Uploaded by ovie tobi

3934465 1348704859 AMASAutosaved (1)

Advanced measurement and data analysis
List of contents
Content no.
Name of content
Page location
Task-1 Measurement system
Problem-1 Transducer
Problem-2 CMM
Problem-3 SMM
Task-2 Selection consideration of AMDS
Task-3 Non linear square method
Task-4 Least square algorithms
Task-5 Arguments with this task
Task-6 Research method of project
The advanced measurement system and data observing is a process of a measuring and
usually it considers a special designed specification that is used to observing the components
of difference in the measurement process. According to this process the produced item may
be vary. Obtaining technique of measurement and collected data may have some variation
and may cause of incorrect results. A advanced measuring process solve out error of checking
method and measurement equipments and the whole process of calculating value for ensuring
the integrity of the data that is used for calculation. It is also used for implementation of
measurements mistake for decision made about a product. It is also a main element of 6
sigma methodology and another quality system.
This process calculates of the instruments, operation, procedure, operating system and which
impacts the task of a quantity to a calculation characteristic. A measurement system calculate
according to this points1. By choosing the accurate measurement.
2. By evaluation the measurement tools.
3. By evaluation the process and operator.
4. By evaluation any other measuring process.
5. Analysis of the measurement uncertainly of single measurement devices or
measurement systems.
The advanced measurement system analysis is a test instrument or a gauge prior to
experimentation is a winning strategy for making useful decision in the production design by
observing the experimental results. We can take a simple example, the multiple operators
measure a group of components various time by using a measuring tool. After analyzing the
results the instructor decides that how to use this data of measurement. In this simple case of
work the components cannot be changed from between successive measurement and no any
other components contribute noise to test. The AMSA can get tricky to the destructive tests
and tests with factors rather than operators and other components. The thing can get even
more interesting when one of the factors is tough to change in the experiment. The US
synthetic has already completed an AMSA on a test with these complications. The purpose of
doing this test is to find out the measurement complication.
The main objective of doing this task is to demonstrate depth knowledge of our college of the
principle of advanced measurement system and data analysis and provide them the abilities to
apply this system to solve practical problems related to advanced measurement system. In the
process of understanding the AMAS we are going to study about these following points1. Understanding of measurement system including transducers, CMMs and surface
measuring machines.
2. Consideration and error source and calibration.
3. Selection considerations.
4. Understanding of nonlinear least square method.
5. Data analysis algorithm/coding.
6. Argument discussions.
Task-1 Measurement system
The measuring of any quantity is essential a role or the magnitude of comparing between
object whose magnitude is not specified and a specified value. Sine two objects are
compared, the observation is expressed in a numeric value. So we can say that measuring of
any object is the process by which we can change physical parameters to meaningful
Significance of measuring can be explained in the terms, according to famous physicist Lord
Kelvin “he often say that when we can measure what we are speaking about and can express
it in numbers, we know something about it, when we cannot express in it numbers our
knowledge is of a meagre and unsatisfactory kind.”
The techniques of measurements can be classified in two categories broadly:
1. Direct technique.
2. Indirect technique.
1. Direct technique- In this type of method the measured object is directly compared
with a standard measurement and the magnitude of this is shown in a numeric value
and a unit of its. This method is common for the measuring of physical quantities like
length, mass and time.
2. Indirect technique- The measurement by the direct technique method is not every time
correct. They are a little sensitive. So that direct technique methods are not used and
they are less used. In the engineering measurement applications Measurement
Systems are used. Which require the need of indirect technique.
Measurement system- The measurements contain the use of equipments as a physical means
of calculating quantities or variables. In easy case, an equipment is consisted by a one unit
who gives us an output signal according to the quantity or input signal which has been
applied on it. In extra complex methods, a measurement can be made lots of several elements.
These systems may be consisted from transducing components, who changes the measured to
an analogous style. After that this signal is passed by some intermediate means and then it fed
to end’s device for presenting the result of the measuring for the cause of the display and
control. Measurement system can be classified in to these categories broadly1. Mechanical instrument
2. Electrical instrument
3. Electronic instrument
Problem-1 Transducers
An electronic instrument technique is consists of a number of electronic elements for doing
practical a measurement and collect record its results. The general measurement technique
consists of three measurement system-
An input machine.
A signal processing machine.
An output machine.
The input machine gets the signal under measuring process and gives a proportional analog
electrical signal to signal amplifying device. There signal is amplified, attenuated, filtered
and modulated.
The input signal for most instrumentation techniques is a non electrical object. For using
electrical methods for measuring, manipulation and controlling, the non electrical signal is
normally changed into an electrical form by a machine known as transducer. We can say that
a transducer as a machine, that is used when the need of actuated transforms energy from one
forms to another form.
Electrical transducerThe process of electrical measurement has been chiefly used for measuring of electrical
signals and quantities but its magnitude in making measurement of non linear electric
quantity in modern time of automation is still growing. In process to measure non electrical
signal or objects, a detector is used, who usually changes the physical form in displacement.
This displacement activates the electric transducer, which is playing as a secondary
transducer, who gives an output that is having electrical nature. The electrical quantity so
produced is calculated by the best methods used for electrical measuring purpose.
Advantage of transducersThere are numbers of transducers are presents, who is used for transforming variety of
physical quantities and phenomenon into electric signals. The advantages of changing
physical quantities into analog electric quantities are:
The electric amplification can be done easily.
The effects of mass inertia are minimised.
The fraction’s effects are minimised.
The electric and electronic circuit can be operated with little electricity power.
The electric result can be used easily.
Classification of transducers1. For the purpose of transduction process being used.
2. Primary and secondary transducers.
3. Passive and active transducers.
4. Analog and digital transducers.
5. Inverse transducers.
1. Base of principle used of transduction- The transducer can be divided on the base of
principle of transduction like resistive, inductive, capacitive etc. It depends upon how
they change the input quantity into resistance, inductance and capacitance
respectively. They can be divided into piezo electric, thermoelectric,
magnetorestrictive, electro kinetic and optical.
2. On the base of Primary and secondary transducer- The bourdon tube is playing as a
primary detector, it senses the pressure and change the pressure in a displacement.
The displacement moves the core of a LVDT, who produce and output that is
proportional to displacement of the free end who is in turn is proportional to the
pressure. Thus there are two level of transduction, firstly the pressure is changed into
a displacement by the bourdon tube, then the displacement is changed into an
analogous voltage by L.V.D.T. the bourdon tube is called primary transducer and
LVDT is called secondary transducer. As shown in the diagram-
3. Passive and active transducera. Passive transducers- These types of transducers derive the power is needed for
transduction from a reserve storage. It can derive a part of the electricity needed
for converting from the physical quantity under measuring process. They are
called as extra ordinary powered transducer. The classic example of this
transducer, are resistive, inductive and capacitive transducers.
b. Active transducers- These types of transducer who do not needed reserve storage
of electricity to pass their result. They are called as self generating type transducer
because they develop their voltage itself. The required energy for producing of
output signal is taken from the physical quantity that is being measured.
4. Analog and digital transducersa. Analog transducers- These types of transducers change the input quantity into an
analog output signal, who is continuous function of time.
b. Digital transducer- These types of transducer changes the input signal to an
electric output signal which is present in form of pulses.
5. Inverse transducers- An inverse type of transducer is described as a system who
changes an electric quantity into a non electric quantity.
Errors of transducersThe errors present in transducers may be because of they do not follow many situations in
input output relationship that is q0=f(qi). Before departing from the above specified
relationship results errors. For example, the output of an account of input, qi has to be q0 but
in practice an account q0 is obtained, then the errors of the instruments is,
𝜀 = 𝑞′ − 𝑞0
Errors can be classified into three categories1. Scaling error.
2. Dynamics error.
3. Error from noise and drift.
1. Scaling error- The scale error is divided in four different types of errors;
a. Zero errors- In this error, the output deviates from the accurate value by a constant
factor over the whole domain of the transducer. As shown in diagram-
b. Sensitivity errors- This error may be when the observed output deviates from the
accurate constant value. As shown in the diagram.
c. Non-conformity errors- This type of error may be when the experiment contains
transfer function deviates from theoretical transfer function for the every input. As
shown in diagram-
d. Hysteresis errors- All types of transducers are applied to effects of hysteresis. The
output of transducers not only depends upon the input but also depends upon in input
quantity that is applied to it before. As shown in diagram-
2. Dynamic errors- These errors usually may be, when the input is varying with respect
to time. This is happened, the systems contain electrical energy storage components
and cause of this the output is not follow the input properly but with a time lag. Let us
consider an R-C series circuit to which a step input of magnitude E is applied, the
voltage through the capacitor after a time, t of step input is,
Ec = [ 1-exp(-t/𝜏) ]
3. Errors from noise and drift- These noise and drift signals, who are passing through
from the transducers vary with, the difference between the noise and drift and this
noise consists from a signal of random amplitude and random frequency of transducer
while the drift is a slow change with respect to time.
Problem-2 Coordinate measuring machine (CMM)
A CMM is consisted in a way of bridge style that is used to accurate measuring of the 3D of
an object along the dimension X, Y and Z axes using a tough trigger and used for scanning
for getting a series of a pre decided axix on the surface of an object. It is made from major
qualities of substance however a combination of granite and aluminium has been broadly
adopted by the industry cause of its stiffness for the weight ratio.
Use of CMMsThe traditional handheld methods are having their limit and depends on heavily on skill of the
personnel inspection the parts. The inaccurate produced product may be rejected and may be
dispatched to customer. In making the manufacturing design becomes better, the parts are
made complex, its meaning some features can only be correct measured by the use of CMM.
Errors of CMMs- In present time CMM is broadly used by the industry because of common
purpose’s measurement instrument with high accuracy. It is the quality assuring tools of
mechanically measurement.
1. Mechanical errors- the CMM is having errors, because it consists including various
parts of machining, in the calibration process. Normally according to the geometric
parameter of the error in all direction, there is need of using this machine with
2. Measuring error- It is used for the measuring of parts for calculating size errorand
position error measuring purpose especially, it is having high accuracy, lots of
efficient and a big range in form of error measurement. We are having a great number
of technique to measure form and position errors, there are five error detection
principle, compared with the legal element principles we are having, the principle of
measurement of the coordinates. And it is also listed over 100 kinds of measuring
3. Human error- Common reason of human error is the point record that is taken under
certain load situation. Human error may be when manual collecting point is not taken
Problem-3 Surface measurement machineThe surface measurement machine or surface metrology, it is used for a little size of scaling
features on surface measurement. Primary surface and surface roughness are the parameter of
using this device and these are related with field. This is mandatory to have disciplines and is
known for the machining of pre decided parts and assemble. Which contains a mating surface
and it is operated with high internal pressure.
Working of SMMs- The profilometer is used for diamond sapphire. The sapphire is a run
perpendicular to layout of surface. The product normally traces in form a straight line on a
plane surface and for a circular arc around a cylindrical surface. The length of the path that it
traces in the path, is known as length of measurement. The wavelength of the least frequency
filters, who will be used for calculating the data, which is often described by the length of
Errors of thisThe main demerit of profilometer is that, not to having accurate when size of the feature on
the surface, which is close to the same size as the sapphire. Another demerit of prifilometers
have hard to detect the flows of same size of roughness having by the surface. There are also
a few limitations for non-contacting instruments. For example the equipment, those are
applied on optical interference it cannot be resolved features who are less than some fraction
of the operated wavelength. This limitation makes this device hard to use for accurate result
even for a normal object.
Task-2 Selection consideration of AMDS
Here the term AMDS refers that advanced measurement and data analysis. By the
improvement in the sensor technology and the warrants those are needed for high accuracy
advanced measurement system. For achieving high accuracy to make use of the state of the
art sensors, require in deep analysis in advanced measurement system. In the starting, we
have to choose an appropriate ADC for the design the critical design decision. This requires
research of accuracy requirements, to determine the minimum effective number of bits of
ADC. In making this the sampling frequency with which the anolog inputs needs to be
calculated and also plays an important role.
After that this analog front end circuit for the anlog inputs needs to be selected very carefully.
AFE may be required for scale down the input voltage or changing the current input to
voltage type or for buffering. Any external component present in the AFE will affect the
measurement accuracy. Now all the AFE parts need to be high prediction parts to reduce
impact on accuracy.
Since the censors are connected with the measurement system from foreign sources, it is
mandatory to have protection against ESD, EFT, a surge etc. By the leakage of current of the
protection may be another factor who can lead to measurement errors. For architecture and
parts of the protection circuit needs to be selected with the aim of reducing the leakage
current to minimum.
Once the components are selected, one of the easier method is to prepare an error analysis
sheet which includes all the single error introduced by the components. One component can
have multiple errors factors and all the factors from all contributing components needs to be
considered for checking. For example an ADC can have multiple errors inducing parameters
such an INL, DNL, offset error, gain error, offset drift and gain drift etc.
If there is a scope for calibration, then errors which can be removed using by the calibration,
may be neglected during the analysis. But the only way to remove these parameters
completely, is to calibrate each single errors separately. If the calibration is performed as a
system then these errors cannot be eliminated completely due to inherent limitation of the
calibration algorithm. Once the analysis sheet is prepared, the root mean square method can
be used to predict the system measurement accuracy. This process can be iterated multiple
times to analyze the impact of each component or to improve the measurement accuracy.
In addition to this careful design of board layout is mandatory for achieving good accuracy.
The isolation of analog sections from high frequency digital section, sufficient clearance
analog traces, maintaining uniform grounding are some of the general techniques used to
make sure that board level noise does not impact on the accuracy.
Designing a measurement system with high accuracy requires multi level design skills.
Selection of the proper components, accuracy analysis at design stage, careful PCB layout of
suitable calibration method can help in realizing a high accuracy measurement system.
Task-3 Non linear least square technique
As the name the equation of this is given byy=f(x;𝛽) + 𝜀
1. The function part of this model, is not linear with respect to the variables,
2. The technique of least square is used for predicting the values of the variables.
3. The function is smooth with respect to variable, and
4. The least square criteria that is used to contain the parameter prediction has a unique
AdvantagesBeing a least square method, the non linear technique has some of the advantages with
compare to linear square regression. Non linear can generate good prediction of the variable.
Another advantage is non linear least square method shares with linear least square method is
a fairly well designed theory for a computing, prediction and calibration of the interval to
answer scientific and engineering questions.
DisadvantageThe disadvantages with the linear least square method, it includes a strong sensitivity to the
outliers. Now just as in a linear least square, by the presence of one or two outliers in
recorded data can have some seriously impacts, results of a nonlinear calculation. There are
unfortunately fewer model validation devices of detecting of outliers in nonlinear method.
Task-4 least square algorithm
Least square is a process of fit a unique curve through the given points. These points are
(x1,y1), (x2,y2)--------- (xn,yn).
The difference between them because we cannot calculate the ideal condition and difference
is known is errors. It is denoted by the e1, e2, ------ en. And
&= e12 + e22 --------+ en2 .
This curve is the best fit curve. Now we can say that the sum of square of errors is minimum
that is called principle of least square.
Method of least square isIn this method we have write the equation of given curve, like the equation straight line and
parabola is given belowy= a + bx is a straight line and
y= a + bx + +cx2 is a parabola,
Now for solving the regression by least square method, we have to follow these points.
1. Write the normal equation of curve.
2. Solve to them constant.
3. Put constant in the equation of the curve.
Now the equation of the circle is
(x-h)2 + (y-k)2 = r2
Where this equation having the centre being at point (h,k) and the radius being r. Thus the
form of the equation is helpful since we can easily fine the centre of the circle.
The process of measurement uncertainties evaluated1. Specify the process and equation- In this we have see first that what is being
measured. We have to follow these points.
What is measured?
How it will be measured?
What equipment is used?
Who will do measurement?
Where the measurement is performed?
What factors may be impact the measurement results?
After answering these question, we use our answer to identify the what measurement
process we are evaluating. Once we have selected what are we evaluating, we move
one step.
2. Identify and characteristic the uncertainty sourceIf we are evaluating an equation then the process is a little different. We will want to
identify each variable in the equation and think about what influences each variables.
3. Quantify the magnitude of uncertainty componentsTo get started, we may want to gather the following items. They will be helpful when
anything data.
Calibration reports.
Repeatability studies.
Experiment results.
Manufacture manuals and specification.
Technical documents and guide.
Published papers, studied, journal articles, etc.
4. Convert uncertainly components to standard deviation equivalentsSome of the most common probabilities disruption used are:
Normal and Gaussian.
Rectangular and uniform.
Lag normal.
U shaped.
How to reduced measurement uncertaintiesWe can reduce the uncertainties by these methods. Which are given below:
1. Test and collect data- when our aim is to reduce measurement uncertainty, reason of
my research is perform and collect lots of data. What kind of data? These are the
repeatability and reproducibility data.
2. Select a better calibration laboratory-One of the very easy method to reduce
measurement uncertainty, is to decrease the traceable uncertainty related with
calibration results. It may be accomplished by selecting best laboratories or
calibration’s service providers.
3. Removing bias and characterize- One another way to reducing uncertainty is, to
reduce the uncertainties is measurement bias. The bias is the systematic error related
with the calibration data of your standard. By removing bias, we can reduce the
uncertainty related
Task-5 Arguments with this task
By the use of the transducer we can measure of physical quantity accurately. The transducer
is having these advantage which are given below-
The electrical system may be operated with a very small quantity of power.
The electrical output who comes from electric transducer may be simply processed
and took to a stage, that suitable for output machine, which may be an indicator or
The electric output is easily used for transmitted processed, for the purpose of
measuring process.
By having with advantage of integrated circuit technology, the electronic circuit have
become extra ordinary compact in size and it requires a little space for operation.
It is having no moving parts those are involved in the systems. Therefore there is no
possibility of mechanical errors and tears.
A part from having advantages, the transducer is having disadvantages also. That is
mentioned below-
The electrical transducer is a little reliable because of it, the ageing and drift of the
active equipment.
By having the sensing components and the related signal processing circuitry are
From the use of best quality materials, modern technology and circuits, the range of
accuracy and stability have increased for the electric transducers.
By the use of negative feedback technique, the accuracy of measuring process and
stability of this systems have improved, but all the system expanse has also increased.
Drawbacks of CMMsWithout having any doubt in mind, CMMs is a crucial part to the prosperity and safety of
production need. This is mainly because we will able to focus our energies elsewhere
once we allow the system to do what it was made for. There are a few of the most
practical and profitable merits of CMMs are;
1. The life of hardware is lasting for a long time- The device is well maintained, so it
will not wear out during its life. It may need a charge of motor or some parts, but the
working of this machine is guaranteed to having the life for several years. It means we
will not have the need of replacing our CMM.
2. The software continuously getting better with time- There is a great improvement in
the graphical driven software and its ability to recover and storing a wealth of data.
Metrology experts say that the software will continue to getting more affordable,
accurate, user friendly, and standardized with the increasing of time.
3. You can upgrade the machine by the upgrading software- Many coordinate measuring
machines may have need to software upgrading for five times and they give us the
same result. Many of the owners of CMM will say for a software upgrade more times
compare than asking for an upgrade in machine’s hardware.
4. New models are now resistant with a little controlled environments- many of the
owner want to haviirng a CMM in the shop floor for the purpose of increasing
efficiency, and the measuring devices of today let you to do just that. Now they are
having more resistant to most shop floor influences, like that vibrations and
temperature changes.
Now CMM is having disadvantages apart from having advantages, which are given
1. There is no standard yet- Now there are lots of different kinds of CMMs are exists,
many of manufactures, and various software programs are being used fir running of
the machines. This means that it is much hard to interchanging of software in the
coordinate measuring machines.
2. CMMs systems may be complicated sometime- Not all the operators of CMMs are
knowledge able about the principles of CMMs. It is mostly manufacturing and
production experts who use to operate these machines, and they are having need to
work dynamically because they need to do make more production for making more
money. They do not have much time as having quality engineers so they need
systems, who is simpler.
Drawbacks of surface measuring machineThe main advantage of surface measurement machine is that it is capable to capture clear
wave profile and it is also capable to capture long distance measurement.
Disadvantages1. Sapphire wear- The contact type surface roughness testing operators, on the sapphire
must be polished because of it that, the tip will wear down over time. The mode of
wearing may be varies, so the sapphire’s tip may become flat or rounded, it is
depending on the material and shape or size of the measuring aimed object. The
different sapphire shapes will naturally generate different wave profiles.
2. Stylus’s marking on a sample- Styluses are made from sapphire or diamonds, such
type of hard materials can scratch the surface of any object. Mostly when the time of
repeating parallel adjustments, it is very easy for the stylus to scratching the sample.
3. Grooves narrower than the radius of the stylus’s tip cannot be measured- This is
happened because the tip of the stylus, having spherical shape, the stylus cannot trace
the shape properly, if the width of the groove is narrow compare than the radius of the
stylus tip.
Task-6 Research method of engineering projects
A. On the social media the user of electrical bikes have posted the concerns that how
well the electric vehicles will suit according to their lifestylesWe are having three groups1,4 and 7 , the average use of electrical vehicle in their daily life
is –
The owner of group 1is having the ownership is less than 3 years. The use of vehicle in this
group users is less than 10k KM. The consumer of group 4, is having the ownership is
between 5 to 8 years, so they are using the vehicle more than group 1, they need to a good
mileage electric vehicle so that they can travel in low cost. The group 7 will use the vehicle
till the end of their life, so there is need to produce the vehicle who is having a good life and
need to use good quality material.
Now we are having three group the group 2,4 and 8. They use the vehicle till 10k to 20 k
KM. So we need to produce for group 2 good mileage vehicle and for group 4 and 8 the good
life of vehicles.
Now we are having the group 3, 6 and 9, these groups use the vehicle daily a lot of. So we
need to generate good life and efficiency of vehicles to them.
B. Our company is going to provide a service, in which we will provide the facility of
unique selling point and a free membership of next 2 years. In this service the you can
book the from 30 minutes up to 2 months. You can book on our website and app. I
will see how many person is using social media, I can update on social media on the
page of company and how many people is using the smart phone. I can text them
about the service. And I will offer them a cashback on their digital wallet. I will offer
to consumers discount if they will use our facility and also researched about the area
that how type of area is? How much vehicle is needed.
Lat three digits of my student id is 576, so now the value of
A= segment5, B= segment 7 and C= segment 6
Now applying standard deviation method on these segments
For segment A
Mean of segment A = 6.75
Value of whole square of (xi-𝜇) = 0, 0.05, 1.96, 0.01, 0.15
Summation of whole square of (xi-𝜇) =0.43
Now 𝜎 = 0.72
Similarly for segment B and C = 0.18 and 0.30.
(b) For the segment A is having more various online usage compare than segment B and C.
Segment C is having lowest use of online usage.
B. a. I would like to segment C for low capacity user, segment B for medium capacity user
and segment A for high capacity users.
b. There is 70% probability for getting these ideas by the online users, Because we have
designed according to their requirements and it is also economical and according to their
purpose, how to use of it daily.
Problem-3 Field research proposal
These is industries is using the 3 D printers –
1. Aerospace industry.
2. Medical industry.
3. Dental industry.
4. Architecture industry.
Now for increasing selling in the small sized market we need to do marketing in these
industries. And have to understand the use of 3 D printers to peoples. The 3D printer can
make the job of production before going under production with the predict dimensions. By
the 3d printer we can make the design of any object that is common in the markets. And tell
the supplier according to our need of products and how to make it with the help of 3D
Thus we have studied the device who changes the one form of energy into another form is
called as transducer. The process of changing energy is known is transduction. The changing
is done by sensing and transducing of the physical quantities like temperature, pressure, and
sound etc. The electric transducer changes the mechanical energy into an electric output. The
electrical output may be voltage, current and frequency. The production of the output, is
depends having the nature being resistive inductive and capacitive effects of the physical
input. And it is difficult to calculating the exact magnitude of the present physical forces like
temperature, pressure, etc. But if the physical force is changed into an electric signal, then
their value is easily calculated with the help of the meters. The transducers are used for
changing the physical forces into an electrical signal which can help easily be handled and
transmitted for the measurement.
We have studied about coordinates measuring machine. The main benefits of CMMs is that it
helps in measurement of surface and we can say that CMMs is a flexible measuring machine
that is used for measuring purpose of the physical geometrical characteristic of any given
object. A CMM can be operated manually or automatic. It precise records the X, Y and Z
coordinates by using a probe that is placed manually by an operator, may be automatically via
direct computer.
We also have studied the surface measurement machine that is known as surface metrology,
this term refers to measurement the roughness of surface. The surface measurement is
essential for determining a surface suitability for a particular application. The element
failures can often be traced back to a precision surface that was not manufactured for the
specification, either due to an improper set up of a machine or use of a process that is not
capable of repeatable producing the quality of surface.
1. Barker R M, Cox M G, Forbes A B and Harris P M. (2007). Software Support for
2. Bell S A. (2001). A beginner’s guide to uncertainty in measurement. NPL good
practice guide No. 11.
3. Best Practice Guide No. 10: Discrete Modelling and Experimental Data Analysis.
National Physical Laboratory, Teddington.
4. Flack D R and Hannaford J. (2005). Fundamental good practice in dimensional
metrology”. NPL Good practice guide No. 80.
5. Fraden J. (2015). Handbook of modern sensors: physics, designs, and applications.
6. Higham D J, Higham N J. (2016). MATLAB Guide, Third edition. Philadelphia:
Society for Industrial and Applied Mathematics.
7. Leach R. (2014). Fundamental principles of engineering nanometrology (Micro and
Nano Technologies). Elsevier.
8. Morris A S. (2012). Measurement and instrumentation: theory and application.
Academic Press.