By LaVar Clegg - Interface, Inc. Presented at the NCLSI - Northwestern US Region Measurement Training Summit - May 21, 2014

1. by
LaVar Clegg
Interface, Inc.
Presented at the NCLSI
Northwestern US Region
Measurement Training Summit
May 21, 2014
1

2. 2

3. Measurement
An established process performed to determine
a physical property of an object quantitatively
True Value
The correct value of a measurand
3

4. Poor accuracy
due to
inconsistency
4
Poor accuracy
due to lack of
trueness
Accuracy
Closeness of a measured value to the true
value

5. Reading (RDG)
The direct measurand output
Full Scale (FS)
The measurand output corresponding to the Maximum
or Rated input in a specific calibration or application
5

6. Error
The difference between the measured value
and the true value
Measurement Uncertainty
An estimate of the range of measured values
within which the true value lies or,
alternatively, the degree of doubt about a
measured value
6

7. The GUM
Evaluation of measurement data — Guide to the
expression of uncertainty in measurement
This Guide establishes general rules for evaluating and
expressing uncertainty in measurement that are
intended to be applicable to a broad spectrum of
measurements
7
Responsibility is shared jointly by the JCGM (BIPM, IEC, IFCC, ILAC,
ISO, IUPAC, IUPAP and OIML) and comparable to NIST Technical
Note 1297

8. Calibration
A documented procedure that compares the
measurements performed by an instrument to
those made by a more accurate instrument or
standard
In the case of Load Cell Calibration, the
procedure establishes a relationship between
the input and the output of the load cell
8

9. 9
Methods of Load Cell Calibration
Approximate
feasible
expanded
uncertainty
Direct Dead Weight ( best for accuracy but
slow and space inefficient) 0.005%
Leveraged Dead Weight (medium for
accuracy but slow and space inefficient) 0.01%
Hydraulic Force Generation Comparison
(fast and space efficient with reasonable
accuracy)
0.04%

10. Self-contained for
minimum floor space
Automated to reduce
human error
Fast
Tension and Compression
10
Interface 10Klbf Calibration
Machine Exemplifies
advantages of Comparison
Method

11. Inside view of Calibration Machine
11
Hydraulic
Pump
Fluid
Reservoir
Cylinder
Control
Feedback
Amplifier
Servo
Amplifier for
driving Servo
Valve

12. Calibration Machine
Load String
12
Load Cell Under Test
Standard Load Cell
Servo System Feedback
Load Cell

13. 13

14. A. Determine what parameter is to be measured and the units of
measure.
B. Identify the components of the calibration process and the
accompanying sources of error.
C. Write an expression for the uncertainty of each source of error.
D. Determine the probability distribution for each source of error.
E. Calculate a standard uncertainty for each source of error for
the range or value of interest.
F. Construct an uncertainty budget that lists all of the
components and their standard uncertainty calculations
G. Combine the standard uncertainty calculations and apply a
coverage factor to obtain the final expanded uncertainty.
14

15. Block
Diagram:
15
Load Frame
Test
Transducer
Standard
Transducer
Feedback
Transducer
Hydraulic
Force
Generator Servo Valve
Servo Amplifier &
Controller
Data Archive
Computer
Gold
Standard
Software
HRBSC
HRBSC
Printer
Monitor

16. 1. Interface servo-controlled hydraulic load frame
2. Interface model 1600 Standard Transducer
3. Industrial computer
4. HRBSC mV/V signal conditioning instruments
5. 8-wire Interconnect cables
6. Gold Standard software for automation and data
handling
16

17. A. (Cont’d)
What we are actually measuring is the mV/V
signal from two load cells.
The association of these signals to units of
force is done by mathematics in software.
We will express uncertainty in units of %RDG.
17

18. The overall expression for Vtest as a function of uncertainty contributors:
Vtest = f (CS, DS, PS, TS, RF, CH, DH, TH, LH, NH, RH CH, DH, TH, LH, NH, RH)
Where
CS = Calibration of a Standard Transducer.
DS = Drift in Standard Transducer since last Calibration.
PS = Creep in the Standard Transducer.
TS = Temperature Effect On Output of the Standard Transducer.
RF = Nonreproducibility of the hydraulic load frame due to errors in
alignment, thread concentricity, parallelism, and flatness
of the load string components.
CH = Calibration of HRBSC Indicating instrument.
DH = Drift in HRBSC Indicating instrument since last calibration.
TH = Temperature effect on HRBSC Indicating instrument.
LH = Nonlinearity of HRBSC Indicating instrument.
NH = Noise of HRBSC Indicating instrument.
RH = Digital resolution of HRBSC Indicating instrument.
18

19. For example, for the parameter
LH = Nonlinearity of HRBSC Indicating instrument.
Nonlinearity was measured on several instruments over
many calibration intervals over several years making 720
data points. The result:
Maximum Nonlinearity = 0.00007 mV/V
Standard Deviation = 0.00002 mV/V
19

20. For illustration, consider a scenario where both the test
and the Standard transducers have rated sensitivity of 4
mV/V at the same capacity.
We desire to evaluate uncertainty at 20% of capacity.
(0.8mV/V)
We must express the uncertainty in units of %RDG.
Then
LH = 0.00007 mV/V = 0.00007 / 0.8 = 0.0088 %RDG
20

21. We generally choose among 3
distribution types Factor
Normal – fits many natural 1
phenomena
Rectangular or Uniform – fits 0.557
parameters with limits
Triangular – fits parameters 0.408
with a central tendency
21

22. For the LH example, a central tendency was observed in
the data being analyzed. This is consistent with the
large difference between the Std Dev and the Peak Error
and therefore suggests a triangular distribution.
Selecting the probability distribution is often a judgment call.
22

23. Multiply the uncertainty expression by the distribution factor.
For the LH example,
Standard uncertainty ui = 0.0088 (0.408) = 0.0036 %RDG
23

24. In similar manner, derive the standard uncertainty for all
other error sources by determining the expression of
uncertainty and the probability distribution, and then
calculating the standard uncertainty.
Express each component in units of %RDG.
Sources are usually evaluated by actual data and/or
established specifications.
The following slide shows a summary for typical values.
24

25. Example for 4 mV/V load cells at 20% of capacity:
25
Interval Interval Probability Uncertainty
Source of Uncertainty Type Expression (%RDG) Distribution Factor ui (%RDG)
CS NIST Cal of Standard A
0.00160%Cal
Range
0.0128 Std Dev 1 0.0128
DS Drift in Standard B 0.012% RDG 0.0120 Triangular 0.408 0.0049
PS Creep in Standard B 0.0055% RDG 0.0055 Rectangular 0.577 0.0032
TS Temperature Effect on Std B 0.0029% RDG 0.0029 Rectangular 0.577 0.0017
RF Nonreproducibility , load frame B 0.0130% RDG 0.0130 Std Dev 1 0.0130
CH Cal of HRBSC, Std B 0.0056% RDG 0.0056 Rectangular 0.577 0.0032
DH Drift in HRBSC, Std A 0.0009% RDG 0.0009 Std Dev 1 0.0009
TH Temperature Effect HRBSC, Std B 0.0020% RDG 0.0020 Rectangular 0.577 0.0012
LH Nonlinearity of HRBSC, Std B 0.00007 mV/V 0.0088 Triangular 0.408 0.0036
NH Noise of HRBSC, Std B 0.00004 mV/V 0.0050 Rectangular 0.577 0.0029
RH Digital Resolution HRBSC, Std B 0.00001 mV/V 0.0013 Rectangular 0.577 0.0008
CH Cal of HRBSC, Test B 0.0056% RDG 0.0056 Rectangular 0.577 0.0032
DH Drift in HRBSC, Test A 0.0009% RDG 0.0009 Std Dev 1 0.0009
TH Temperature Effect HRBSC,Test B 0.0020% RDG 0.0020 Rectangular 0.577 0.0012
LH Nonlinearity of HRBSC, Test B 0.00007 mV/V 0.0088 Triangular 0.408 0.0036
NH Noise of HRBSC, Test B 0.00004 mV/V 0.0050 Rectangular 0.577 0.0029
RH Digital Resolution HRBSC, Test B 0.00001 mV/V 0.0013 Rectangular 0.577 0.0008

26.  Per the GUM, we combine the component standard
uncertainty numbers using the root-sum-of-squares
method.
 The combined RSS result will have a confidence
level of only one standard deviation or about 68%.
It is more practical to have higher confidence.
Therefore we apply a coverage factor of 2 meaning
the confidence of all results being within 2 standard
deviations which confidence is 95%. The following
budget chart includes the RSS combination and the
Expanded Uncertainty with coverage factor = 2.
26

27. Expanded uncertainty U estimation example complete
27
Interval Interval Probability Uncertainty
Source of Uncertainty Type Expression (%RDG) Distribution Factor ui (%RDG)
CS NIST Cal of Standard A 0.00160%Cal Range 0.0128 Std Dev 1 0.0128
DS Drift in Standard B 0.012% RDG 0.0120 Triangular 0.408 0.0049
PS Creep in Standard B 0.0055% RDG 0.0055 Rectangular 0.577 0.0032
TS Temperature Effect on Std B 0.0029% RDG 0.0029 Rectangular 0.577 0.0017
RF Nonreproducibility , load frame B 0.0130% RDG 0.0130 Std Dev 1 0.0130
CH Cal of HRBSC, Std B 0.0056% RDG 0.0056 Rectangular 0.577 0.0032
DH Drift in HRBSC, Std A 0.0009% RDG 0.0009 Std Dev 1 0.0009
TH Temperature Effect HRBSC, Std B 0.0020% RDG 0.0020 Rectangular 0.577 0.0012
LH Nonlinearity of HRBSC, Std B 0.00007 mV/V 0.0088 Triangular 0.408 0.0036
NH Noise of HRBSC, Std B 0.00004 mV/V 0.0050 Rectangular 0.577 0.0029
RH Digital Resolution HRBSC, Std B 0.00001 mV/V 0.0013 Rectangular 0.577 0.0008
CH Cal of HRBSC, Test B 0.0056% RDG 0.0056 Rectangular 0.577 0.0032
DH Drift in HRBSC, Test A 0.0009% RDG 0.0009 Std Dev 1 0.0009
TH Temperature Effect HRBSC,Test B 0.0020% RDG 0.0020 Rectangular 0.577 0.0012
LH Nonlinearity of HRBSC, Test B 0.00007 mV/V 0.0088 Triangular 0.408 0.0036
NH Noise of HRBSC, Test B 0.00004 mV/V 0.0050 Rectangular 0.577 0.0029
RH Digital Resolution HRBSC, Test B 0.00001 mV/V 0.0013 Rectangular 0.577 0.0008
uc Combined Uncertainty Root Sum of Squares Method 0.0207
U Expanded Uncertainty U = k uc where k = 2 for confidence level of 95% 0.041

28. A. We determined that we were measuring mV/V output of load cells in
a comparison method.
B. We identified the components of the calibration process that
contribute error.
C. We wrote an expression for the uncertainty for an example source of
error.
D. We determined the probability distribution for the example source of
error.
E. We calculated a standard uncertainty for the example source of error
for a range of interest.
F. We constructed an uncertainty budget using typical values for all of
the sources and their standard uncertainty calculations
G. Combine the standard uncertainty calculations by the RSS method
and applied a coverage factor of 2 for 95% confidence in U.
28

29. These parameters are typically stated on transducer
data sheets and are often confused with “accuracy”:
Nonlinearity
Hysteresis
Static Error Band
They are “relative” because they are only ratios and are
stated in units of “% Full Scale” rather than in force units
or mV/V units.
29

30. One could ask, “Can a calibration process that has an expanded
uncertainty of approximately 0.04% produce a valid test for a
nonlinearity specification of 0.02%FS, for example”?
The answer is yes. The reasoning lies in these facts:
1. The 0.04% is the uncertainty of a measurement of physical
units, say mV/V or lbf or kN. The measurement has scale.
2. Whereas nonlinearity is a relative quantity that ratios
measurements at 2 different input values, all other
conditions remaining constant. The quantity has no scale.
3. Most of the uncertainty sources are errors that are constant
as %RDG over a wide range of inputs.
4. The readings for the relative ratio are taken at nearly the
same time and in the same setup under similar conditions.
30

31. 31
Source of Uncertainty Comment
CS NIST Cal of Standard
Fitted Curve minimizes nonlinearity
over wide range
DS Drift in Standard Linear as %RDG
PS Creep in Standard Linear as %RDG
TS Temperature Effect on Std Linear as %RDG
RF Nonreproducibility , load frame Near linear as % RDG
CH Cal of HRBSC Linear as %RDG
DH Drift in HRBSC Linear as %RDG
TH Temperature Effect HRBSC Linear as %RDG
LH Nonlinearity of HRBSC Nonlinear but small contributor
NH Noise of HRBSC Nonlinear but small contributor
RH Digital Resolution HRBSC, Std Nonlinear but small contributor

32. Measurement uncertainty for relative errors is not
normally reported or stated.
To show that relative errors can be tested with the
process for absolute uncertainty herein discussed, 3
demonstrations are presented.
a. Use of fitted curves for standard transfer function
b. Linearity of load cell drift over time
c. Interface tests of nonlinearity and hysteresis
compared to NIST
32

33. The above plot shows an extreme case of high nonlinearity that
contributes small error due to the 5th degree polynomial fit
33

34. -0.040
-0.020
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
1980 1984 1988 1992 1996 2000 2004 2008 2012 2016
OutputDeviationfromNominal(%RDG)
History of NIST Calibration, STD-18
4K T 10K T 4K C 10K C
34

35. 35
-0.200
-0.180
-0.160
-0.140
-0.120
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
0.100
1986 1990 1994 1998 2002 2006 2010 2014
OutputDeviationfromNominal
(%RDG)
History of NIST Calibration, STD-16
100K Ten 200K Ten 100K Comp 200K Comp

36. 36
Standard 10, FS=75Klbf
6/28/2013 2/10/2009 4/11/2005 Average
LAB TENSION (%FS) (%FS) (%FS) (%FS)
NIST Nonlinearity -0.027 -0.026 -0.026
Interface Nonlinearity -0.027 -0.028 -0.029
Difference 0.001 0.002 0.003 0.002
NIST Hysteresis 0.033 0.036 0.035
Interface Hysteresis 0.033 0.035 0.032
Difference 0.000 0.001 0.003 0.001
COMPRESSION
NIST Nonlinearity -0.026 -0.026 -0.026
Interface Nonlinearity -0.028 -0.023 -0.023
Difference 0.003 -0.004 -0.004 -0.001
NIST Hysteresis 0.033 0.035 0.032
Interface Hysteresis 0.031 0.031 0.034
Difference 0.002 0.004 -0.002 0.001

37. 37
Standard 13, FS=25Klbf
11/17/2011 10/23/2007 6/22/2005 Average
LAB TENSION (%FS) (%FS) (%FS) (%FS)
NIST Nonlinearity -0.012 -0.012 -0.012
Interface Nonlinearity -0.012 -0.009 -0.010
Difference 0.001 -0.003 -0.002 -0.002
NIST Hysteresis 0.022 0.023 0.023
Interface Hysteresis 0.024 0.027 0.022
Difference -0.002 -0.004 0.001 -0.002
COMPRESSION
NIST Nonlinearity -0.015 -0.015 -0.017
Interface Nonlinearity -0.015 -0.013 -0.012
Difference 0.000 -0.002 -0.005 -0.002
NIST Hysteresis 0.025 0.027 0.029
Interface Hysteresis 0.024 0.024 0.024
Difference 0.001 0.003 0.005 0.003
Interface and NIST tests have minimal
difference in NL & H (25 Klbf example)

38. The preceding charts of actual data show
that it is very feasible to test relative
parameters (in units of %FS) for tolerances
tighter than the uncertainty of the absolute
measurements (in units of force).
38

39. Answer: In many applications the gain or scale of the system
is set on site, a separate operation from the load cell
calibration and usually at a different place and time. This is
where the load cell mV/V output is converted to other physical
units.
Often this gain setting or conversion process has no capability
for nonlinearity and hysteresis correction. Therefore it is
desirable for these parameters to be minimal.
39

40. 40