Sampling for capability studies for variables and attributes

enorht

Starting to get Involved
#1
Hello,

Context: It is very difficult to explain the necessity of validation to our supply so we do not have a solid OQ (meaning no identification of critical parameters such as speed, ...). I just have a machine capability performed on a complex and aluminum product using all the axes (8 or 9) of one equipment. As all the equipment are of the same brand, we decided to accept this "OQ".

I am currently performing a performance qualification of CNC equipments. They are used for the manufacturing of orthopaedic implants (screws, rods, nuts, ...). We have decided to manufacture for each kind of product (based on their physical dimensions) at least three batches representative of the routine. We already identified for each of them critical dimensions and critical aspect. Most of them are measured but few of them are controlled by a GO/NO test or visual aspect.

we agreed with the supplier for the three first batches of each product reference to control and record:
- 100 measures for each dimension per batch --> my aim was to have enough data to perform a capability study and calculate the lower bound of capability index with a confidence level of 95%. I saw that 100 measures are a good sampling to have relevant confidence in the capability indexes (and i will have 300 measures if there are no variation inter lot). But i did not find relevant sources.
- 100% of control GO/NO GO and 100% for the visual aspect. honestly, the production was launched without ending the protocol writting so we decided to have the maximum of values. but I do not know if I have to write a rationale with an approach of LTPD/AQL for critical defauts or do i need to also perform a capability study (with minitab). How can i justify this sampling in my protocol?

The aim is to validate the manufacturing process by showing that:
- for the dimensions measured, the process is stable and have a pp/ppk lower bound at 95% of confidence > 1.33. After that, should I calculate the Z score, calculate the %ppm and link to the AQL/LTPD too?
- for the characteristics controlled by visual inspection or GO/NO GO controls, i do not know if i i have to use capability studies too or claim a NQA/LTPD %...

Thanks for your help,
 
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#2
This is only true if you have identified the correct distribution. Machining variation should NOT be normal, so standard Ppk calculations would not apply. As much data as you have, if you measure your diameters and capture the highest value and lowest value on the diameter slice, you pick up your with-part variation (often ignored to analytical peril). Then following that data over a time-ordered sequence should see the values gradually increase until the part reaches an upper limit where it needs to be offset. It should be offset to a lower limit, then allow the tool to continue to wear. This sawtooth is the continuous uniform distribution - and should be evident in your process. If so, set you control limits to 75% of your tolerance and you have a 1.33 capability. Other dimensions, such as concentricity, parallelism, etc. that are unilateral need curve fitting to determine capability. Using either Cpl or Cpu alone is crap statistics because the process behavior is not modeled best by "1/2 a normal distribution". Curve fitting is more correct. 125 samples is considered a good number.

As far as go/no go - you can also do capability but not to Ppk. It is pretty much % good. You might want to do Gage R&R first, using the attribute agreement method to see how well your operators can find the defects. It ends up being far more interesting.
 

enorht

Starting to get Involved
#3
Thank for your reply. I am not sure to understand everything about you said. I plan to measure diameter, length of thread, tap. Do you have a link to illustrate the sawtooth that you describe.
I was planning to use the lower bound of the capability index estimate in order to state something like "I am confident at 95% that my process capability is at least 95%". Is it not correct? What do you mean by curve fitting?

For GO/NO GO, we cannot perform GR&R because we do not have the ressources (only one controller) and I cannot convince my supplier. So the best for GO/NO GO would be to calcule a %good with the capability analysis of Minitab?

I am not english native speaker so i am sorry to ask you to explain me more clearly. I did not understand everything, do not hesitate to give me some illustrated links.

Thanks,
 
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