On Estimating<i>X</i>Control Chart Limits

Abstract

In this paper we address the issue of estimating the Shewhart X̄ control chart limits when the values of the process parameters are not known. Recently it has been shown that in order for the estimated control limits to perform similarly to the true, but unknown, limits, they should be based on data from at least 400/(n – 1) subgroups, where n denotes the subgroup size. In this paper, we propose an approach for constructing control limits that attempt to match any specific percentile point of run length distribution of the true limits, even when the limits are estimated using data from only a few subgroups. This approach would enable the user to start monitoring the process with an X̄ control chart at an earlier stage than would be possible with the standard approach. We compare the performance of the proposed approach with that of the standard approach through Monte Carlo simulation experiments. The simulation results show that the control limits constructed using our proposed method perform similarly to the true limits even when estimated from a small number of subgroups.