# Working with sample sizes and control charting

Six Sigma – iSixSigma Forums Old Forums General Working with sample sizes and control charting

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• #51601

newbie
Participant

How do a reconcile sample size calculation with control charting?  For example, if I am working with binary data and I would like to use an np chart to test for stability prior to calculating capability and also wish to use the proper sample size for a given CI & CL, is the following sequence correct:

Determine sample size using:  n = (2Z/Delta)^2 * p * q

Example:  n = (2*1.96/.04)^2 *.5 * .5 = 2,401= n
Choose a subgroup size (k) to ensure > 20 np points

n = 50
k = 48
Plot the 48 np data points and determine np’
Calculate the USL/LSL and look for special cause
Recombine the data set to determine avg yield with the original CL & CI (n = 2401).
Repeat during CONTROL to show effects of change.
Thank you and happy holidays!

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#179248

Participant

This looks like a reasonable algorithm if the process is stable or the samples are drawn from one lot.

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#179249

Mikel
Member

case sample size and using 50 may not be a big enough sample
based on what is known about p.np should be >/= 5.

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#179251

Participant

I thought the rule was that the average number of defects per sample should be 1 or greater. If he has taken 2400 observations, he probably has a good idea what the p-bar is.  If it is less than 1, find a sample size that will make it 1.

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#179252

Mikel
Member

p and np charts assume normality. The assumption is accompanied by
the rule that np > 5 to approximate a Poisson distribution using
normal.

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#179253

newbie
Participant

Thanks for the feedback Stan, but I am still not fully tracking:

I assume you are telling me it is better to take an initial sample and calculate a preliminary p, then base the sample size calculation on this value.
I am still confused how one incorporates an overall sample size calcualtion into np chart sample size.
And for “np should be greater than or equal to 5”, what is np?  The number of nonconformances in the sample size?  In other words, the sample size in the np chart should be large enough to ensure at least 5 nonconformances per subgroup?  Thanks for your time!

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#179254

Mikel
Member

Correct

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#179255

Darth
Participant

If the np>5 you might even consider moving to an Individuals chart as recommended by Wheeler.

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#179256

newbie
Participant

Thanks doc!

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#179257

newbie
Participant

Thanks Stan!

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