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# Minimum sample size

## Minimum sample size

(OP)
Hi,

If I have, say, 250 components and they may or may not have defects bigger than a specification I built up from some empirical evidence on the subject, how do I work out how many components ( hopefully less than 50) I need to scan for defect sizes in order to statistically validate my spec.?

Any thoughts would be welcome as all the stuff I can find is on human statistics..

Simmantix
---------
Phases of a Project:
Exultation, Disenchantment, Search for the Guilty, Punishment of the Innocent, Praise for the Uninvolved...

### RE: Minimum sample size

What confidence do you need to work to?

Are you prepared to measure a few to get an idea of the stats and then take more samples if necessary?

Are you confident that all 250 are from the same population and there is no trend say with run order?

Are they a gaussian distribution?

A simple histogram of the results from say 10 will tell you what you really need to know.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Minimum sample size

(OP)
What confidence do you need to work to? 95 or 99%

Are you prepared to measure a few to get an idea of the stats and then take more samples if necessary? No.. Maybe but they just want to do a number that's worth doing and that's it

Are you confident that all 250 are from the same population and there is no trend say with run order? Yes

Are they a gaussian distribution? No idea.

A simple histogram of the results from say 10 will tell you what you really need to know.. Is this just from experience? This is the kind of number I need but would prefer some maths behind it. Even just a level of confidence/accuracy associated with doing say, 10.

Simmantix
---------
Phases of a Project:
Exultation, Disenchantment, Search for the Guilty, Punishment of the Innocent, Praise for the Uninvolved...

### RE: Minimum sample size

No, no maths behind 10. It's enough that a distribution is likely to look recognisable.

If you don't know the shape of the distribution then any calculation is going to be a bit tricky- despite the efforts of bad statisticians throughout history, stats is not a black box.

IF the distribution is Gaussian you can use a chi square test to estimate the variance for your population, to a confidence level, from a given number of samples. This may not be strictly appropriate for a population that is not all that much greater than the sample size, but I am slightly beyond the ragged edge of my experience here. FWIW, at 95% confidence, the estimate for sigma^2 from 15 samples estimate for s^2 is in the range s^2*2.5 to s^2*0.54 .

To that you'll need to add the error in estimating mu which from 15 samples is likely to be pretty good.

So as I said, a bit of preliminary work will be a big help.

I can actually look this stuff up, tomorrow, but if you don't know the shape of the distribution then all the fancy footwork is to no avail.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Minimum sample size

Here's a little toy. column b I filled with 250 gaussian random numbers using the random number generator, with a mean of 20 and an sd of 1.

If you change the sample size in the yellow box then it pulls that number of samples, if you press F9 it'll take another set of samples. Then it tells you the mean and standard variation of the sample, and the +/-3 sigma limits. keep pressing F9 to get an idea of what sort of repeatability you'll get

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Minimum sample size

There are several military standards and handbooks on this subject, since much of military procurement is predicated on qualification with a small sample. MIL-HDBK-108, MIL-HDBK-109, MIL-HDBL-53, MIL-STD-105, etc.

### RE: Minimum sample size

(OP)
Hi again,

Here's hoping that Greg or someone is still interested? So Greg, thanks for your spreadsheet, it helped me make my own and taught me more about normal distributions, etc. than I ever thought I would want to know. Only in doing these sheets, etc. have i learned more about the actual question I am asking. Having spent some time reading about confidence intervals, standard deviations, etc. I thought I would come back on here and try to phrase the question again..

So, my lot size is 250 but most of these parts are sold. My Maximum sample size is 30 as these are in stores or coming back in at some point. I am measuring the OD of the part and this dimension now has a new outer and inner limit. I have approximated a data set using the Excel RNG using Mean:75, STDEV: 0.3, 250 numbers in the same way as on GLs sheet. The limits are, say, 0.29 either side of the mean.

My question is: If I measure the dimension on 30 parts, I might find that eg. 70% of them would be in spec. therefore my rate of attrition is 30% but how confident am I in this attrition rate? Also, how much less confident would I be if I only measured 20 or 10 of them.

At work, we started some Excel-based discussions about confidence intervals and things of this nature but I think we got to the pass rate without knowing how confident we were in the rate we got to. My thoughts were, if you sampled 250 of the 250, you would KNOW with 100% confidence that the attrition rate was 70% and if you measured none, you would have 0% confidence. So what is equation that lets you know how confident you are based around the sample rate versus the lot size?

Or am i getting confused still? I am happy to make assumptions to help with the answer and we will be scanning 10 as above to get the distribution but once we have that, what will I have

Simmantix
---------
Phases of a Project:
Exultation, Disenchantment, Search for the Guilty, Punishment of the Innocent, Praise for the Uninvolved...

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