3 ms·

Yes, in XmR the mR is the moving range -- ie the range between consecutive individual measurements, not the range of a single sample of multiple measurements.

Yes, in XmR the mR is the moving range -- ie the range between consecutive individual measurements, not the range of a single sample of multiple measurements. I can't think of a reference for the different charts off the top of my head. Certainly working SPC-kit helped me to better understand the differences and how they relate to each other. But that's not a very scalable way to transmit information.

OJFord 3y ago
No worries, I'll have a read of your code and comments at least as you suggested in another comment. Just a quick question though if I may - why/when would I want a n>1 group to average instead of treating them all independently as in XmR? Is it if you have multiple categories (of say machine operators, production lines, or software servers) and that variable (the category) isn't the one (x) you're interested in? So for example the first sample is the time taken by each of 8 machinists to fabricate the first nail, etc., so each x_i bar is the mean time for a nail over time (i). Or if we were interested in comparing the machinists, then x_j would be employee #j and for each one we'd be taking the mean of their n nails.
- jacques_chester 3y ago
  > Just a quick question though if I may - why/when would I want a n>1 group to average instead of treating them all independently as in XmR? Two reasons come to mind. First, for whatever reason, it might not be economical to measure every individual in the population. There might be too many, or the thing being sampled is a continuous flow (eg liquid product in a chemical processing plant) or perhaps the sampling is destructive (imagine a pressure failure test, or a reagent test). Second, you might just naturally have a sample. For example, each YJIT benchmark is run multiple times because there's variability in the measurement not due to changes in YJIT. Since you have n runs of the benchmark, you naturally have a sample size of n. It doesn't make sense to think of them as consecutive measurements. The rest of your comment goes to the business of selecting what the grouping of samples is (the term is "rational subgrouping"). A lot of pages are given to this question in the SPC books I've read, because it's not difficult to unintentionally mask signal by combining things that shouldn't be combined. An example is checking the precision of piston machining. It might be you take all the pistons in a given engine as your sample. But later you discover that one of your four machining stations is off-center, which was masked by the ordinary variation of the other three. In this case the sampling should have been per-station, not per-engine.
  - OJFord 3y ago
    That's helpful, thank you.

OJFord 3y ago

No worries, I'll have a read of your code and comments at least as you suggested in another comment. Just a quick question though if I may - why/when would I want a n>1 group to average instead of treating them all independently as in XmR? Is it if you have multiple categories (of say machine operators, production lines, or software servers) and that variable (the category) isn't the one (x) you're interested in? So for example the first sample is the time taken by each of 8 machinists to fabricate the first nail, etc., so each x_i bar is the mean time for a nail over time (i). Or if we were interested in comparing the machinists, then x_j would be employee #j and for each one we'd be taking the mean of their n nails.

jacques_chester 3y ago
> Just a quick question though if I may - why/when would I want a n>1 group to average instead of treating them all independently as in XmR? Two reasons come to mind. First, for whatever reason, it might not be economical to measure every individual in the population. There might be too many, or the thing being sampled is a continuous flow (eg liquid product in a chemical processing plant) or perhaps the sampling is destructive (imagine a pressure failure test, or a reagent test). Second, you might just naturally have a sample. For example, each YJIT benchmark is run multiple times because there's variability in the measurement not due to changes in YJIT. Since you have n runs of the benchmark, you naturally have a sample size of n. It doesn't make sense to think of them as consecutive measurements. The rest of your comment goes to the business of selecting what the grouping of samples is (the term is "rational subgrouping"). A lot of pages are given to this question in the SPC books I've read, because it's not difficult to unintentionally mask signal by combining things that shouldn't be combined. An example is checking the precision of piston machining. It might be you take all the pistons in a given engine as your sample. But later you discover that one of your four machining stations is off-center, which was masked by the ordinary variation of the other three. In this case the sampling should have been per-station, not per-engine.
- OJFord 3y ago
  That's helpful, thank you.