# How to decide on a sampling size for Xbar-R charts

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#### bmunger

Hello,

I've found one discussion on the internet of this subject here (the link is intentionally crippled because of this forum's restrictions, you need to fix it by removing the spaces around the domain name):
www . winspc . com /what-is-spc/ask-the-expert/334-how-should-the-subgroup-size-be-selected-for-an-x-bar-chart-part-i

But the formulae presented in textbooks vary a lot and I'm unsure how to choose the right formulae to use. There are 8 different forumlae presented in the textbook from Wiley entitled "Probability and Statistics in Engineering and Management Science" among which the one from the internet reference above is present.

But it's not presented as THE one that should be used, in fact none of them are.

So how to we choose which formulae to use to determine the sample size? Is that something personal or is there a scientific/mathematical basis for it?

Thanks!
Bernard

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Generally the sampling size should be "rational", based upon the process itself. Such as perhaps a "production lot" happens to be 12 items. If pushed for a number, I've generally seen "4 or 5", with 4 having historical preference because it is easy to figure out the square root of four.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
To add to Steve's response, the sample size is not generally 'statistically' selected - except potentially for categorical - or pass/fail - data. All of the common sample size formulas are meant for 'point estimates' of some population or static set of data. Control Charts are for monitoring processes over time. This enables the use of much smaller sample sizes. As Steve alluded to the size typically is based in some rational understanding of how the process can vary. Typically 3-5 sequential pieces is sufficient for moderate to high volume production. For lower volume - such as with functions of complex assemblies I use a subgroup size of 1 and measure every assembly.

The best way is to plot your data in time series and then think about the science of the process and the data - what makes sense? how many samples do you need for each subgroup and how often should you subgroup in order to detect changes?

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