and unknown failures. This paper proposes an adaptive T² scheme, which can successfully capture the unknown shift patterns of a multivariate system via an exponentially weighted moving average (EWMA) forecasting procedure. The adaptive scheme preserves the optimality of a directionally variant chart, while provides a scalable extension to Hotelling´s T² procedure. The smoothing parameter of the proposed scheme can be tuned for desired shift sizes. Significant improvement of sensitivity over an intended range is demonstrated by Monte Carlo simulation.