[chbot] Is there a statistician in the house?

[Henri Shustak]

Hi if it helps. I do know a statistician. Let me know if you would like me to ask them about this?

Henri

> On 19/10/2020, at 12:01 PM, Charles Manning <cdhmanning at gmail.com> wrote:
> 
> The biggest problem with statistics is misuse due to making invalid assumptions of randomness.
> 
> This particularly applies to things like testing components which are batch built and sampling a whole lot of items from the same batch can give you poor results.
> 
> 
> On Sun, Oct 18, 2020 at 7:26 PM Helmut Walle <helmut.walle at gmail.com> wrote:
> You can use a normal distribution for your random variable (the number of failures within a
> sample) if the pass-fail outcomes of the individual elements of that sample (the units) are
> statistically independent of each other, and identically distributed (but these individual
> outcomes need not be following a normal distribution themselves).
> In practice this means that you cannot easily analyse the situation if your process is drifting
> throughout the production of one batch - in that case you would have to stabilise your process
> first. But as long as there are just some random variations, you just have to select the units
> that go into the sample as randomly as possible.
> 
> With that given, the number of failures in a sample then follows a normal distribution (for
> large sample sizes, that is - strictly speaking, it is a binomial distribution for finite sample
> sizes, but in practice this can be approximated by a normal distribution even for sample sizes
> as low as 100). You can calculate the average and standard deviation of the distribution.
> Confidence intervals for a certain target confidence level can then be expressed as multiples of
> the standard deviation. If you want a higher confidence obviously your confidence intervals will
> be wider. Conversely, if you want a narrower range of outcomes your confidence will be low.
> 
> A few references that may help for your use case:
> 
> https://www.qualtrics.com/au/experience-management/research/determine-sample-size/?rid=ip&prevsite=en&newsite=au&geo=NZ&geomatch=au
> https://www.dummies.com/education/math/statistics/choosing-a-confidence-level-for-a-population-sample/
> https://www.quanterion.com/test-samples-how-many-are-needed/
> 
> Kind regards,
> 
> Helmut.
> 
> 
> On 18/10/2020 17:57, Stephen Irons wrote:
> > I seem to remember doing calculations like this a long time ago...there are a number of
> > variations which are probably all related. I have not been able to find any Google search terms
> > that give me anything useful.
> > 
> > A factory produces a batch of 10_000 units.
> > 
> >   * I test 100 units; there are 3 failures. What failure rate can I expect from the whole batch?
> >     What is my confidence in that estimate?
> >   * I test 100 units; there are 0 failures. What failure rate can I expect from the whole batch?
> >     What is my confidence in that estimate?
> >   * How many units do I need to test to have 99% confidence that there will be less than 1%
> >     failure rate from the whole batch?
> > 
> > Can someone tell me what you call this type of calculation? Point me to a suitable reference site?
> > 
> > All of the examples I find online are of the form: a factory produces widgets with x% failure
> > rate; out of a sample of y units, what is the probability of finding z defective units...this is
> > probably the same calculation from the other direction.
> > 
> > This is just for interest. In my specific case, I had 36 failures out of a sample of 50 taken
> > from a batch of a few thousand -- this is clearly not acceptable. But we now have a repeatable
> > test that causes the failure.
> > 
> > Stephen Irons
> > 
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