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# Determining Sample Size for Attribute Data

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Post Number #1
30th June 2006, 07:33 AM
 nwillnow Total Posts: 7
Determining Sample Size for Attribute Data

Hey everyone. I'm currently trying to prove that a system I have in place is reliable to the severity level required and I'm in need of sampling plan information. I have a standard operation procedure which tells me that for 95% confidence and 95% reliability (1.0 AQL) that I need 59 samples for c=0, and 95 for c=1, but no information for c=2,3,4,...

All it tells me about the plan is that "The attribute data sample
sizes are based on the binomial distribution for the corresponding reliability and confidence level requirements." I've tried using Statgraphics and MiniTab to help calculate what the c=2 sample would be, but I can't figure out how.

Is this a common standard I'm looking at? My problem is that I'm working backwards. I'm trying to use pass/fail data I have collected over a number of weeks to show that the number of failures I'm seeing per week is acceptable, as opposed to structuring a validation around a sample size to test.

I've looked at the ANSI/ASQC Z1.4 standard, but that seems entirely different. Any suggestions?

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Post Number #2
30th June 2006, 08:15 AM
 Michael Walmsley Total Posts: 157
Re: Determining Sample Size for Attribute Data

What you have referenced comes from the Bayes Success-Run Theorem.
for c = 1 thru 10 reference the following (the theoretical aspects can be found on the attached link.

Rel 0.95
Conf 0.95
# Fail allowed "c" 0 1 2 3 4 5
n = 58.4 93 124 153 180.4 207.4

# Fail allowed "c" 6 7 8 9 10
n = 234 260 285.4 311 336

http://www.weibull.com/LifeDataWeb/d...est_design.htm
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Post Number #3
30th June 2006, 08:56 AM
 Tim Folkerts Total Posts: 972
Re: Determining Sample Size for Attribute Data

A while back I posted a spreadsheet for calculating sampling plans and it can determine the numbers you are looking for:
Sampling Spreadsheet to help determine the sample size for sampling plans

For 95% reliability, enter 5% in the "Unacceptable Quality Level" cell
For 95% certainty, enter 5% in the "Beta Risk" cell

Then adjust the sample size cell (or the slider) and watch the "RE" cell (the reject number). Once it changes, then you have the smallest sample needed to acheive your goals. Keep increasing the sample size and you will reach Re=1, Re=2, ... I checked a few and they agree with the numbers posted already.

Obviously, you could change the "Unacceptable Quality Level" and the "Beta Risk" for other levels. You can also "reverse engineer" the formulas to see how I got the results.

Tim
Post Number #4
30th June 2006, 10:26 AM
 nwillnow Total Posts: 7
Re: Determining Sample Size for Attribute Data

Sound. Cheers for that lads! Never would have found that on me own.

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