I think I am having a day of brain freeze...

I have a part that has 5200 failure/fault opportunities.
I want to meet a Cpk of 1.33 or better (DPMO = 6,210, sigma = 4.0)

How do I calculate the mimimum number of parts I need to inspect to achieve a 95% confidence level?

Heres a sigma level calculator.

Enter fields in yellow.

Hope this helps.........

I haven't often heard people talking about confidence intervals for capability indices, which is too bad since these calculations are subject to uncertainty, too. Results will change from sample to sample, so there will certainly be some changes from one time to the next.

There are two different ways I could interpret your question. You could ask something like "How many parts to determine a 95% confidence interval of 0.1." In other words, Cpk is between 1.23 and 1.43 with 95% confidence.

I haven't thought about exactly how you would do this, since both the standard deviation and the mean have an uncertainty, and both of these figure into the calculations.

In another thread, I actually tried some sample data and saw how much variations there was in Cpk calculations. http://elsmar.com/Forums/showthread.php?t=20424

A second interpretation would be "I want to be 95% certain the Cpk is at least 1.33". Here the size needed would depend on the relative results. For example, if the Cpk was 3, then a realtively small sample would convince you that the value was above 1.33. If the true Cpk was 1.4, then you would need a much larger sample to be surfe the result was truly above 1.33.

Tim F

Thanks Tim.

I guess the best way to express this is...


I am going to process parts that each have 5200 opportunities for a 'fault'. We will measure the faults as defects per million opportunities (DPMO).

I have an acceptance criteria of 1.33 Cpk. Based on the calculations, a 1.33 Cpk (sigma = 4) requires DPMO <= 6210.

I can process parts and measure DPMO, but where do I come up with the quantity of parts required to get to a 95% confidence level?


Is 4 (sigma) an AQL level?

This is a customer requirement to validate a process. The sample size will equal the lot size. I just need the minimum lot size. I have to push back on my instinct to question whether all faults can be on one or two of the sample rather than distributed. I think this is where the 'statistical' tag (95% confidence) clears up the issue.

How do I calculate the mimimum number of parts I need to inspect to achieve a 95% confidence level?

http://elsmar.com/Forums/showthread.php?t=7519&page=2

Look at the attachement Cpk_Limits.xls

Is 4 (sigma) an AQL level?

A big NO, AQL means the minimum amount of Defects (as a %) that the lot can have and I (as a customer) am agree to accept to the provider (minimization of type A error), no the % of defects of the lot.

I figure out that your costumer asked for a specific AQL, the sample size is calculated taken in acount the lot size and using the tables to obtain the sample size.