Individual Charts and Additional Tests for Changes in Spread

Abstract
A number of authors have indicated that it is not a good idea to use the MR-chart with an individuals chart to detect shifts in the spread. However, the combination of these charts is still used in practice and even presented as `best practice' in some cases. In addition, some more recent articles present arguments that justify the use of the additional MR-chart in specific situations. In this paper we investigate these arguments and add to the literature by providing two more reasons not to use the MR-chart. First, the merit of using an R-chart is never evaluated before in the context of runs rules. Earlier papers investigate the change in performance as a result of adding an MR-chart to a bare individuals chart. We show that relative to existing well-known runs rules, there is no dvantage in using a close alternative to the MR-chart. Secondly, we investigate the suggestion of some of the proponents of the MR-chart that its weak performance is due to a bad design. We show that this is not the case. We evaluate the ARL performance of the combination of an individuals chart and an MR-chart under the most favorable circumstances for several out-of-control situations by optimizing the design of the two charts for each situation. Our
results show that even this `best-case' performance of the combination is hardly better than that of the individuals chart alone.