How to Determine Sample Size for Cp Cpk

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RoscoeSplevins

#11
We are high precision machining. Very accurate, usually small, low mass. Capability per feature on those parts we have done studies is very high; 2.0 and better. Item in question is low sophistication. Simple geometry, managable size. We just don't study these.

We feel comfortable with our study method. We may not be the best at statistical studies but we make a damn good part.

Our issue is HOW do we select and justify our sample size. Customer is expecting a calcualtion and reasoning. We need to reference some (any) industry standard or practice. A white paper or 6 sigma techique would suffice. But our contact is pushing for detail. This customer is isnsiting on approval of content pre-PPAP.
 
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Bev D

Heretical Statistician
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#12
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!
You must know the ~ total standard deviation of the process.
What typically freezes peopel for new products is that any capability study is an iterative process - it is not a one time thing.

A first approximation is to use what you already know about similar processes and characteristics. how much variation do you typically experience? Is the variation 'homogenous' (in other words is the largest amoutn of variaiton seen from piece to piece) or are tehere large differences between setups, raw material batches, operators, beginning to end of a run (do you have shifts, drifts or cycles?)
 

bobdoering

Stop X-bar/R Madness!!
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#13
We are high precision machining. Very accurate, usually small, low mass. Capability per feature on those parts we have done studies is very high; 2.0 and better. Item in question is low sophistication. Simple geometry, managable size. We just don't study these.
Are these short run parts? It sounds like you do not do SPC on this process for control, is that true?
 
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RoscoeSplevins

#14
Short run, usually 200-500 per order. Next run may not be for months. May be next week.
This is a new part, projected for long term. We don't normally do SPC. We will do data collection and post-completion reporting when required. Ours is a high precision environment. Variation is usually limited to tool wear. Cycle times are such that operators can (but not requried) to 100% for critical dims. Most do. Our run charts are kind'a sawtooth shaped, random up and down is for the most part measurement error (a function of tolerance and machine capability) and very small.
 

bobdoering

Stop X-bar/R Madness!!
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#15
Short run, usually 200-500 per order. Next run may not be for months. May be next week.
This is a new part, projected for long term. We don't normally do SPC. We will do data collection and post-completion reporting when required. Ours is a high precision environment. Variation is usually limited to tool wear. Cycle times are such that operators can (but not required) to 100% for critical dims. Most do. Our run charts are kind'a sawtooth shaped, random up and down is for the most part measurement error (a function of tolerance and machine capability) and very small.
Perfect. That is exactly what you should see in precision machining. That means Cpk calculations are not correct for your operation. It is non-normal. The next question is what do you run your characteristics to, 75% of the tolerance or so to allow for the part measurement error?
 
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RoscoeSplevins

#16
Production has min/max limits lower than print spec. Usually about 75%. Process inspection has min/max limits set a little higher (varies by situation). Final inspection uses print spec.

Long term data is kind'a upside down bathtub shaped. I have been told Cpk is not valid for this type capbility but never heard a good explanation. Not covered in college, not covered in SPC seminars. Found a book with detail, but didn't want to spend 120.00! WHAT technique should be used with non-normal, repetitive data?
 

bobdoering

Stop X-bar/R Madness!!
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#17
Production has min/max limits lower than print spec. Usually about 75%. Process inspection has min/max limits set a little higher (varies by situation). Final inspection uses print spec.

Long term data is kind'a upside down bathtub shaped. I have been told Cpk is not valid for this type capability but never heard a good explanation. Not covered in college, not covered in SPC seminars. Found a book with detail, but didn't want to spend 120.00! WHAT technique should be used with non-normal, repetitive data?
If you use 75% as production "limits" and you get sawtooth curve between them, then the

Capability is: (USL-LSL)/.75(USL-LSL) or 1.33

The explanation is that the sawtooth curve is a non-random continuous uniform distribution. Cpk calculations are for random distributions, typically normal discrete processes. The book that describes it correctly is linked in the area you go if you click my name, view public profile - and go to the website cited there. You can read most of the info for free here. Long term data is more affected by sop/start locations and special causes - such as warm up, material changes, other lot to lot issues, etc. Long term data is less representative of the process capability than the actual sawtooth curve you get.

Even if it was covered elsewhere...it was probably covered wrong. If you read the blog you will see it makes a lot of sense to somebody that really does precision machining.
 
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