The median chart with estimated parameters

A modified median chart with estimated control limits is proposed for monitoring the mean value of a normal process. The estimates for the nominal process parameters used to set up the control limits in Phase I are the average of the sample medians and the average of the sample ranges of m initial subgroups of size n. The run length properties of the chart are examined, and the obtained results lead us to conclude the proposed chart present an interesting RL performance (at least for an adequate choice of the chart parameter used to determine the control limits). Control chart parameters are provided for a specific in-control average run length of 370.4 for several combinations of n and m, which facilitates the use of the chart by practitioners, and an illustrative example of implementation of the chart is presented. Some recommendations are also given about the minimum number of initial subgroups m that must be considered to implement the chart with the constant parameter used in the case of known nominal values, and in order to obtain the expected performance.