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# Inspection Frequency

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## Inspection Frequency

(OP)
This might be too simple for  those gifted in stats. For me, not so simple.

We inspect 5% of our pipe prior to PWHT. We inspect 100% of it after PWHT. The second inspect shows a defect rate of 6%. The first inspection shows a defect rate of 0%.

I am looking for the probability/likelyhood that we'll catch a defect at the first inspection. (ie. we've made 100 - seems like a small enough number that we simply picked 5 good pieces for primary inspection). After how many can I expect to see a failure ont he first inspection?

Note: I am assuming all defects are present at the first inspecion.

### RE: Inspection Frequency

Give us some additional info. What's the material? What are the defects? I assume PWHT stands for post weld heat treat. Is the PWHT causing the defects or making the defects more visible? Are the defects variables(dimensional) or attributes? Are the samples truly randomly picked?

### RE: Inspection Frequency

(OP)
More details. 9Cr1Mo steel. Cracking in the weld. Weld is from an E8018 electrode.

We are trying to determine if the PWHT:
- causes the cracking
- makes the cracking visible
- has no effect (ie. it was there before)

The 5% inspection rate is theoretically random. All pieces are now being inspected prior to PWHT.

### RE: Inspection Frequency

Just from straight statistics: 0.94^5 = 0.73, e.g., 73% of the time, you would get no defects from pulling 5 parts/100 with a 6% defect rate.

TTFN

### RE: Inspection Frequency

I would have thought this was a binomial test. Download this http://www.statpac.com/statistics-calculator/free-version.htm and run this problem under 'counts' for binomial. If you use 5  trials with a success rate of 0.06 then the probablity of success is 0.2. About 17 tests will give you a 72% chance of finding a defect.

corus

### RE: Inspection Frequency

The problem is to minimize the number of samples for inspection and to get the minimum fault rate. The concept of AQL seems very good to me. Basicaly you accept some level of faults that you tolerate. Then test some number n1 of samples and if a proportion of samples is within the limits you admit that your batch is within your specifications. If the proportion is not within a (tabulated)limits, you test some additional, n2 samples. Now the proportion of faults is much more restrictive.If you still do not pass the test then you take another samples, say n3. Now they should all pass the test. If they do not, your batch is unaccepted. In that case you can only change your criteria of acceptance and the proportion of nonconforming products. It is good to know that it it really does not matter how bad your item under test is, 0,001% off the limits is equaly bad as 30% off the limits.
I am working in ISO domaine so I can direct you towards the ISO 2859(1989)part 1,2,3 and ISO 3951. There is surely an ASTM issue.An odd reading with terrific effect!
m777182

### RE: Inspection Frequency

corus, why doesn't your figure agree with IRStuff's? his approach is the same I'd have used.

Cheers

Greg Locock

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