[chbot] Is there a statistician in the house?

[Charles Manning]

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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