Another Look at the EWMA Control Chart with Estimated Parameters

Abstract

When in-control process parameters are estimated, Phase II control chart performance will vary among practitioners due to the use of different Phase I data sets. The typical measure of Phase II control chart performance, the average run length (ARL), becomes a random variable due to the selection of a Phase I data set for estimation. Aspects of the ARL distribution, such as the standard deviation of the average run length (SDARL), can be used to quantify the between-practitioner variability in control chart performance. In this article, we assess the in-control performance of the exponentially weighted moving average (EWMA) control chart in terms of the SDARL and percentiles of the ARL distribution when the process parameters are estimated. Our results show that the EWMA chart requires a much larger amount of Phase I data than previously recommended in the literature in order to sufficiently reduce the variation in the chart performance. We show that larger values of the EWMA smoothing constant result in higher levels of variability in the in-control ARL distribution; thus, more Phase I data are required for charts with larger smoothing constants. Because it could be extremely difficult to lower the variation in the in-control ARL values sufficiently due to practical limitations on the amount of the Phase I data, we recommend an alternative design criterion and a procedure based on the bootstrap approach.