Feedback quality adjustment with Bayesian state‐space models

In this paper we develop a Bayesian procedure for feedback adjustment and control of a single process. We replace the usual exponentially weighted moving average (EWMA) predictor by a predictor of a local level model. The novelty of this approach is that the noise variance ratio (NVR) of the local level model is assumed to change stochastically over time. A multiplicative time series model is used to model the evolution of the NVR and a Bayesian algorithm is developed giving the posterior and predictive distributions for both the process and the NVR. The posterior distribution of the NVR allows the modeller to judge better and evaluate the performance of the model. The proposed algorithm is semi‐conjugate in the sense that it involves conjugate gamma/beta distributions as well as one step of simulation. The algorithm is fast and is found to outperform the EWMA and other methods. An example considering real data from the microelectronic industry illustrates the proposed methodology. Copyright © 2006 John Wiley & Sons, Ltd.