Design of Experiments (DOE)

By Awad Nasser Albalwi

Contents

Why experimental designWhen to Use DOE

Planning for the Experiments

1 -Introduction: Field of application

planning in the beginning of a project

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Factorial design Model

Experimental design example

Introduction

Field of applicationExperimental 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.

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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.

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When to Use DOEUse 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

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Planning for the Experiments2 .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 ?

نها؟ التحقق يمكن التي ?What do we need to investigateالمتغيراتTo 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.

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Early words of adviceplanning in the beginning of a project

المشكله :Specify the problemتحديدReview the whole procedure—different moments, critical steps, raw material, equipment, etc. Try to get aholistic view of the problem.

/ / ¯ المخرجات القيم االستجابات تعريف :.Define the responsesتحديدقياسها يمكن التي االستجابات او القراءات Which responses. can beماهي

measured?توقعها الممكن االخطاء مصادر ?Which sources. of errors can be assumedأي

Is it possible to follow the change in responses in course of time?الوقت / تغير مع القراءات االستجابات في التغير تتبع ممكن هل

المتغيرات :Select variablesاختياردراستها يمكن التي التجريبية المتغيرات Which experimental variables are possibleأي

to study?Review and evaluate the variables—important, probably unimportant, etc.

التجربه مجال .Select experimental domainاختيارالمختار تجريبي المجال في لالهتمام مثيرة المتغيرات كل all variables interesting in the selectedهل

experimental fieldالعوامل؟ / المتغيرات بين المتوقعه التفاعليه Which interaction effects can beاآلثار

expected?تفاعلي؟ تأثير لها ليس ربما التي Which variables are probably notالمتغيرات

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. بداية في التخطيط في تقضيه الذي الوقت

المطاف نهاية في بالفائدة لك يرجع راح .المشروع

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Factorial design ModelIn 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.Back

Factorial design

No of Exp = 2^K

For two levels

2 factors 3 factors 4 factors

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calculate the signs for the interaction effects

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Between x1 x2

Between x1 x3

Between x2 x3

Between x1 x2 x3

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population

Experimental group ConditionIV present

Sample

Control group ConditionIV absence

Measure DV Measure DV

Differences

Conclusion

generizlation

Experimental design example The aim

?Select sample

Random selection tech

Compare the result

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The aim: Does playing violent video games cause

people to become Violent? ألعاب ممارسة هلسلوك الى تؤدي ، العنيف الطابع ذات الفيديو

؟ عنفواني

The Aimwhat is the problem?

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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?

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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

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Control condition : The student play non violent video

games

Control Condition

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Experimental Condition: The students play violent video games .

Experimental Condition

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dependent Variables This will be Violent behaviours (effect)

dependent Variables

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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

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1- Experimental design and optimization , Lundstedt et al1998.

2- General Introduction to Design of Experiments (DOE) Badr Eldin,2011

3-

References

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جميعا لكم الشكر

Terminology

3. TerminologyTo simplify the communication a few different terms are introduced and defined. Others will be defined whenthey 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 otherIndependent variables same as factorsContinuous variables independent variables that can be changed continuouslyDiscrete variables independent variables that are changed step-wise, e.g., type of solventResponses the measured value of the results. from experimentsResidual the difference between the calculated and the experimental result

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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

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Factorial design

  Input A Level Input B Level

Experiment #1

-1 -1

Experiment #2

-1 +1

Experiment #3

+1 -1

Experiment #4

+1 +1Note: The required number of experimental runs can be calculated

using the formula 2n where n is the number of factors. Back

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

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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

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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

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