TOPIC 1:

MEASUREMET AND ERROR

DEE1012- MEASUREMET

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Learning outcome:

1) Understand measurement process; primary sensing

element, variable manipulation element and data

presentation element.

2) Understand error in measurement; gross error,

systematic error, absolute error, relative error.

3) Understand Standards used in measurement;

international standard, primary standard, secondary

standard, working standard.

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INTRODUCTION

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INTRODUCTION

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INTRODUCTION

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INTRODUCTION

• Measuring is basically is used to monitor a process or

operation or as well as the controlling process

• For example thermometers, barometers, are used to

indicate the environmental conditions

• Similarly water, gas and electric meters are used to

keep track of the quantity of the commodity used,

and also special monitoring equipment used in

hospital

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DEFINITION OF MEASUREMENT

• The process of determining the amount, degree, or

capacity by comparison ( direct or indirect) with the

accepted standards of the system units being used.

(Electronic measurement, H.s Kalsi)

OR

• The process by which physical parameters can be

converted to meaningful numbers. (Bhavani and

Vasantha)

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DEFINITION OF MEASUREMENT

PROCESS,

MACHINE

OR SYSTEM

BEING

MEASURED

MEASUREMENT

SYSTEM

OUTPUT INPUT

True value

of

variable

Measured

value of

variable

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Before make a measurement, the

things that must be considered is:

• Measurement method

• Identify which parameter to be measured

• How much measurement should be taken

• Select the appropriate instrument

• Have the knowledge and experience of handling

equipment

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ELEMENT OF MEASUREMENT SYSTEM

• Any instrument or a measuring system can be described

in general by using block diagram.

• The block diagram indicates the necessary elements and

their functions in a general measuring system

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BLOCK DIAGRAM OF FUNCTIONAL

ELEMENTS OF AN INSTRUMENT

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Converted signal Amplified

signal

Human readable

form

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Example of element in measurement

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The various elements can be grouped

as: 1. Primary sensing element.

2. Variable conversion element.

3. Variable manipulation element.

4. Data transmission element

5. Data presentation element.

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i. Primary sensing element:

• An element of an instrument which makes first, the

contact with the quantity to be measured.

• In ammeter, coil carrying current to be measure is

primary sensing element.

• In most of the cases, a transducer follows primary

sensing element which converts the measured into

a corresponding electrical signal.

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ii. Variable Conversion Element (Data

Conditioning)

• The output of the primary sensing element is in electrical

form such as voltage, frequency or any other electrical

parameter.

• Such an output may not be suitable for the actual

measurement system.

• For example of the measurement system is digital then

the analog signal obtained from the primary sensing

element is not suitable for the digital system.

• Thus analog to digital converter is required which is

variable conversion element.

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iii. Variable Manipulation Element

(Data Conditioning)

• The level of the output from the previous stage may not

be enough to drive the next stage.

• Thus, variable manipulation element manipulates the

signal, preserving the original nature of the signal.

• For example an amplifier which just amplifies the

magnitude of the input, at its output, retaining the

original nature of the signal.

• It is not necessary that variable manipulation element

must be always after variable conversion element

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iv. Data transmission Element

• When the elements of the system are physically

separated, it is necessary to transmit the data from

one stage to other.

• This is achieved by the data transmission element.

• The transmitted data may be used by the system,

finally for monitoring, controlling or analyzing

purposes.

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vi Data presentation element:

• the person handling the instrument must get information in the proper form, according to the purpose for which it is intended.

• If the data is to be monitored, then visual display devices are used as data presentation element.

• If the signal is to be recorded for analysis purpose, then magnetic tapes, recorders, high speed cameras are used as data presentation elements.

• For control and analysis purpose, the microprocessors, computers and microcontrollers may be used as data presentation elements.

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Example: Analog meter

• Consider a simple analog meter used to measure current or voltage as shown in Figure 3.

• The moving coil is primary sensing element.

• The magnets and coil together act as data conditioning stage to convert current in a coil to a force.

• This force is transmitted to the pointer through mechanical linkages which act as data transmission element.

• The pointer and scale act as data presentation element.

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Example Analog meter

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TERMINOLOGY OF SCALE AND RANGE

• Scale

• A series of marks at regular intervals on an instrument

that is used for measuring. It is a part of the

instrument that shows the value of a parameter

measured. The scale is depending on the range.

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TERMINOLOGY OF SCALE AND RANGE

• Range

The minimum and maximum values of a quantity for

which an instrument is designed to measure is called

its range . E.g ammeter range : 0mA to 5 mA

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DEFINITION OF ERROR

• The deviation/ different between true values (computed) and measured values of

quantities

• Factors that affect the measurements are related to

the measuring instruments

the person using the instrument

• Error may be expressed either as absolute or as

percentage relative error

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1.ABSOLUTE ERROR

• The difference between the true value of the

variable and the measured value of the variable

• Can be expresses as,

𝑒 = 𝑌𝑛 − 𝑋𝑛

• Where;

• e = absolute error

• Yn = expected value (calculate)

• Xn= measure valued

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2. PERCENTAGE OF RELATIVE ERROR

Can be express as,

%𝑒 =𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑒𝑟𝑟𝑜𝑟

𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑥 100%

%𝑒𝑟𝑟𝑜𝑟 =𝑒

𝑌𝑛 𝑥 100%

%𝑒𝑟𝑟𝑜𝑟 =𝑌𝑛−𝑋𝑛

𝑌𝑛 𝑥 100%

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𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = 100% − %𝑒𝑟𝑟𝑜𝑟

EXAMPLE OF ABSOLUTE AND RELATIVE ERROR

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EXAMPLE 1

• A voltmeter reads 7.2 V and the true value of the

voltage is 7.5 V. Determine the absolute error and

percentage of relative error

• Solution:

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Yn = 7.2 V

Xn = 7.5 V

e = Yn -Xn= 7.5V-7.2 V=0.3V

% e = Yn – Xn X 100 = 7.5 V-7.2 V X100 =4%

Yn 7.5V

EXAMPLE 2

• A circuit below have 20V power supply connected

parallel to resistor R1 = 15k and R2 = 7k. A volt

meter connected to R1 resistor and give 19.5V

measured value. Calculate percentage relative error

of that meter.

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Solution:

R1 and R2 parallell with power supply 20V. So VR1 and

VR2 =20 V.

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Yn = 20 V

Xn = 19.5V

% e = Yn - Xn X 100 %

Yn

= 20 - 19.5 X 100%

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= 2.5 %

EXERCISE

1. A Voltmeter reads 111.5V. The error taken from an

error curve is 5.3%. Calculate the true value of the

voltage.

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Answer: 117.74V

%𝑒𝑟𝑟𝑜𝑟 =𝑌𝑛−𝑋𝑛

𝑌𝑛 𝑥 100%

%𝑒𝑟𝑟𝑜𝑟 =𝑌𝑛 − 111.5

𝑌𝑛 𝑥 100% = 5.3%

(𝑌𝑛−111.5

𝑌𝑛)𝑥100% =

5.3

100

𝑌𝑛 − 111.5 = 0.053𝑌𝑛 𝑌𝑛 − 0.053𝑌𝑛 = 111.5

𝑌𝑛 = 117.74V

MAIN TYPES OF ERRORS

• Classified by THREE:

1. Gross Errors

2. Systematic Errors

3. Random Errors

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1. GROSS ERROR

• These are mainly due to human mistakes :

carelessness or lack of experience of human being

mistakes in reading, recording observation and

calculating results

incorrect adjustment of instruments

Improper applications of instruments: Using a 0–100

V voltmeter to measure 0.1 V, etc.

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1. GROSS ERROR

• The complete elimination of gross error is not

possible, but can minimize them by:

taking reading (at least 3seperate reading),

recording and calculating properly

Make sure know use the meter or instrument

• This error cannot be treated mathematically

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2. SYSTEMATIC ERROR

• Occur due to shortcomings of the instruments, such as defective or worn parts, ageing effects and environmental effects.

• 3 types of systematic errors :

1. Instrumental error- friction, magnetic and zero & full scale adjustment.

2. Environmental error – due to surrounding external condition such as temperature, pressure, humidity, stray magnetic and electrostatics fields

3. Observation error- parallax error

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2. SYSTEMATIC ERROR

• Way to minimize :

Calibrate meter ( instruments)

Choose suitable meter ( instuments)for measurement.

Reduce effects caused by temperature change,

humidity, magnetic and electrostatic by using

magnetic

cleaning the instruments, and housing the instruments

properly depending on the application and type of

the instrument.

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3. RANDOM ERROR

• These are errors that remain after gross and

systematic errors have been substantially reduced.

• These errors are due to unknown causes.

• Way to minimize:

increase number of observation

using the statistical methods to obtain best

approximation reading

• This error can be treated mathematically

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CHARACTERISTICS OF MEASUREMENT

1. Accuracy – Closeness with which an instrument

reading approaches the true value of the variable

being measured.

2. Precision –A measure of consistency or

repeatability of measurement.

If the readings are taken repeatedly does not

change, the instrument have high precision.

Accurate instruments, precision must be high. But

precision does not guarantee accuracy

Digital instruments are more precise than analog instruments

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CHARACTERISTICS OF MEASUREMENT

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CHARACTERISTICS OF MEASUREMENT

3. Resolution – The smallest change in the measured

value to which the instrument can respond. It is the

smallest change the instrument can measure.

4. Significant Figure - Significant figures convey actual

information regarding the magnitude and the

measurement precision of a quantity. The more

significant figures , the greater the precision of

measurement.

Example 68Ω, 69Ω- two significant figures.

68.0Ω, 67.9Ω- three significant figures

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Country significant figures

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Number Significant Figures

52 2

520 3

5.14 3

5.014 4

5.1250 5

0.0034 2

21000 5

0.0213 3

1.000 4

1000.0 5

STANDARD IN THE MEASUREMENT

• Measurement Standard is a measurement devices or

measurement system that define, create and

protect the quantity value for comparison with other

measurement devices.

• It is consists of 4 categories as follows:

1.International Standards

2.Primary Standards

3. Secondary Standards (Reference standard)

4. Working Standards

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1.International Standards

• Define by international agreement. They represent

certain units of measurement to the closest possibly

accuracy that production and measurement

technology allow.

• Example BSI(British Standard Institution),

IEC(international Electro technical commission) and

ISO (International Organization for Standard)

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1.International Standards

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1.International Standards

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2.Primary Standards

• Maintain by national standards laboratories in

different parts of the world.

• The main function is the calibration and verification

of secondary standards

• Example, Makmal Metrologi Kebangsaan Malaysia

SIRIM.

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Makmal Metrologi kebangsaan (NML)

(dibwh sirim) merupakan badan yang bertanggungjawab ke atas piawaian

pengukuran unit SI yang kita gunakan

sehingga kini.

3. Secondary Standards (Reference

standard) • It is basic reference standards used in industrial

measurement laboratories.

• Each industry has its own secondary standard.

• Example: SIRIM, Timbang & Sukat kem. Perdagangan

& perindustrian, Pusat penyelidikan pertahanan,

local universiti and industries

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4. Working Standards

• Working standard is the principle tools of a

measurement laboratory and the lowest level of

standards.

• They are used to check and calibrate general

laboratory instruments for accuracy.

• Example : The resistor manufacturing industry

maintains a standard resistor in the laboratory for

checking the values of the manufactured resistors.

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STANDARD IN THE MEASUREMENT

• International Standards (defined based on

international agreement )

• Primary Standards (maintained by national

standards laboratories)

• Secondary Standards ( used by industrial

measurement laboratories)

• Working Standards ( used in general laboratory)

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