The EWMA median chart with estimated parameters

The usual practice in control charts is to assume that the chart parameters are known or can be accurately estimated from in-control historical samples and the data are free from outliers. Both of these assumptions are not realistic in practice: a control chart may involve the estimation of process parameters from a very limited number of samples and the data may contain some outliers. In order to overcome these issues, in this article, we develop an Exponentially Weighted Moving Average (EWMA) median chart with estimated parameters to monitor the mean value of a normal process. We study the run length properties of the proposed chart using a Markov Chain approach and the performance of the proposed chart is compared to the EWMA median chart with known parameters. Several tables for the design of the proposed chart are given in order to expedite the use of the chart by practitioners. An illustrative example is also given along with some recommendations about the minimum number of initial subgroups m for different sample sizes n that must be collected for the estimation of the parameters so that the proposed chart has identical performance as the chart with known parameters. From the results we deduce that (i) there is a large difference between the known and estimated parameters cases unless the initial number of subgroups m is large; and (ii) the difference between the known and estimated parameters cases can be reduced by using dedicated chart parameters.