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Resistance Test Uncertainty Analysis: Overview of Procedure

The uncertainty associated with all the laboratory measurements involves a random precision error and

a fixed bias error. The errors can each be broken down further into three components. !" calibration

errors #" data ac$uisition errors and %" data reduction errors& and '" conceptual basis erros.

Recall: Random precision errors are observed in repeated independent measurements, while bias is the

difference between an average set of readings and the true value. An example of a bias error is thesensor uncertainty as specified by the sensor manufacturer.

The procedure attempts to $uantify the bias and precision limits& and total uncertainty for the totalresistance coefficient (T" and residuary resistance coefficient (R".

To do this& the bias error associated with these coefficients is determined from:

BCT#=CT

B#

CT!

B!#

CTRx

BRx#

CT

B#

since (Tis a function of )&*&Rxand density:

CT

Tm=

Rx

Tm

+.,!#

and

BCR#

=CRCT

BCT

#

CR " B"#

CRC#

BC#

#

since (Ris a function of (T& k& (-:

CR=CT!,deg

!"C#!, deg

)o& the maority of the procedure is concerned with obtainin/ the uncertainty associated with each of

the variables above. The sources of error are or/ani0ed into the followin/ flowchart& where the

variables of interest are estimated for each individual measurement system under the cate/ories ofcalibration& data ac$uisition& data reduction& and conceptual basis.

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1ote as well that the total uncertainty for (Tand (Ris /iven by the root sum s$uare of the uncertainties

of the total bias and precision limits.

$CT#=BCT

#%CT

#

$CR #

=BCR #

%CR #

The uncertainty number is some combination of the bias and the precision errors and has a simpleinterpretation: the lar/est error reasonably expected. -or example& the interval

&$

represents a band within which the true value of the measurement is expected to lie& A1)23A)45&

!67,".

-inally& note that the bias limit associated with the temperature conversion is not considered in the

analysis& so 8(T!, de/rees9 8(T

Tm

#inal note regarding lab data:'ver the course of testing, it was clear that repeatability was going to be an issue (witnessed by what

appeared to be a substantial drift in the resistance reading over time). This may be due to the model

si*e, or insufficient settling time between runs (although +-+ minutes was allotted for settling timeduring the test). /n order to illustrate typical results and ma"e the uncertainty analysis meaningful to

the students, rather than s"ewed by these precision results, the resistance values of the repeated runs

were estimated.