1. Design of Experiments
(DOE)
By
Awad Nasser Albalwi

2. Contents
Why experimental design
When to Use DOE
Planning for the Experiments
1- Introduction: Field of application
planning in the beginning of a project
Factorial design Model
Experimental design example

3. Introduction
Field of application
Experimental design and optimization are tools that are used to systematically
examine different types of problems that arise within, e.g., research,
development and production.
a study design used to test cause-and-effect relationships between variables.
The classic experimental design specifies an experimental group and a control
group. The independent variable is administered to the experimental group and
not to the control group, and both groups are measured on the same
dependent variable. Subsequent experimental designs have used more groups
and more measurements over longer periods. True experiments must have
control, randomization, and manipulation.

4. Why experimental design
It is obvious that if experiments are performed randomly
the result obtained will also be random. Therefore, it is a
necessity to plan the experiments in such a way that the
interesting information will be obtained.

5. When to Use DOE
Use DOE when more than one input factor is suspected of
influencing an output. For example, it may be desirable to
understand the effect of temperature and pressure on the
strength of a glue bond.
DOE can also be used to confirm suspected input/output
relationships and to develop a predictive equation suitable for
performing what-if analysis.
When to Use DOE

6. Planning for the Experiments
2. Definition of aim
What is the aim?
When the aim is well defined the problem should be analysed with the help of the
following questions:
What is known?
What is unknown?
‫يمكن‬ ‫التي‬ ‫المتغيرات‬‫نها؟‬ ‫التحقق‬What do we need to investigate?
To be able to plan the experiments in a reasonable way the problem has to be
concret real.
Which experimental variables can be investigated?
Which responses can be measured?
When the experimental variables and the responses have been defined the
experiments can be planned and performed in such a way that a maximum of
information is gained from a minimum of experiments.

7. Early words of advice
planning in the beginning of a project
‫تحديد‬‫المشكله‬Specify the problem:
Review the whole procedure—different moments, critical steps, raw material, equipment,
etc. Try to get a
holistic view of the problem.
‫تحديد‬/‫االستجابات‬ ‫تعريف‬/‫المخرجات‬ ‫القيم‬¯ Define the responses.:
‫قياسها‬ ‫يمكن‬ ‫التي‬ ‫االستجابات‬ ‫او‬ ‫القراءات‬ ‫ماهي‬Which responses. can be measured?
‫توقعها‬ ‫الممكن‬ ‫االخطاء‬ ‫مصادر‬ ‫أي‬Which sources. of errors can be assumed?
Is it possible to follow the change in responses in course of time?
‫االستجابات‬ ‫في‬ ‫التغير‬ ‫تتبع‬ ‫ممكن‬ ‫هل‬/‫تغير‬ ‫مع‬ ‫القراءات‬‫الوقت‬
‫المتغيرات‬ ‫اختيار‬Select variables:
‫دراستها‬ ‫يمكن‬ ‫التي‬ ‫التجريبية‬ ‫المتغيرات‬ ‫أي‬Which experimental variables are possible to study?
Review and evaluate the variables—important, probably unimportant, etc.
‫مجال‬ ‫اختيار‬‫التجربه‬Select experimental domain.
‫المختار‬ ‫تجريبي‬ ‫المجال‬ ‫في‬ ‫لالهتمام‬ ‫مثيرة‬ ‫المتغيرات‬ ‫كل‬ ‫هل‬all variables interesting in the selected experimental field
‫اآلثار‬‫التفاعليه‬‫المتوقعه‬‫المتغيرات‬ ‫بين‬/‫العوامل؟‬Which interaction effects can be expected?
‫ربما‬ ‫التي‬ ‫المتغيرات‬‫تفاعلي؟‬ ‫تأثير‬ ‫لها‬ ‫ليس‬Which variables are probably not interacting?
This gives a list of possible responses, experimental variables and potential interaction
effects.
The time spent on planning in the beginning of a project is always paid back with interest
at the end. ‫الذي‬ ‫الوقت‬‫في‬ ‫تقضيه‬‫المشروع‬ ‫بداية‬ ‫في‬ ‫التخطيط‬‫بالفائدة‬ ‫لك‬ ‫يرجع‬ ‫راح‬‫المطاف‬ ‫نهاية‬ ‫في‬.

8. Factorial design Model
In a factorial design the influences of all experimental variables, factors, and
interaction effects on the response or responses are investigated.
If the combinations of k factors are investigated at two levels, a factorial design will
consist of 2k experiments. In Table 1, the factorial designs for 2, 3 and 4 experimental
variables are shown.
To continue the example with higher numbers, six variables would give 26 = 64
experiments, seven variables would render 2^7 = 128 experiments, etc.
The levels of the factors are given by – (minus) for low level and + (plus) for high level.
A zero-level is also included, a centre, in which all variables are set at their mid value.
Three or four centre experiments should always be included in factorial designs, for the
following reasons:
• The risk of missing non-linear relationships in the middle of the intervals is
minimised, and
• Repetition allows for determination of confidence intervals.

9. Factorial design
No of Exp = 2^K
For two levels
2 factors 3 factors 4 factors

10. calculate the signs for the interaction effects

11. Between x1 x2
Between x1 x3
Between x2 x3
Between x1 x2 x3

12. population
Experimental group Condition
IV present
Sample
Control group Condition
IV absence
Measure DV Measure DV
Differences
Conclusion
generizlation
Experimental design example
The
aim?
Select sample
Random selection tech
Compare the result
End

13.  The aim:
 Does playing violent video games cause people to
become Violent? ‫ألعاب‬ ‫ممارسة‬ ‫هل‬‫الفيديو‬، ‫العنيف‬ ‫الطابع‬ ‫ذات‬
‫؟‬ ‫عنفواني‬ ‫سلوك‬ ‫الى‬ ‫تؤدي‬
The Aim
what is the problem?
Back

14.  Population :
Population Is a group of people that are interest in our
study?
Our population is Korean teenagers .
It is not possible to test every Korean teenagers , so
instead we are going to select sample
Define the Population?
Back

15.  Sample:
 Our sample a group of people who are selected to
take part in our research.
 It is important the sample represent our population .
 To select the sample use teenagers names randomly
selection.
 We will contact all Korean high school to ask them if
possible select 200 students randomly to take part in
the study.
Sample
Back

16.  Control condition :
 The student play non violent video games
Control Condition
Back

17.  Experimental Condition:
 The students play violent video games .
Experimental Condition
Back

18.  dependent Variables
 This will be Violent behaviours (effect)
dependent Variables
Back

19.  Compare the results
 Is there differences between the results coming
from experimental Conditions playing violent video
games and Control condition behaviours after
playing non violent video games .
 And if there is deference statistics significant ?
 If the statistics is significant that mean the our result
must highly due to independent variable and not by
chance.
Compare the results
Back

20.  1- Experimental design and optimization , Lundstedt
et al1998.
 2- General Introduction to Design of Experiments
(DOE) Badr Eldin,2011
 3-
References
Back

21. ‫جميعا‬ ‫لكم‬ ‫الشكر‬

22. Terminology
3. Terminology
To simplify the communication a few different terms are introduced and defined. Others
will be defined when
they are needed.
Experimental domain the experimental ‘area’ that is investigated defined by the
diversity of the experimental variables.
Factors experimental variables that can be changed independently of each other
Independent variables same as factors
Continuous variables independent variables that can be changed continuously
Discrete variables independent variables that are changed step-wise, e.g., type of
solvent
Responses the measured value of the results. from experiments
Residual the difference between the calculated and the experimental
result

23. 1- get a full understanding of the inputs and outputs being
investigated. A process flow diagram or process map can be
helpful.
2- Determine the appropriate measure for the output. A variable
measure is preferable. Ensure the measurement system is stable
and repeatable.
3- Create a design matrix for the factors being studied The design
matrix will show all possible combinations of high and low levels
for each input factor.
DOE Procedure

24. Factorial design
Input A Level Input B Level
Experiment #1 -1 -1
Experiment #2 -1 +1
Experiment #3 +1 -1
Experiment #4 +1 +1
Note: The required number of experimental runs can be calculated
using the formula 2n where n is the number of factors.

25. For each input, determine the extreme but realistic high
and low levels you wish to investigate. In some cases the
extreme levels may be beyond what is currently in use.
The extreme levels selected should be realistic, not
absurd. For example:
Factorial design
-1 Level +1 Level
Temperature 100 degrees 200 degrees
Pressure 50 psi 100 psi

26. Enter the factors and levels for the experiment into
the design matrix. Perform each experiment and
record the results. For example:
Factorial design
Temperature Pressure Strength
Experiment #1 100 degrees 50 psi 21 lbs
Experiment #2 100 degrees 100 psi 42 lbs
Experiment #3 200 degrees 50 psi 51 lbs
Experiment #4 200 degrees 100 psi 57 lbs

27. Calculate the effect of a factor by averaging the data collected at
the low level and subtracting it from the average of the data
collected at the high level. For example:
Effect of Temperature on strength:
(51 + 57)/2 - (21 + 42)/2 = 22.5 lbs
Effect of Pressure on strength:
(42 + 57)/2 - (21 + 51)/2 = 13.5 lbs
Calculate the effect of a factor