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probabilistic Design analysis • 91
3.2.5.4 Comments

The Weibull distribution is used extensively in reliability applications to
model failure times. In engineering, the Weibull distribution is most often
used for strength or strength-related lifetime parameters, and it is the stan-
dard distribution for material strength and lifetime parameters for very brit-
tle materials (for these very brittle materials the “weakest-link-theory” is
applicable).

3.3 Choosing a distriBution for a random
VariaBLe

The type and source of the data you have determines which distribution
functions can be used or are best suited to your needs.

3.3.1 MeASUReD DATA

If you have measured data then you first have to know how reliable that
data is. Data scatter is not just an inherent physical effect, but also includes
inaccuracy in the measurement itself. You must consider that the person
taking the measurement might have applied a “tuning” to the data. For
example, if the data measured represents a load, the person measuring the
load may have rounded the measurement values; this means that the data
you receive are not truly the measured values. Depending on the amount
of this “tuning,” this could provide a deterministic bias in the data that
you need to address separately. If possible, you should discuss any bias
that might have been built into the data with the person who provided that
data to you.
If you are confident about the quality of the data, then how to proceed
depends on how much data you have. In a single production field, the amount
of data is typically sparse. If you have only few data then it is reasonable to
use it only to evaluate a rough figure for the mean value and the standard
deviation. In these cases, you could model the random input variable as a
Gaussian distribution if the physical effect you model has no lower and upper
limit, or use the data and estimate the minimum and maximum limit for a
uniform distribution. In a mass production field, you probably have a lot of
data, in which case you could use a commercial statistical package that will
allow you to actually fit a statistical distribution function that best describes
the scatter of the data.