# P Charts - Subgroup Sizes? Process Control Indicator

U

#### UK Steve

Afternoon All

I seem to remember reading somewhere (can't remember where) that a P chart becomes ineffective in detecting whether or not a point is out of control if the sub group size drops below 'x'. However I can't recall what 'x' was or even if the statement is true. Can anyone help?

Steve

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Re: P Charts - Subgroup Sizes?

The only issue here might be when using the binomial standard deviation (p times (1-p) over sample size) starts to give odd answers by counting three standard deviations rather than the binomial distribution probabilities. You also get into discreteness problems - such as when the sample size is one, you are only able to get 0% or 100%.

If you pushed me, I'd recommend going no smaller than 5, and would prefer to stay at 20 or greater if practical. In the "real world" I haven't run into much problem with small sample sizes. You can always adjust your subgrouping to include more points if you need to.

S

#### Sturmkind

Hi! A recommended and very readable reference is 'Statistical Quality Control' by Grant & Leavenworth where they demonstrate that the sensitivity of the p-chart is affected by sample size:
"Consider, for example, samples of various sizes drawn from product that is 2% rejectable. A sample of 5 will either be 0 or 20% nonconforming (that is, it will contain either 0 or 2 rejects). A sample of 20....0 or 10%....A sample of 100....0 to 6%.....A sample of 2000....1.06 to 2.94%....A sample of 50,000.....1.82 to 2.19%."

So your sample size choice may be based on actually expected or observed reject rates balanced against the velocity of production and your need for sensitivity. If my bonus was based on reducing real observed non-conformance, I would take the n=50,000!

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