Dear Experts,
Can we use Xbar–R charts if the subgroup size is 15, or we have to use Xbar-s chars?
Thanks.

Dear Experts,
Can we use Xbar–R charts if the subgroup size is 15, or we have to use Xbar-s chars?
Thanks.

As a measure of variation, "R" works OK when the sample size is small, let's say 5 or below. "R" is based on only two values. As the sample gets larger (15 as in your example), "s" works better because it takes all values within the sample in consideration to calculate the variation. Bottom-line? XBar-s is the better choice.

Hope this helps a little.

Stijloor.

I got this somewhere on the free e-libraries. Not sure how this data was taken but it shows relative efficiencies of R vs. S charts with respect to sample size. I only have up to 10, but guessing by the trend, i'll recommend the same as previously advised. Use the Xbar-S

n: Relative efficiency (r/stdev)
2: 1.000
3: 0.992
4: 0.975
5: 0.955
6: 0.930
10: 0.850

I'll add another vote for S-bar. Range is easier to explain and is easier to calculate by hand, but Standard Deviation is more accurate (and easier to calculate on most spreadsheets).

The impression that "s-bar should only be used for large subgroups" is a common misconception. I've seen it propagated in a number of places. There was I question like that on the CQE exam I took this past year, and I'm not completely convinced that ASQ got the answer right - one of several question I felt inclined to comment on.


Tim F

Personally, I use sigma on all my x-individuals charts. But, most of the literature (especially from Dr. Wheeler) advocates the use of range.

I can say that Dr. Shewhart in Economic Control of Quality of Manufactured Product does compare the use of the range to the standard deviation, and makes an argument that the standard deviation is the more statistically powerful of the two. The difficulty was that in the 1930's, range was much easier to calculate than the standard deviation.

I prefer range from standpoint that it's far easier for most people (in all the companies I've worked at) viewing the charts to understand.
Software makes calculating s easy; getting fairly high turnover, hourly machine operators to understand it is not.

If it was just me and my QC staff reviewing the charts I'd probably be more open to Xbar-s.