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3.2 Uncertainty Analysis
Uncertainty Analysis I
Quantifying the unknown and the
unknowable
Definitions I: Error
•Th
e
Error
, is the difference between the
true value,
x
, and a measured value,
x
i
:
• Since,
x
is unknown, then so is
Error
.
•A
lw
ay
s
.
i
x
x
Error
−
=
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View Full Document Definitions II: Uncertainty
• For multiple measurements, a mean value,
,
can be estimated, hence:
• Since
x
remains unknown, then
Bias
is still
unknown.
•Un
c
e
r
t
a
i
n
ty
,
u
x
,
∆
x
, is an estimate
of
Bias
.
x
x
x
Bias
−
=
Classification of errors
• Systematic
→
bias, may
be measured and
corrected.
•R
and
om
.
The likely
magnitude of the
remaining error must be estimated.
• Use the larger of: (
i
) instrument resolution,
(
ii
) standard deviation, (
iii
) precision.
•(
ii
) & (
iii
) require multiple measurements
Single sample uncertainty I
Imagine a ruler with two scale resolutions:
• Suppose the scale marks exactly represent the limit of
our ability to locate the blob.
We may say only which
mark is closest.
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This note was uploaded on 10/12/2009 for the course AME 341AL at USC.
 '07
 Pottebaum

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