Design and Performance Analysis of the Exponentially Weighted Moving Average Mean Estimate for Processes Subject to Random Step Changes

The exponentially weighted moving average (EWMA) is a well-known and popular statistic used for smoothing and forecasting time series and as a process mean estimator, due to its simplicity and ability to capture nonstationarity. The EWMA statistic has been shown to be an optimal mean estimator for a certain disturbance process and an effective estimator for various other processes. In this article we focus on a practical disturbance process—relatively small random step changes that are difficult to distinguish from white noise and usually overlooked by practitioners. We propose an optimal EWMA parameter for step-change disturbance processes, as well as methodologies to identify and estimate the process models. The EWMA estimator’s performance is then evaluated analytically. We demonstrate that a well-designed EWMA control scheme can effectively reduce the process variation even for processes subject to infrequent, small step changes. A semiconductor process example illustrates the design and analysis.