MECHANICAL
ENGINEERING SYSTEMS
LABORATORY
Group 02
Asst. Prof. Dr. E. İlhan KONUKSEVEN
FUNDAMENTAL
CONCEPTS IN
MEASUREMENT AND
EXPERIMENTATION
MEASUREMENT ERRORS
AND
UNCERTAINTY
THE “ERROR” IN A MEASUREMENT IS
THE DIFFERENCE BETWEEN THE
MEASURED VALUE
AND THE
TRUE VALUE
OF THE “MEASURAND”
The error in a measurement is not known since
the true value of the measurand is not normally
known. But, “estimates” of the nature and the
magnitude of the error can be given.
SINCE THE
TRUE VALUE
IS UNKNOWN
THE DIFFERENCE BETWEEN
THE TRUE VALUE
AND
MEASURED VALUE
CAN ONLY BE ESTIMATED
THE ESTIMATION OF
THE DIFFERENCE BETWEEN
THE TRUE VALUE
AND THE MEASURED VALUE
IS CALLED
UNCERTAINTY
Measurement Error and
Uncertainty
Measurement
Uncertainty
Error
Measured Value
True Value
TYPES OF ERRORS
1. GROSS ERRORS
2. SYSTEMATIC (FIXED)
ERRORS (BIAS)
3. RANDOM ERRORS
1. GROSS ERRORS
LARGELY HUMAN ERRORS DUE TO
MISREADING INSTRUMENTS
INCORRECT ADJUSTMENT
or
IMPROPER USE OF INSTRUMENTS
COMPUTATIONAL MISTAKES
This type of errors can be minimized by proper training
and experience of the personnel involved in
measurement processes.
2. SYSTEMATIC (FIXED)
ERRORS (BIAS)
THESE ERRORS ARE DUE TO
INSTRUMENTS
OR
THEIR ENVIRONMENTS
TYPICAL INSTRUMENT CHARACTERISTICS
WHICH LEAD TO SYSTEMATIC ERRORS ARE :
• FRICTION
• IRREGULAR SPRING TENSION
• IMPROPER CALIBRATION
TYPICAL ENVIRONMENTAL BASED SYSTEMATIC
ERRORS ARE :
• EFFECT OF CHANGES IN
SURROUNDING TEMPERATURE
• HUMIDITY
• BAROMETRIC PRESSURE
• MAGNETIC OR ELECTRICAL FIELDS
ENVIRONMENTAL BASED SYSTEMATIC ERRORS
CAN BE MINIMISED BY
• PROPER CONDITIONING OF THE
ENVIRONMENT
• ISOLATING OR SHIELDING
IN GENERAL
SYSTEMATIC ERRORS CAN BE OVERCOME
BY
APPLYING CORRECTION FACTORS
AFTER DETERMINING THE AMOUNT OF
ERROR
OR
BY CALIBRATING THE
INSTRUMENTS
EXAMPLE :
A THERMOMETER IS CALIBRATED AND THUS
MARKED AT THE FACTORY.
THIS CALIBRATION MAY BE DONE BY EITHER
FULLY OR PARTIALLY IMMERSING THE
THERMOMETER INTO THE CALIBRATION
ENVIRONMENT.
IF A FULL IMMERSION THERMOMETER (ROOM
THERMOMETER) IS PARTIALLY IMMERSED IN A
FLUID THEN A STEM CORRECTION WILL BE
NECESSARY
3. RANDOM ERRORS
THESE ERRORS ARE MOSTLY DUE TO
UNKNOWN AND RANDOMLY OCCURRING
CAUSES
THEY ARE DIFFICULT TO DETERMINE AND
PREDICT
THEY ARE DEALT WITH BY STATISTICAL
METHODS
The only way to offset them is to increase the size of the
data and to use statistical techniques so that the best
estimate of the true value of the measured is obtained.
CALIBRATION
BY CALIBRATION
THE STATIC RESPONSE
OF AN INSTRUMENT IS DETERMINED
DURING CALIBRATION
ALL INPUTS TO THE MEASUREMENT SYSTEM
ARE KEPT CONSTANT EXCEPT THE MEASURAND
WHICH IS VARIED IN A CONTROLLED MANNER
CALIBRATION
A CALIBRATION STANDARD SHOULD,
IF POSSIBLE, BE ABOUT 10 TIMES
MORE ACCURATE THAN THE
INSTRUMENT BEING CALIBRATED
ACCURACY
DEGREE OF CLOSENESS OF
MEASUREMENTS TO THE TRUE VALUE OF
THE MEASURAND
ACCURACY IS DETERMINED BY
COMPARISON WITH CALIBRATED VALUES
ACCURACY
THE ACCURACY OF AN INSTRUMENT IS
EXPRESSED AS :
*
ABSOLUTE ACCURACY
*
RELATIVE ACCURACY
RELATIVE ACCURACY IS DEFINED WITH
RESPECT TO
*
ACTUAL READING
*
FULL SCALE READING
OF THE INSTRUMENT
PRECISION
(REPEATABILITY)
THIS IS THE DEGREE OF AGREEMENT
BETWEEN REPEATED MEASUREMENTS
A precise data implies a small degree of dispersion
(scattering) which may or may not be close to the true
value of the measurand.
ACCURACY AND PRECISION
Instrument
Readings
True
Value
Accurate
&
precise
Inaccurate
but
precise
Imprecise
but
accurate
Inaccurate
&
imprecise
RESOLUTION
IS A MEASURE OF THE SMALLEST
CHANGE IN THE INPUT SIGNAL
THAT THE MEASUREMENT
SYSTEM CAN DETECT
RESOLUTION
MEASURAND AS
MEASURAND AS
MEASURED BY MORE MEASURED BY LESS
ACCURATE
ACCURATE
INSTRUMENT
INSTRUMENT
(Measurement)
(True Value)
10.48
10.50
10.49
10.50
10.50
10.51
10.51
10.52
10.52
10.53
10.53
10.53
10.54
10.53
10.55
10.55
10.56
10.55
16 bit Digital A/D 216=65536 Range = 0-10 Volt
Res= 1 bit Volt Res=1.52 10-4 Volt
Resolution
0.02
0.01
0.01
0.01
0.03
0.02
0.01
0.02
?
THRESHOLD
STARTING FROM ZERO INPUT, IF A
SIGNAL IS SLOWLY INCREASED,
THERE WILL BE SOME MINIMUM
SIGNAL LEVEL BELOW WHICH NO
OUTPUT CHANGE CAN BE DETECTED
HYSTERESIS
If an instrument provides different readings for the
same measurand values depending on whether
measurand is increased or decreased, then the I/O
characteristic of this instrument is said to have an
hysteresis.
Measurement
Output
Measurand
SPAN
THIS IS NORMALLY ACCEPTED AS THE
INPUT SIGNAL RANGE THAT THE
MEASUREMENT SYSTEM WILL MEASURE
EXAMPLE
THERMOMETERS USED BY DOCTORS HAVE A SPAN OF
RANGING FROM
35 °C TO 42 °C
7°C
DYNAMIC RANGE
THIS IS THE SPAN OF AN INSTRUMENT
EXPRESSED IN TERMS OF RATIO OF
THE HIGHEST AND LOWEST VALUES
OF THE MEASURAND
SENSITIVITY
THE SENSITIVITY OF AN INSTRUMENT IS THE RATIO OF
THE CHANGE PRODUCED IN THE INSTRUMENT OUTPUT
TO THE CHANGE IN THE MEASURED VARIABLE
qo
q O
SENSITIVITY 
q i
qi
SENSITIVITY
O Higher
Sensitivity
O
High
Sensitivity
Regions
Lower
Sensitivity
Low
Sensitivity
Region
I
I
ZERO DRIFT AND SENSITIVITY DRIFT
DRIFT IS A VARIATION IN THE OUTPUT OF A
MEASUREMENT DEVICE WHICH IS NOT CAUSED
BY ANY CHANGES IN THE INPUT SIGNAL
ZERO DRIFT AND SENSITIVITY DRIFT
A shift in calibration curve in vertical direction is called
“Zero Drift”.
ZERO DRIFT AND SENSITIVITY DRIFT
A shift in calibration curve to change the sensitivity is
called “Sensitivity Drift”.
LINEARITY
IF AN INSTRUMENT IS SUPPOSED TO
BE LINEAR, THE LINEARITY GIVES THE
INDICATION OF THE MAXIMUM
DEVIATION OF ANY CALIBRATION
POINTS USUALLY FROM A LEAST
SQUARES BEST STRAIGHT LINE FIT
THROUGH THE CALIBRATION DATA
LINEARITY
An instrument is called LINEAR when its I/O relation
(calibration curve) İs a straight line, indicating that the
output is proportional to the input
O
Best
straight
line
I
LINEARITY
The most common method to find the “best fitted
straight line” for a series of calibration data is the
least squares.
Linearity is desirable in most applications. It
eliminates the need of referring to a “calibration
chart” or a “conversion data”.
However, the linearity does not imply a better
accuracy, a higher precision, or greater sensitivity.
INDEPENDENT
LINEARITY
An indication on the max deviation of any calibration
point from the best fitted line expressed as
O
± x % of the
full scale
I
PROPORTIONAL
LINEARITY
An indication on the max deviation of any calibration
point from the best fitted line expressed as
O
± x % of the
actual
reading
I