Chapter 1 Error Mesurement PDF
Chapter 1 Error Mesurement PDF
Chapter 1 Error Mesurement PDF
and Measurements
(BEH 10102)
Basic Concept of
Instrumentations and
Measurements
Instrumentations
And
Measurements
Instruments
A device or mechanism used to determine the
present value of a quantity under observation
Purpose: supply information about some variable
quantity that is to be measured
Basic functions:
Indicating: Provide a visual indication to the quantity being
measured
Recording: Store the quantity in a permanent record
Controlling: Control the quantity
Measurement
The process of determining the amount,
quantity, degree, or capacity by
comparing an unknown quantity with an
accepted standard quantity.
Purposes:
To monitor a process or operation
To control a process
Measurement Processes
Measurement is a process where physical parameters
are changed to significant figures by using certain
instruments.
Those significant figures must followed by units for
showing the characteristic of the measured physical
parameter
Input Signal Output Signal
Measuring
instrument
Physical Electrical
parameters parameters
Before Measurements
1. Measurement method: Identify what are the
parameters to be measured, what the best method is,
how much measurement is needed and how to record
the results.
Digital instrument
Values of the measured parameters are shown in digital form
(significant figures) where it can be read directly.
With this method, parallax error is eliminated.
Digital instruments use digital signals, which is logic binary 0
and 1 method.
Example: digital multimeters, frequency counters etc.
Characteristics of an
Instrument
Accuracy: Showing how close the readings
shown by the instrument to the exact values of
the measured parameters. Usually, the accuracy
of an instrument is depicted in percentage (%).
Expected The design value, i.e. the most probable value that
calculations indicate one should expect to
value measure.
1
The percent of error = 100 % = 2%
50
Accuracy
Percent accuracy:
a = 100% - 2% = 98%
= A x 100% = 0.98 x 100% = 98%
Exercise 1.0
The expected value of the voltage across a
resistor is 80 V. However, the measurement
gives a value of 79 V. Calculate:
(i) absolute error,
(ii) % error,
(iii) relative accuracy, and
(iv) % of accuracy.
Solution
Precision
A measure of the consistency or repeatability of
measurements
A quantitative or numerical indication of the closeness with
which a repeated set of measurements of the same variable
agrees with the average of the set of measurement
Xn Xn
Precision 1
Xn
X n : the value of the n th measuremen t
X n : the average of the set of n measuremen ts
Example 1.4
Table 1.1 gives the set of 10 measurement that were recorded in the
laboratory. Calculate the precision of the 5th measurement
Measureme Measurement
nt Value
Number Xn (volts)
1 98
2 102
3 101
4 97
5 100
6 103
7 98
8 106
9 107
10 99
Solution
Exercise 1.1
Measurement Measurement Value
Number Xn (volts) Calculate the precision Precision
of the 4th measurement
1 98
2 102
3 101
4 97
5 100
6 103
7 98
8 106
9 107
10 99
Solution
Xn Xn
Precision 1
Xn
97 101 .1
1
101 .1
1 0.04
0.96
Static Error
gross errors or
Static human errors,
errors are systematic
categorized errors,
as and random
errors.
a. Gross Error
The fault of the person using the
instruments
Due such things as incorrect reading of
instruments, incorrect recording of
experimental data, or incorrect use of
instruments
b. Systematic Error
Due to problems with instruments,
environmental effects, or observational errors
Recur if several measurements are made of the
same quantity under the same conditions
Instrument errors
Environmental errors
Observational errors
i. Instrumental Errors
(Reference Book/Modul)
If a resistor is known to have a resistance of 100 with possible
error of 10 , the 10 is an absolute error (This is because
10 is stated as an absolute quantity, NOT as a percentage of
the 100 resistance)
E = V1+V2
E = V1-V2
E E
R
I I
Solution
E E E
R Percent error in
I I I
IR IR E E E IR
E E IR I 100 %
R E
I
E E IR I
E IR
I I 100 %
E
E IR
100 %
E E
E I
100 %
E I
5. Quantity Raised to a Power
When a quantity A is raised to a power B, the
percentage error in AB can be shown to be
This is the departure of a given reading from the arithmetic mean of the
group of readings. If the deviation of the first reading, x1 is called d1
and that of the second reading x2 is called d2 and so on,
Deviation: the difference between each piece of test data and the
arithmetic mean. The deviations from the mean can be expressed as
Therefore, the limiting error for the power calculation is the sum of
the individual limiting errors involved. Therefore, limiting error =
2.143 % + 2.813 % = 4.956 %
Dynamic Characteristics
Any instrument that closely obeys above Eq 1.2 over its intended
range of operating conditions is defined as a zero-order instrument.
If in Eq. (1.1) all a's and bs other than ai ao, bo are taken as zero, we get
Any instrument that follows this equation is called a first order instrument.
V 8.14
R 3.493562232 k incorrect
I 2.33
Use the same number of significant figures as in the
original quantity
V 8.14
R 3.49k correct
I 2.33
Review Questions
1. Define the terms accuracy, error, precision, resolution, expected
value, and sensitivity.
2. State the three major categories of error.
3. A person using an ohmmeter reads the measured value as 470 ,
when the actual value is 47 . What kind of error does this
represent?
4. State the three types of systematic errors, giving examples of
each.
5. State the difference between accuracy and precision of a
measurement.
6. Define the following terms:
i. Average value
ii. Arithmetic mean
iii. Deviation
iv. Standard deviation
Practice Problems
1. The current through a resistor is 2.5 A, but the
measurement yields a value of 2.45 A. Calculate the
absolute error and the percentage error of the
measurement.
2. The value of a resistance is 4.7 k, while
measurements yield a value of 4.63 k
calculate
i. the relative accuracy of measurement, and
ii. % accuracy.
3. The output voltage of an amplifier was measured at
eight different intervals using the same digital
voltmeter with the following results: 20.00, 19.80,
19,85, 20.05, 20,10, 19.90, 20.25, 19.95 V. Which is
the most precise measurement?
Practice Problems..
4. A 270 . 10% resistance is connected to a
power supply source operating at
300 V dc. What range of current would flow if
the resistor varied over the range
of 10% of its expected value? What is the
range of error in the current?
5. A voltmeter is accurate to 98% of its full scale
reading.
i. If a voltmeter read 200 V on 500 V range, what is
the absolute error?
ii. What is the percentage error reading of part (i)?