The reason why there are multiple methods in JMP for calculating what is effectively the standard deviation used in various process capability index estimates is there are varying ways in which the data has been collected and or practical considerations that need to be accounted for. These varying methods have their own unique ways of estimating the standard deviation to provide the best unbiased estimate of said quantity.
For any within subgroup variation statistic this assumes that, indeed, your data collection method supported the formation of rational subgroups. Hence you're probably using xBar/R charts to assess process stability. If rational subgroups have indeed been formed, then this is generally the preferred method.
But what about the case where the means by which the data was collected does NOT support formation of rational subgroups? The most common manifestation of this scenario is using individuals/mR charts. As such, in this case, using the moving range method is generally recommended.
All of the above methods presume a steady stable process, with no evidence of assignable cause variation for both sets of control charts, regardless of subgrouping methodology. If this presumption can't be satisfied...then calculating process capability indices is generally considered a waste of time and worse yet less than sound practice of sound quality/statistical methods. Any casual reading of anything by Deming or Wheeler in this subject matter will enlighten.
Hope this helps?
