The exponentially weighted moving average applied to the control and monitoring of varying sample sizes

The exponentially weighted moving average (EWMA) can be used to report the smoothed history of a production process, and has some considerable advantages over a simple moving average (MA). Discussion of these advantages includes comparison of the filter characteristics of the EWMA and MA in the frequency domain. It is shown that the EWMA provides a much smoother filter than does the MA, and the corresponding implications of this difference are examined in the time domain. In smoothing a production process, the successive entities being smoothed commonly have varying "weights", where the weights may be such quantities as tonnage, value or time interval. Standard textbook treatments of moving averages and exponential smoothing are generally confined to equal spaced data of equal weight. Adapting the average to cope with items of varying weight is shown to be trivial for the case of MA, but is not so obvious for the EWMA. This paper shows how the exponential smoothing constant has to be adapted to provide a consistent EWMA. Applications of the EWMA in process control are discussed, with particular reference to quality control in the mining industry.