How to Determine Sample Size for Cp Cpk

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RoscoeSplevins

#1
We have a request from a customer for a Cp/Cpk study specific to their part. Normally we pull a 30 piece sample and do the study. This customer wants justification for whatever sample we decide to do. I'd like to use the most appropriate sample and be able to justify that. We have no present data on this part, no prior Cp, no run chart, no standard deviation. Our run will be 200 to 300 pieces. What's my first step?
 
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Pudge 72

#2
Re: Determine Sample size for Cp Cpk

Minitab will do a calaculation that is based on AQL levels in combination with Percent Defective including both Alpha and Beta Risk.

All you have to do is figure a PPM that would be acceptable (zero of course is what everyone is after, however - if we were perfect we certainly wouldn't be here :D) to you and your customer for both AQL and RQL.
After that, you enter the tolerance for the feature that you are measuring and let the software do the work.

IE - I entered an AQL of 1, an RQL of 5 ; .05 Alpha .05 Beta using Percent Defective with a Lot Size of 300 Pieces and a .125 LSL and .135 USL, Minitab came back and said measure 70 Pieces. If I change RQL to 3 - it tells me to measure 176 Pieces & Voila!

Not endorsing Minitab - just sayin'.........
 

smryan

Perspective.
#3
Re: Determine Sample size for Cp Cpk

:) Just learned this little "visualization technique" myself and I rather like it... You plot a running Avg and StdDev. The flatter they get the closer you are to "statistical significance".
 

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RoscoeSplevins

#4
Re: Determine Sample size for Cp Cpk

After a little looking, I found the MiniTab pulldown and ran your numbers. Got the same answer! I must have done something right !!!

Now, what is my justification to my customer for the use of AQL inspection levels to determine Pp/Cp? This customer will expect some sort of technical / statistical reasoning behind the selection of the method of calculation and the risk inputs.

Separately, what is the "k" distance?

Thanks, you guys are fast !!
 

Miner

Forum Moderator
Staff member
Admin
#5
You need a sample size of approximately 100 to obtain a Cp/Cpk with a reasonable confidence interval.

The confidence interval for the mean narrows quickly and at a sample size of 30 - 50 reaches an acceptable level. Not so the confidence interval of the standard deviation. It requires approximately 100 samples to obtain a confidence interval of .88*SD to 1.16*SD.

Lest you say that the sample size of 50 gives a confidence interval of .84*SD to 1.25*SD, recall that the Cp/Cpk calculation involves both the mean AND the standard deviation. This widens the confidence interval even more.

I have run Monte Carlo simulations on this, and 100 is the best trade-off on sample size versus confidence interval size.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#6
actually, the AQL approach is not approriate for determining the sample size for a capability study.

the first issue is that AQL formulas are for categorical (aka attribute) data (number of defects) while 'traditional' Cpk indices are calculated using continuous (aka variables) data (using the average and standard deviation vs the secification limits). It seems you are using continuous data?

if so there are various approaches to determining an apropriate sample size. believe it or not there is no exactly correct answer. although there are a LOT of incorrect sample sizes there are many that are good enough and none that are exactly correct as this is an estimate.

more important than the sample size is the sampling structure. the sample must be representative of the population. This means random and taken from across enough setups to represent the true variation that your process will experience.

in general, a sample size of 30 is substantiated as a decent estimate of a process average. If one is really concerned about the standard deviation then the rule of thumb is a sample size of 100. (which is why you see these numbers generally documented as 'the sample sizes' for capability studies. The formulas for being more 'statistically' confident about the Cpk estimate require some knowledge of the process standard deviation. without any information about the process perfomance one can only guess at the actual standard deviation. (in real life, knowledge of the process behavior is an iterative process, while many customers ignorantly require a one time single point estimate that is either true OR more likely just a number to put in their supplier quality form.)

tomorrow I - or others - will post the formulas for estimating averages and standard deviations...
 
K

kaikai

#7
The confidence interval of Cp,Cpk tend to be broad when sample size is small.So as Miner said, you should take more sample than you normally do.

And there is more important things when you select the samples for the calculation of Cp,Cpk.
Does the data include all of variance source at the time of manufacture?
I always take into account the variability of these when I evaluate production variability.
 
R

RoscoeSplevins

#9
PORDUCTION
The product in question is new but similar to other products for this customer and other products we make for others. Data will be taken from the first production run. Historically, using the equipment, process, and geometry of the product, we should hit this dead-on after setup.
SAMPLING
Our sampling is done in time sequence. Collection is in a plastic tray marked and separated from the remaider of the production (usually 300-500 pieces). Usual operator activity; machine offsets, inspections, breaks are carried on as usual.
MEASUREMENTS
Measurements are done in another area post production. Experienced QC do the measurements and recording. All are currently in calibration. I will do the entry to Excel or MiniTab. Normally when we do such a study, the product is a more complicated item than the one in question. As a matter of fact, I've never done a study on this class of product! Thus no history.

As stated before, our customer wants justification for our sample size. "Rule of thumb" will not keep them happy. We are given thier requirements of confidence and a "power" for our calculations. But were not given sample size or a formula for sample size. A request for direction or requirement got us the -no rule of thumb, and justification memons!

Thanks for all the assistance thus far. I've spent hours reviewing older training materials with no progress. You guys have gotten me farther in one afternoon...
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#10
First of all, the correct answer to any question is "it depends." It depends on the process, its total variance equation and the statistically significant distributions that impact the total variance value. Sure, you can take 30 to 100 samples and - unless you have a truly random variation (which is rare) - you need them in time order, but whether they are 100 pcs in order or every 5 pcs, etc. depends on the process. 100 pcs in a row may still be insignificant in some processes.

More importantly, Cp and Cpk may be insignificant or not applicable for some processes. It depends...

What kind of process are you trying to determine capability on?
 
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