X-Charts versus X / MR Chart Combinations: IID Cases and Non-IID Cases

The effectiveness of the X-Chart alone (X-only Chart) is compared to that of the Individuals and Moving Range Chart Combination (X/MR Charts), in terms of Average Run Length (ARL) after designing for a common “all OK” (in control) ARL. Comparison is made under five different non-standard conditions, including both iid and non-iid circumstances. We conclude that adding the Moving Range chart to an X-chart, while generally not helpful for detecting iid departures from standard conditions, can be beneficial in detecting some non-iid conditions.