Involved In Discussions
One of our manufacturing facilities asked me to review their SPC X-Bar & R chart for them, and I happened to notice that they are not taking a consistent # of samples per day; therefore the "n" is different for each day.

So when their Range is being calculated, apparently it auto-calculates/changes the D4 constant according to the max number of "n" over the total sample size; so basically, at the end of the month, D4 will have been calculated according to the max subgroup size (4), even if only one day of the month had n = 4 and the rest of the days maybe had n = 3 or n = 2.

Is this OK? I think it's flawed, but I'm getting a headache trying to remember all the rules and calculations that go along with this.

If someone could shed some light on this for me, I would appreciate it greatly!!


Forum Moderator
Staff member
The success of an Xbar/R control chart depends heavily on the correct selection of rational subgroups. If the changing sample size impacts the rational sub-grouping, it is definitely NOT okay. If the changing sample size does not impact the rational sub-grouping, it may be okay, but is not necessarily wise to do as it could encourage an attitude that collecting the correct subgroup size is not important, or that the chart itself is not important.


Starting to get Involved
I prefer Miner's advice to keep the subgroups consistent. If that is not possible, this might be an Xbar-S chart application.


Involved In Discussions
Have you inquired as to why the sample size is changing on different days? For example, are they instructed to pull one every 2 hours but on some days the process is down for part of the shift so they pull fewer samples. Maybe its something relatively benign like that day was the holiday party so noone ran the equipment in the afternoon. Alternatively, perhapse the operators are occasionally finding nonconforming parts and rather than reporting/charting them...

Alternatively, if youre only pulling a few samples every day, you might be better off running an i-MR or other individual sample SPC chart rather than a multiple sample.


Steve Prevette

Deming Disciple
Staff member
Super Moderator
To answer the statistical question - it is possible to do such a thing, but it makes the average and standard deviation of the range very difficult to deal with. If you really have to have changing sample sizes, you would be best served going to an X-sigma set of charts concept.

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