Unit-1 DOE.ppt

18MEO113T
Design of Experiments
SRM Institute of Science and Technology ,
Kattankulathur
1

Purpose /aim of this
course
• To learn the fundamentals of design of experiment
techniques.
• To familiarize in how to setup experiments and
accomplish all analyze tasks using software
packages like Minitab, Qualitek , etc.
• After this course , You will be ready to apply the
technique confidently to all of your projects .
2

What is experiment?
• Experiment is an important activity performed by
all in day to day activity.
• An experiment is a test or a series of tests
conducted to analyse, understand or improve
the system.
• The only way to learn anything about a system is
to disturb it and then observe it.

Example of an experiment
Aluminium Pot Ceramic Pot
Constant
Heat, Same
amount of
water
Outcome : Time taken to Boil
Other Variables : source of heat, without lid, Material, shape of
pot etc…

Example…
Other Factors : Weather, Cloth, location
Same person,
day,
playground
Outcome : Time taken to reach Target
Spike shoe
Sports shoe

Basic Terminologies
Outcomes = Response
Variables / Attributes = Factors
Types of factors:
Numeric: Quantative
Categorical : Qualitative
Objective:
Combine outcome by adjusting choosing the variable
Some eg.
Maximize the profit , yield
Minimise the expense, loss, energy

Experiment …..
• Efficiency is doing the least amount of work
and getting the most amount of information.
• Objective is to improve outcome and there
are two or more factors we can change to
make that improvement or influence the
outcome.
• So there's an outcome/response and there
are factors that we want to improve.

Identify
Aluminium Pot Ceramic Pot
Constant
Heat, Same
amount of
water
Other Factors : source of heat, without lid, Material,
shape of pot etc…
Control Variable : Aluminium Pot
Experiment Variable : Ceramic Pot
Independent Variable : Type of material used for pot
Dependant Variable : Time taken to Boil
Outcome
Objective : Minimise the time taken to Boil

Process or System Model
⮚ A process can be any manufacturing process or service Process
which is used for experiment
⮚ An experiment involves a test or series of test in which purposeful
changes are made to the input variables of a process or system so
that changes in the output responses can be observed.

Objective of experiment
1. Determining which Control variables (Input)
X, are most influential on the response
(output), y
2. Determining where to set the influential ‘X’ so
that ‘y’ is near the nominal requirement.
3. Determining where to set the influential ‘x’ so
that variability in ‘y’ is small.
4. Determining where to set the influential ‘x’ so
that the effect of uncontrollable variables ‘z’
are minimized.

Terms used in Design of Experiments
RESPONSE:
A measurable outcome of interest. e.g.:time, etc.
FACTORS:
Controllable variables that are deliberately manipulated to
determine the individual and joint effects on the response(s),
OR Factors are those quantities that affect the outcome of an
experiment ,e.g.: heat source, lid, shape of pot etc.
LEVELS:
Levels refer to the values of factors ie. the values for which
the experiments will be conducted ”, e.g.:
Level–1 heat input=low
Level–2 heat input=high

TREATEMENT:
A set of specified factor levels for an experiment or run ,e.g.:
Treatment–1 : heat input=low and with lid
Treatment–2 : heat input = high and without lid
NOISE:
Variables that affect product/ process performance, whose
values cannot be controlled or are not controlled for economic
reasons. Eg. Climate, enironment etc….
REPLICATION:
Replication is a systematic duplication of series of experimental
runs. It provides the means of measuring precision by
calculating the experimental error.

Conventional Strategies
Trial Factor Test Result Test Average
1 A1 - - Y1
2 A2 - - Y2
One Factor at a time
Several Factor One at a time
Trial
Factor Test Result Test
Average
A B C D
1 1 1 1 1 - - Y1
2 2 1 1 1 - - Y2
3 1 2 1 1 - - Y3
4 1 1 2 1 - - Y4
5 1 1 1 2 - - Y5

Conventional Strategies
Trial
Factor Test Result Test
Average
A B C D
1 1 1 1 1 - - Y1
2 2 2 2 2 - - Y2
Several Factors at same time
Drawbacks:
• Not possible to attribute the change in result to any of the
factor/s.
• Effect of interaction between factors cannot be studied
• These are poor experimental strategies and there is no
scientific basis. The results cannot be validated.

Strategic Design
Trial
Factor
Response
A B
1 1 1 - -
2 1 2 - -
3 2 1 - -
4 2 2 - -
Full Factorial Design
❖ It is balanced and also orthogonal
❖ factor A does not influence the estimate of the effect of factor B and
vice versa.
❖ both factor and interaction effects can be estimated.
Limitations:
✔ Only few factors can be investigated.
✔ When several factors are to be investigated, the number of experiments
to be run under full factorial design is very large.

Need for Strategic Design
❑ To obtain unambiguous results at minimum cost.
❑ Permits consideration of all possible variables/factors
simultaneously
❑ A valid evaluation of the main factors effects and the
interaction effects can be obtained.
❑ With limited number of experiments the crucial factors can be
obtained.
❑ The statistical concepts used in the design form the basis for
validating the results

Steps in Experimentation
1. Problem statement
2. Selection of factors, levels and ranges
3. Selection of response variable
4. Choice of experimental design
5. Conducting the experiment
6. Analysis of data
7. Conclusions and recommendations

Design of Experiments(DOE)
DOE : Sir R.A Fisher in England in the early 1920s-
Powerful technique used for exploring new processes;
gaining increased knowledge of the existing processes ;
optimizing these processes for achieving world class
performance.
21
“The great New York Yankees catcher Yogi Berra said that “ . . . you
can observe a lot just by watching.” However, to understand what
happens to a process when you change certain input factors, you have
to do more than just watch—you actually have to change the factors”
DOE : DOX or Experimental design

DOE Definition
• Design of experiments is a systematic method to
determine the relationship between factors affecting
a process and the output of that process
• In other words, it is used to find cause and effect
relationships.
22

What is DOE all about?
• Helps us to study many factors simultaneously and most
economically
• By studying the effects of each factor on the results , the best
factor combination can be determined.
• When applied to product or process design, the technique
helps to seek out the best design among the many
alternatives
• Used to solve scientifically problems whose solutions lies in
the proper combination of ingredients rather than innovations
or a single identifiable cause.
24

DOE : Necessity
• Experiments are performed today in many manufacturing
organizations
• For continuous improvement in product/process quality, it
is fundamental to understand the process behavior, the
amount of variability and its impact on processes
• Relationship between input (process variables or factors)
and output performance characteristics (quality
characteristics or response)
25

Experiments ?
In an engineering environment, experiments are often
conducted to explore, estimate or confirm
• Exploration refers to understanding the data from the
process
• Estimation refers to determining the effects of process
variables or factors on the output performance
characteristic
• Confirmation implies verifying the predicted results
obtained from the experiment
26

Experiments?
• Ex Metal cutting operation ; Input : cutting speed, feed rate, type of
coolant, depth of cut, etc. Output : surface finish of the finished part
• One of the common approaches employed by many engineers
today in manufacturing companies is One Variable At a
Time(OVAT), where we vary one variable at a time keeping all
other variables in the experiment fixed
• Depends upon guesswork, luck, experience and intuition for its
success. Unreliable, inefficient, time consuming and may yield false
optimum condition for the process
27

Few Salient points
• Statistical thinking and statistical methods play an
important role in planning, conducting, analyzing
and interpreting data from engineering experiments
• When several variables influence a certain
characteristic of a product, the best strategy is then
to design an experiment so that valid, reliable and
sound conclusions can be drawn effectively,
efficiently and economically
28

Few Salient points
• In DOE , engineers can make deliberate changes in input
variables and determines how output functional performance
varies
• Importantly , not all variables affect the performance in same
manner
• Some may have strong influence, some may have medium,
some have no influence at all
• Therefore, the objective of a carefully planned designed
experiment is to understand which set of variables in a
process affects the performance most and then determine the
best levels for these variables to obtain satisfactory output
functional performance in products 29

Industrial Experiments
Industrial experiments involves a sequence of activities
1. Hypothesis an assumption that motivates the
experiment
2. Experiment a series of tests conducted to
investigate the hypothesis
3. Analysis involves understanding the nature of data
and performing statistical analysis of the data
collected from the experiment
30

4. Interpretation is about understanding the results of
the experimental analysis
5. Conclusion involves whether or not the originally
set hypothesis is true or false Very often more
experiments are to be performed to test the
hypothesis and sometimes we establish new
hypothesis which requires more experiments
31

DOE : Benefits
• All kinds of industries(products and processes) , service
industry
• Produce maximum returns when applied to research,
concept design, and product development.
• Engineers and scientific personals should learn and
apply DOE
• DOE should be an essential skill for all manufacturing
and process specialists
• Engineers at a manufacturing plant should routinely use
DOE techniques to improve production processes.
32

Applications of DOE
• Improved process yield , stability , profits , return on
investment , and process capability.
• Reduced process variability and hence better product
performance consistency; Reduced manufacturing costs;
Reduced process design and development time
• Increased understanding of the relationship between key
process inputs and output(s); Increased business profitability
by reducing scrap rate, defect rate, rework, retest, etc.
33

Process/system
Z1
4
Z2 Zn
X1 X2 Xn
Input (s)
Y
Output (s)
Introduction to Experimental Design
Controllable variables (factors)
Uncontrollable variables (factors)
•Output(s) – performance characteristics
•Controllable factors – easily varied - vital for process characterization
•Uncontrollable factors – difficult to control – attributed to variability/inconsistency in product
performance
•Fundamental strategy of robust design is to minimize the effect of Z’s by optimally control X’s

Basic Principles of DOE
4
• The success of any industrially designed experiment
depends on sound planning, appropriate choice of
design, statistical analysis of data and teamwork skills.
• Principles of experimental design :
– Randomization; Replication; Blocking.
• Applied to reduce or even remove experimental bias (in
some cases, could mask the effect of the really
significant factors).

Randomization
4
• The use of statistical methods requires randomization in any
experiment.
• Dorian Shainin - ‘failure to randomize the trial conditions
mitigates the statistical validity of an experiment’.
• The allocation of experimental units (samples) for conducting
the experiment as well as the order of experimentation should
be random.
• When complete randomization is not possible, appropriate
statistical design methods shall be used to tackle restriction
on randomization.

Randomization
6
• The following questions are useful if you decide to apply
randomization strategy to your experiment.
● What is the cost associated with change of factor levels?
● Have we incorporated any noise factors in the experimental
layout?
● What is the set-up time between trials?
● How many factors in the experiment are expensive or difficult
to control?
● Where do we assign factors whose levels are difficult to change
from one to another level?

Replication
5
• Replication involves the repetition of the experiment and
obtaining the response from the same experimental set up
once again on different experimental unit (samples).
• An experimental unit may be a material, animal, person,
machine, etc.
• The purpose of replication is to obtain the magnitude of
experimental error. This error estimate (error variance) is used
for testing statistically the observed difference in the
experimental data.

Replication
5
• Replications also permit the experimenter to obtain a precise
estimate of the effect of a factor studied in the experiment.
Finally, it is to be noted that replication is not a repeated
measurement.
• Suppose in an experiment five hardness measurements are
obtained on five samples of a particular material using the
same tip for making the indent. These five measurements are
five replicates.

Blocking
5
• Blocking is a design technique used to improve the precision
of the experiment. Blocking is used to reduce or eliminate the
effect of nuisance factors or noise factors.
• A block is a portion of the experimental material that should
be more homogeneous than the entire set of material or a
block is a set of more or less homogeneous experimental
conditions.
• It is also a restriction on complete randomization. More about
blocking will be discussed in factorial designs.

Degrees of freedom (DOF)
54
• In the context of statistics, DOF refers to the number of
independent and fair comparisons that can be made in a set
of data.
• In the context of DOE,
Degrees of freedom for a main effect= Number of levels - 1
• The number of degrees of freedom for the entire experiment
is equal to one less than the total number of data points or
observations.

Degrees of freedom (DOF)
56
• In an 8 trial experiment , where each trial was replicated twice
• So the total observations are 2*8 = 16 , therefore the DOF for
each experiment is equal to 15 (i.e. 16 -1)
• The degrees of freedom for an interaction is equal to the
product of the degrees of freedom associated with each factor
involved in that particular interaction effect.
• An experimenter wishes to study the effect of four process or
design parameters at 3-levels.

DOE Terminology
57
• Factor :
– A variable or attribute which influences or is suspected of
influencing the characteristic being investigated.
– All input variables which affect the output of a system are
factors
– Factors are varied in the experiment
– They can be controlled at fixed levels.
– They can be varied or set at levels of our interest.

DOE Terminology
58
• Factor :
– Two types of variables or factors : quantitative and
qualitative
– Quantitative – how the range of settings to be measured
and controlled e.g. temperature , pressure in the process
yield experiment
– Qualitative – discrete in nature ; requires more levels
e.g. types of raw materials, type of catalysts, type of supplier,
etc.
– These are also called independent variables.

DOE Terminology
59
• Level :
– Specified value or setting of the factor being examined in
the experiment.
– The values of a factor/independent variable being
examined in an experiment.
– If the factor is an attribute, each of its state is a level. For
example, setting of a switch on or off are the two levels of
the factor switch setting.

DOE Terminology
60
• Level :
– If the factor is a variable, the range is divided into required
number of levels. For example, the factor temperature
ranges from 1000 to 1200°C and it is to be studied at three
values say 1000°C, 1100°C and 1200°C, these three
values are the three levels of the factor temperature.
– The levels can be fixed or random.

DOE Terminology
61
• Treatment:
– One set of levels of all factors employed in a given
experimental trial. For example, an experiment conducted
using temperature T1 and pressure P1 would constitute
one treatment.
– In the case of single factor experiment, each level of the
factor is a treatment.
• Run or trial :
– a trial or run is a certain combination of factor levels whose
effect on the output (or performance characteristic) is of
interest.

DOE Terminology
62
• Experimental unit :
– Facility with which an experimental trial is conducted such as samples
of material, person, animal, plant, etc.
• Response :
– The result/output obtained from a trial of an experiment. This is also
called dependent variable. Examples are yield, tensile strength,
surface finish, number of defectives, etc.
• Effect :
– Effect of a factor is the change in response due to change in the level
of the factor.

DOE Terminology
64
• Experimental error:
– It is the variation in response when the same experiment is
repeated, caused by conditions not controlled in the
experiment.
– It is estimated as the residual variation after the effects
have been removed.

Selection of Quality Characteristics for
65
• The selection of an appropriate quality characteristic is
vital for the success of an industrial experiment.
• To identify a good quality characteristic, it is suggested to
start with the engineering or economic goal.
• Having determined this goal, identify the fundamental
mechanisms and the physical laws affecting this goal.
• The quality characteristics is to increase the
understanding of these mechanisms and physical laws.

Selection of Quality Characteristics for
66
1. Try to use quality characteristics that are easy to measure.
2. Quality characteristics should, as far as possible, be
continuous variables.
3. Use quality characteristics which can be measured precisely,
accurately and with stability.
4. For complex processes, it is best to select quality
characteristics at the sub-system level and perform
experiments at this level prior to attempting overall process
optimisation.
5. Quality characteristics should cover all dimensions of the
ideal function or the input–output relationship.

Example 1
67
• Consider a certain painting process which results in various problems such
as
– Orange peel
– poor appearance
– Voids, etc.
• Often, experimenters measure these characteristics as data and try to
optimise the quality characteristic.
• It is not the function of the coating process to produce an orange peel.
• The problem could be due to excess variability of the coating process
due to noise factors such as variability in viscosity, ambient
temperature, etc.

Example 1
68
• We should make every effort to gather data that relate to the engineering
function itself and not to the symptom of variability.
• One fairly good characteristic to measure for the coating process is the
coating thickness.
• It is important to understand that excess variability of coating thickness
from its target value. This could lead to problems such as orange peel or
voids.
• The sound engineering strategy is to design and analyse an experiment so
that best process parameter settings can be determined in order to yield a
minimum variability of coating thickness around the specified target
thickness.

Example 2
69
• In the service organisations, the selection of quality
characteristics is not very straight forward due to the human
behavioural characteristics present in the delivery of the
service.
In the banking sector
- The number of processing errors
- The processing time for certain transactions
- transactions, the waiting time to open a bank account, etc.
• It is important to measure those quality characteristics which
have an impact on customer satisfaction.

Example 3
70
• Health care services
– The proportion or fraction of medication errors
– The proportion of cases with inaccurate diagnosis
– The waiting time to get a treatment
– The waiting time to be admitted to an A&E department
– The number of malpractice claims in a hospital every week
or month, etc.

Understanding key
interactions in a
process
7

Introduction
7
• For modern industrial processes, the interactions between the
factors or process parameters are a major concern to many
engineers and managers, and therefore should be studied,
analyzed and understood properly for problem solving and
process optimisation problems.
• For many process optimisation problems in industries, the
root cause of the problem is sometimes due to the interaction
between the factors rather than the individual effect of each
factor on the output performance characteristic (or response).

Significance of interactions
7
Example : Wave-soldering process of a PCB assembly line in
a certain electronic industry.
Aim : To reduce the number of defective solder joints obtained
from the soldering process.
The average defect rate based on the existing conditions is 410
ppm (parts per million)
To perform a simple experiment to understand the influence of
wave-soldering process parameters on the number of defective
solder joints.

Significance of interactions
Method of Experimentation : OVAT approach – 2 levels , – low
level (represented by −1) and high level (represented by +1) for
each parameter
Table 1 List of Process Parameters and Their Levels
7

The experimental layout (or
design matrix)
Table 2 OVATApproach to Wave-Soldering Process
7

Full factorial experiment
It is possible to study all the interactions among the factors A,
B and C.
Table 3 Results from a 23 FFE
7

Interactions
Table 4 Average ppm Values
7

Interaction graph
10
Effect of conveyor speed on ppm at two different levels of flux density is not the same.
This implies that there is an interaction between these two process parameters.
The defect rate (in ppm) is minimum when the conveyor speed is at high level and flux
density at low level.
Figure 1 Interaction plot between flux density and conveyor speed

Alternative Method for Calculating the
Two-Order Interaction Effect
To calculate the average ppm at high level of (A × B) and low
level of (A × B). The difference between these will provide an
estimate of the interaction effect.
Table 5 Alternative Method to Compute the Interaction Effect
79

To calculate the average ppm at high level of (A × B) and low
level of (A × B). The difference between these will provide an
estimate of the interaction effect.
80

Figure 2 Interaction plot between solder
temperature and flux density.
81
• The graph shows that the
effect of solder temperature
at different levels of flux
density is almost the same.
• Moreover, the lines are
almost parallel, which
indicates that there is little
interaction between these
two factors.
The interaction plot suggests that the
mean solder defect rate is minimum
when solder temperature is at high level
and flux density at low level.
Note : Non-parallel lines are an indicator of the existence of interactions between
two factors and parallel lines indicate no interactions between the factors.

Synergistic Interaction Vs.
Antagonistic Interaction
82
• The effects of process parameters can be either fixed or
random.
• Fixed process parameter effects occur when the process
parameter levels included in the experiment are controllable
and specifically chosen because they are the only ones for
which inferences are desired.
• For example, if you want to determine the effect of
temperature at 2-levels (180°C and 210°C) on the viscosity of
a fluid, then both180°C and 210°C are considered to be fixed
parameter levels.

Synergistic Interaction Vs.
Antagonistic Interaction
83
• Random process parameter effects are associated with those
parameters whose levels are randomly chosen from a large
population of possible levels.
• Inferences are not usually desired on the specific parameter
levels included in an experiment, but rather on the population
of levels represented by those in the experiment.
• Factor levels represented by batches of raw materials drawn
from a large population are examples of random process
parameter levels.

Synergistic interaction
The lines on the plot do not cross each other
84
Figure 3 Synergistic interaction between two factors A and B.

Antagonistic interaction
The lines on the plot cross each other
85
Figure 4 Antagonistic interaction between two factors A and B.

References
97
• Antony, J. (2014). Design of experiments for
engineers and scientists. Elsevier.
• Krishnaiah, K., & Shahabudeen, P. (2012). Applied
design of experiments and Taguchi methods. PHI
Learning Pvt. Ltd.

Unit-1 DOE.ppt

Recommended

Recommended

More Related Content

Similar to Unit-1 DOE.ppt

Similar to Unit-1 DOE.ppt (20)

Recently uploaded

Recently uploaded (20)

Unit-1 DOE.ppt