Comparison of Individual and Moving Range Chart Combinations to Individual Charts in Terms of ARL after Designing for a Common “All OK” ARL

Abstract

In some process monitoring situations, consecutive measurements are spaced widely apart in time, making monitoring process aim and spread difficult. This study uses three cases to compare the effectiveness of two such monitoring schemes, i.e., the X chart alone (X-only chart) and the Individuals and Moving Range Chart Combination (X/MR chars), in terms of Average Run Length (ARL) after designing for a common “all OK” (in-control) ARL. The study finds that X chart alone is sufficient (and hence, recommended) in detecting changes in all the 3 cases: changes in the process mean, changes in the process standard deviation, and changes in both process mean and standard deviation.