This document discusses measurement errors and uncertainty. It defines measurement as assigning a number and unit to a property using an instrument. Error is the difference between the measured value and true value. There are two main types of error: random error, which varies unpredictably, and systematic error, which remains constant or varies predictably. Sources of error include the measuring instrument and technique used. Uncertainty is the doubt about a measurement and is quantified with an interval and confidence level, such as 20 cm ±1 cm at 95% confidence. Uncertainty is important for tasks like calibration where it must be reported.

1. errors of measurement and
systematic errors

2. What is a measurement?
• A measurement tells us about a
property of something.
• A measurement gives a number to
that property.
• Measurements are always made
using an instrument of some kind.
• The result of a measurement is
normally in two parts: a number
and a unit of measurement, e.g.
‘How long is it? ... 2 metres.’
www.theapprentiice.com

3. What is Error …?
• Error in science does not mean the terms of
mistake .
• Error in a scientific measurement means the
different between the individual result and
true value.
• Errors cannot be eliminated although the
measurement is being done very carefully .
• The total value of error is made up of a
number of error source.

4. THE ROLE OF ERROR
• Repeated measurement will contribute the
discrepancy or random errors. The
discrepancy can only be obtained when there
are differences between the readings and the
true value. The smaller the random errors, the
greater the precision.
• If the individual readings are the same, there
still an error called uniform error or systematic
error.

5. Random Error
• a) A component of the error of measurement
which, in the course of a number of
measurements of the same measurand, varies
in an unpredictable way.
• b) The mean of a large number of
measurement influenced by random errors
matches the true value.
• c) It can be evaluate by study the repeated
measurement values.

6. Systematic Error
• a) The exist of the error is known by inference.
• b) A component of the error of measurement
which, in the course of a number of
measurements of the same measurand, remains
constant or varies in a predictable way
• c) The mean of a large number of measurements
influenced by systematic errors deviates from the
true value.
• d) It can be evaluate by comparing the
measurement results with a higher standard,
which is measurement.

7. Sources of Measurement Errors
Dynamic error
Characterised by frequency and phase response
of the system for periodic variations in the
measured input.
Loading error
It is the difference between the value measured
before and after the measurement system is
measured.

8. Static error
It is cause by physical nature of various
components of the measuring system.
Characteristic error
It is the deviation of measurement under
constant environmental conditions from the
theoretical predicted performance.

9. • Elastic deformation
It is divided into two ;
a)Error cause from reflection when end gage is
used for setting or measure.
b)Error cause from deflection due to self weight
of the object.

10. • Parallax
Any instrument that using pointer and scale
may have parallax error because the gap
between pointer and scale is different at any
reading angle.
Contact pressure
While measuring, the pressure at contact
causes some penetration causing error in
measurement.

11. • Backlash
Due to backlash in gears and screw threads,
some motion is lost to overcome backlash
• Hysteretic
It is a source of errors in electrical instruments.
Ascending values are observed when decrease
current or voltage.

12. • Avoidable error
The errors occurred due to non-alignment of
workpiece centre, improper of measuring
instruments, etc.
Human Error
Difficult to detect. It can be include a tendency to
read high or low using a wrong instrument.
Human training is the best way to prevent these
error

13. • Errors in Technique and Experimental Error
If wrong techniques is used. Example: Calibration
technique for vernier is used for micrometer.
Education helps to prevent these errors.
Computational Error
Can be random or continuous, but, once an error
has started, it usually establishes itself in the
computation. This error is affected by
environmental, fatigue and instrumentation.

14. • Chaotic Error
Extreme disturbances that ruin or hide the
measurement results. This error include
vibration, shock, extreme noise and etc.

15. Uncertainty of measurement
www.theapprentiice.com

16. What is uncertainty of measurement?
• The uncertainty of a measurement tells us
something about its quality.
• Uncertainty of measurement is the doubt
that exists about the result of any
measurement.
www.theapprentiice.com

17. Expressing uncertainty of
measurement
Since there is always a margin of doubt about any measurement, we need
to ask ‘How big is the margin?’ and ‘How bad is the doubt?’ Thus, two
numbers are really needed in order to quantify an uncertainty. One is the
width of the margin, or interval. The other is a confidence level, and
states how sure we are that the ‘true value’ is within that margin.
For example:
We might say that the length of a certain stick measures 20 centimetres plus
or minus 1 centimeter, at the 95 percent confidence level. This result
could be written:
20 cm ±1 cm, at a level of confidence of 95%.
The statement says that we are 95 percent sure that the stick is between 19
centimeters and 21 centimeters long.
www.theapprentiice.com

18. Error versus uncertainty
• It is important not to confuse the terms ‘error’ and
‘uncertainty’.
• Error is the difference between the measured value and
the ‘true value’ of the thing being measured.
• Uncertainty is a quantification of the doubt about the
measurement result.
• Whenever possible we try to correct for any known
errors: for example, by applying corrections from
calibration certificates.
• But any error whose value we do not know is a source
of uncertainty.
www.theapprentiice.com

19. Why is uncertainty of measurement
important?
• to make good quality measurements
• to understand the results.
• You may be making the measurements as part of a:
– calibration - where the uncertainty of measurement must be
reported on the certificate
– test - where the uncertainty of measurement is needed to
determine a pass or fail
– or to meet a
• tolerance - where you need to know the uncertainty before you can
decide whether the tolerance is met
• ... or you may need to read and understand a calibration
certificate or a written specification for a test or
measurement.
www.theapprentiice.com