IEEE Solid-State Circuits Magazine - Spring 2014 - 52

Measuring a Small
Number of Samples
and the 3v Fallacy
Shedding light on confidence and error intervals.

M

Hanspeter Schmid
and Alex Huber

any solid-state circuits papers today report the mean n and the standard deviation v of measurement results obtained from a small number of test chips and then compare them with numbers other authors
obtained. Almost none of them discuss confidence intervals, ranges of
values for that standard deviation within which the true value lies with a
certain probability. Many implicitly assume that the n ! 3v range would contain all but 0.27%
of chip samples to be expected in volume production. This is incorrect even if it is certain that
the measured quantity is exactly normal distributed.
In this tutorial article, we shed some light on confidence and error intervals and show how
the naive approach to interpreting n ! 3v can lead to a misjudgment of error probabilities by
orders of magnitude. We show that using standard deviations only works for normal distributions, and then we propose a better, distribution-independent way to report measurements in
the future.
Along the way we show how many ICs you actually need to measure to obtain a range that
contains, with a probability as small as 75%, all but 0.27% of the ICs coming from the same batch
as the measured ICs. This number is 1,027.
Digital Object Identifier 10.1109/MSSC.2014.2313714
Date of publication: 24 June 2014

52	

s p r i n g 2 0 14	

IEEE SOLID-STATE CIRCUITS MAGAZINE	

1943-0582/14©2014IEEE



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