# Testing for Process Confidence - Sample Size

M

#### Mark Smith

Here's the problem.

I want to know how many pieces from some process I need to test (and what the acceptable failure number would be) if I need the process to produce pieces with 95/95 confidence and reliability and I know nothing else about the process. If any failure occurs, how many additional pieces must be tested to achieve the same level of confidence and reliability? I believe I would begin by testing 60 pieces and allow zero failures to achieve this goal. Am I right? explain!

D

#### Don Winton

I apologize for the delayed response. I have 'computerless' at work and the one at home is sorta acting up. Work is OK now and I will have an answer to your request in a day or so. Again, my apologies.

Regards,
Don

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Just the ramblings of an Old Wizard Warrior.

D

#### Don Winton

There is an extensive discussion on sampling, confidence, sample sizes, etc at:

Sampling Plans

Regards,
Don

D

#### Don Winton

Mark Smith Wrote:

Don,

"Thom R Nichols" wrote an article in the June 1997 issue of MDDI Magazine ( Assessing Pass/Fail Testing When There Are No Failures to Assess )that provides a plan for assessing pass/fail testing when no failures occur. Using his chart, I selected 60 samples with zero rejects for 95% confidence. The question is "If a failure occurs, how many additional units need to be tested over 60 with zero additional failures for me to have the same level of confidence in the process producing the product in question?" Can you explain it to me? My statistical background is very limited.

Now I understand the question, I think.

You selected 60 samples with 95% confidence, therefore, from Table I, you were expecting a long term failure rate not to exceed 6.0%. But you had one failure. Now, how many additional units do you have to test to achieve the same 6.0% long term failure rate? Is that it? Let us assume it is.

From Table I, if you test 100 units with one failure, the long term failure rate is predicted to be 5.4%, which is 0.6% less than your original expectation of 6.0%. Therefore, I would test an additional 40 units, and with zero failures, your long term failure rate is predicted to be 5.4%. If the additional 40 units also had one failure, then you would need to work on the process and try the procedure over, based on the info presented in the article. Of course, you could always predict long term failure based on the actual failures. But, that is another story. Test the next 40 and if there are additional failures, we can discuss it then.

Can you explain it to me?
Not really. While I understand why they are presenting this information, I do not know how they derived the charts. The authors chose not to present the statistical theory and I do not have access to references 1 or 2. If you know where they can be found on the web, let me know. My local library sorta sucks in this department. Sorry.

Regards,
Don

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