MEASUREMENT ERROR GOOD PPT TO LEARN TO APPEAR FOR EA

1. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 1--
Fall 2023
Engineering Measurements
(MCE 311)
Sources of Measurement Errors
Dr. Mehdi Ghommem

2. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 2--
Bias or Systematic Errors
➢ Bias errors, are systematic errors that occur in the
same way each time a measurement is made. For
example, an instrument may always read 5% too
high. This can be caused by a erroneous calibration
or a bad use of the instrument.
➢ Cause:
• Calibration Error
• Recurring Human Errors
• Defective Equipment Errors
• Loading Error (a disturbance caused by the
presence of the measuring device)

3. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 3--
Precision or random errors
➢ Precision errors, also called random errors, are different
for each successive measurement but have an average
value of zero.
➢ Cause:
⚫ Human errors
⚫ Equipment disturbance errors
⚫ Fluctuating condition errors

4. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 4--
Illegitimate error
➢ Mistakes during an experiment.
➢ Computational errors after an experiment.
These errors should not be included when reporting
experimental data.
(No excuses…)

5. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 5--
Hysteresis
Many sensors have the undesirable characteristic of giving one value when
the input is increasing and a different when it is decreasing. This is called
hysteresis.
In general terms, hysteresis means a lag between input and output in a system
upon a change in direction.
Example:
Backlash
in Gears


6. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 6--
Instrument Performance Ratings
Accuracy The difference between the measured value and the
actual value, reported as a maximum.
Precision The difference between the instrument’s reported
values during repeated measurements of the same quantity.
Resolution The smallest increment of change in the measured value
that can be determined from the instruments read out.
Usually similar or smaller than precision.
Sensitivity The change in the output of an instrument per unit
change in the input. It is also the slope of a linear static
calibration curve.
Hysteresis As a general term, hysteresis means a lag between
input and output in a system upon a change in
direction.

7. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 7--
Linearity error
• linear input/output behavior, along a
defined range of inputs.
𝒚𝑳(𝒙) = 𝒂𝟎 + 𝒂𝟏𝒙.
• Parameters:
the slope of the input/output relation (𝑎1)
and the zero input value (𝑎0).
• Deviation from linear behavior is
𝒆𝑳(𝒙) = 𝒚(𝒙) − 𝒚𝑳(𝒙).
The spec is usually the percentage error
relative to full scale.

8. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 8--
Threshold
The minimum input that gives a discernable output.
The range (min. value to max. value) for a measured
quantity in an instrument.
Span=Full scale

9. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 9--
Significant Figures
• The number of significant figures is usually inferred by the number
of figures given (except for leading zeros). For example, 706, 3.14,
and 0.00219 are assumed to be numbers with three significant
figures.
• Computers and calculators display calculations to many significant
figures. However, you should never report a number of significant
figures of a calculation any greater than the smallest number of
significant figures of the numbers used for the calculation.
• For example, determine the circumference of a solid shaft with a
diameter of 𝑑 = 11 𝑚𝑚. The circumference is given by 𝐶 = 𝜋𝑑.
Since 𝑑 is given with two significant figures, 𝐶 should be reported
with only two significant figures.

10. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 10--
Number of significant digits
➢ Count
⚫ Every nonzero digit is significant
⚫ Zeroes between non zeroes are significant
⚫ Zeroes at the end (right) of a number with a
decimal point are significant. Ex 300.00 ⟶ 5
➢ Don’t count
⚫ Zeroes in front (left) of non-zero digits are not
significant. Ex 00.300 ⟶ 3
⚫ Zeroes at the end (right) of a number without a
decimal point are not significant. Ex 300,000 ⟶ 1

11. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 11--
Example: Calibration of a spring scale.
Plot of scale
readings.
Table of scale readings.
𝑅𝑏 = 1.290𝑊 − 0.374
𝑊𝑏 = 0.775𝑅 + 0.290
𝐹. 𝑆 = 𝑅𝑏
𝑚𝑎𝑥
− 𝑅𝑏
𝑚𝑖𝑛
= 6.076 − −0.374 = 6.45

12. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 12--
Table of errors
Example: Calibration of a spring scale.
𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = 𝑀𝑎𝑥(𝐷𝑒𝑣)
0.45 𝑎𝑛𝑑 − 0.40
𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦%𝐹𝑆 =
0.45
6.45
= 7%
−0.4
6.45
= −6.2%
𝑅𝑒𝑝𝑒𝑎𝑡𝑏𝑖𝑙𝑖𝑡𝑦 =
𝑀𝑎𝑥(𝑅𝑖
𝑚𝑎𝑥
− 𝑅𝑖
𝑚𝑖𝑛
) = 0.17
𝐻𝑦𝑠𝑡𝑒𝑟𝑖𝑠𝑖𝑠 =
𝑀𝑎𝑥 𝑅𝑖
𝑢𝑝
− 𝑅𝑖
𝑑𝑜𝑤𝑛
= 0.13 − −0.39
= 0.52
At 2.5 cycle 3 and 4
𝐷𝑒𝑣 = 𝑅𝑖 − 𝑅𝑏𝑖
𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑒𝑟𝑟𝑜𝑟 = SE=
𝑀𝑎𝑥 𝑅𝑖
𝑎𝑣𝑒
) − 𝑀𝑖𝑛(𝑅𝑖
𝑎𝑣𝑒
= 0.41 − −0.35 = 0.76
+6.4%, −5.4%

13. Introduction to Engineering
Experimentation, Third Edition
M. Ghommem, Fall 2023, 10:37 AM -- 13--
Plot of average deviation data for scale
calibration
Plot of deviation data for scale calibration
Example: Calibration of a spring scale.