Choosing the EWMA Parameter in Engineering Process Control

Summary: The exponentially weighted moving average (EWMA) of past data is frequently used in process control applications. In engineering process control, the mean level of the quality characteristic is assumed to wander over time. If the integrated moving average IMA (0,1,1) model is used to represent a process disturbance, the EWMA of the past data has optimal properties as a forecast of the next observation. Advantages of this model for representing the process disturbance have been discussed by Box and Kramer. Using the IMA (0,1,1) model, Box and Kramer have also considered a model for feedback control which takes account of the costs of making an adjustment, of taking a sample, and of being off target. Unfortunately, it is sometimes difficult to estimate, using past process data, the smoothing constant needed to update the EWMA of past data. In this article, a simple method for obtaining the maximum likelihood estimate and a confidence interval for the smoothing constant is discussed, and an accurate and efficient computer routine is provided for performing the computations. Two examples which use actual chemical process data are presented. The 95% confidence interval for the smoothing constant is markedly different in both examples, demonstrating the importance of the information contained in past process data.