Design of Experiment for Optimization Analysis

Design of Experiment (DOE) is a set of
experimentally planned test with one or more
input (factors) at two or more settings
(levels) in order to determine the output
(response) variable(s).
WHAT IS DOE???
3

Efficient procedure for planning experiments
so that the response obtained can be
analyzed to produce valid and objective
conclusions.
Systematic method to determine the
relationship between factor(s) affecting
response(s) of the process.
It is used to determine the cause-and-effect
relationships.
It manage process inputs (factors) in order to
optimize the output (responses).
WHAT IS DOE???
4

Conclusions are easily drawn from a well-
designed experiment even though
elementary methods of analysis are
employed. However, the most sophisticated
statistical analysis cannot salvage a
poorly/badly designed experiment.
WHAT IS DOE???
5

Traditional Approach to Experimentation
To study one factor at a time (OFAT) by
holding all other variables constant.
OFAT requires more runs for the same
precision in effect estimation
OFAT cannot estimate interactions
OFAT can miss optimal settings of factors
TRADITIONAL EXPERIMENTATION
6

Factors
independent variables (continuous or
discrete) an investigator manipulates to
capture any changes in the output of the
process.
Levels
specific values of factors an investigator
manipulates to cause a change in the
output.
DOETERMINOLOGIES
7

Response
the output(s) of a process and it is
sometimes called a dependent variable(s).
Replicate
performing the same treatment
combination more than once.
Interactions
occurs when the effect of one factor on a
response depends on the level of another
factor(s)
DOETERMINOLOGIES
8

Replication
it allows an estimate of the random error
independent of any lack of fit error.
Randomization
it is necessary for conclusions drawn from
the experiment to be correct, unambiguous
and defensible.
Blocking
to isolate a systematic effect and prevent it
from obscuring the main effects.
BASICPRINCIPLESOFEXPERIMENTALDESIGNS
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This process determines the purpose of DOE
and it can be classified into three;
Screening
Characterization
 Model equation prediction
Optimization
 Verification/confirmation
CLASSIFICATION OFDOE
10

It refers to an experimental plan that is
intended to find the few significant factors
from a list of many potential ones.
Alternatively, we refer to a design as a
screening design if its primary purpose is to
identify significant main effects, rather than
interaction effects.
If the number of factors exceeds five
screening design is first recommended before
characterization and optimization
SCREENINGDESIGN
11

Screening designs are usually;
Resolution III (Plackett Burman Design)
Design 2 to 47 factors at 2 levels
Useful for rugged testing
Resolution IV (Minimum Run Design)
Design 5 to 50 factors at 2 levels
Estimates main effects
TYPESOFSCREENINGDESIGN
12

Requires more runs per factor than screening
and also gives more information.
Only use it with just a few factors (<10) so
that the number of runs is reasonable.
Determines which factors have significant
effect on the response, including interactions.
Considers adding center points to the design
to detect non linear behaviour.
With center points, factor settings that
maximize or minimize the response(s) if
there is no curvature detected
CHARACTERIZATION DESIGN
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Characterization designs are;
Central Composite Design (CCD)
Box Behnken Design (BBD)
TYPESOFCHARACTERIZATIONDESIGN
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JOURNALSONCHARACTERIZATIONDESIGN
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Requires the most runs per factor but will
give most information.
Use after narrowing down the list of factors
(<6) with optimum within the region being
tested.
Determines important factors and fits a
quadratic polynomial model to the response
to model second order effects (curvature).
Used to find factor settings that maximize or
minimize the response(s).
OPTIMIZATION
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Factorial designs
Full factorial
Fractional factorial
Response surface methodology
Central composite design
Box Behnken design
Taguchi designs
TYPESOFDOE
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Full factorial designs
Designs are based on 2 levels
These levels are called high and low or +1
and -1.
All input factors set at two levels each.
Test all possible combinations of the
factors and levels.
It takes a lot of time and also expensive.
Allows for the measurement of all possible
interactions.
FACTORIAL DESIGNS
20

Fractional factorial designs
It has fewer runs.
It has potential to miss important
interactions.
Does not allow analysis of interactions.
The interactions are confounded with
other effects.
FACTORIAL DESIGNS
21

Full factorial design: 2𝑘
Fractional factorial design: 2𝑘−𝑝
k is the number of factors, p describes the size of the fraction of the full
factorial used
FACTORIAL DESIGNS
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Central Composite Design
Box Behnken Design
RESPONSESURFACEMETHODOLOGY
23

CCD is varied over 5 levels (-α, -1, 0, +1, +α) with
three elements;
Factorial design points
Center points
Star (or axial) points
CENTRALCOMPOSITE DESIGN
24

Factorial design points
Estimates first order and two factors
interactions
Center points
Estimate pure error and tie blocks
together
Star (or axial) points
Estimate pure quadratic effects
CCDs are good designs for fitting second order
(quadratic polynomials)
25

Types of CCD
Circumscribed (CCC)
Faced centered (CCF)
Inscribed (CCI)
To maintain rotatability, the value of α
depends on the number of experimental
runs:
α=[number of factorial runs]1/4
If the factorial is a full factorial, then
α=[2k]1/4
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α=[2k]1/4 where k = 2
Therefore α = 1.41421
Total number of runs = 2k + 2k + n
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α=[2k]1/4 where k = 3
Therefore α = 1.68179
28

Considering 3 factors;
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α=[2k]1/4 where k = 4
Therefore α = 2
30

BBD is varied over 3 levels (-1, 0, +1);
Allows estimation of quadratic models
All factors are held at mid point
Does not contain factorial points
Fewer center points
Do not exist for 2 factors
BOXBEHNKENDESIGN
31

BBD requires fewer runs
than CCD in cases involving
3 or 4 factors.
Less expensive than CCD
It is useful if the safe
operating zone of the
process is known.
BOXBEHNKENDESIGN
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However, it contains regions of poor
prediction quality.
Does not contain factorial points
Fewer center points
Do not exist for 2 factors
Does not contain star (axial) points
BOXBEHNKENDESIGN
33

Taguchi's orthogonal arrays are highly
fractional factorial designs.
They are used to estimate main effects using
only a few experimental runs and sometimes
two factor interactions.
Higher order interactions are assumed to be
non existence.
Deals with only single optimization problems
TAGUCHIDESIGN
34

However, taguchi designs identifies
controllable factors (control factors) that
minimize the effect of noise factors.
It manipulates noise factors to force
variability to occur.
It determines optimal control factor settings
that make a process or product robust, or
resistant to variation from the noise factors..
A product designed with this goal will deliver
more consistent performance regardless of
the environment in which it is used.
TAGUCHIDESIGN
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Consider the L4 array shown in the figure.
The L4 array is denoted as L4(2^3).
TAGUCHIDESIGN
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L4 means the array requires 4 runs. 2^3
indicates that the design estimates up to three
main effects at 2 levels each.
The L4 array can be used to estimate three
main effects using four runs provided that the
two factor and three factor interactions can
be ignored.
TAGUCHIDESIGN
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REALWORLDDOEBUSINESSHEADLINES
John Deere Saves $500K Annually with DOE
Scitech Journal
DOE Saves Kodak Thousands
Metal Forming
DOE Package Optimizes Coverwrap Process
Industrial Engineering Solutions
Using DOE to Prevent Solvent Pop
Paint & Coatings Industry
DOE Helps Clear Wafer Transport Jams
Micro
DOE Attracts 3.5X More to Crayola Website
Harvard Business Review
39

FURTHER READING
by
Mark Anderson and Pat Whitcomb
66

DOE MADE EASY
Best of Luck in your
experiment
THANK YOU FOR
LISTENING
67

Design of Experiment for Optimization Analysis

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Design of Experiment for Optimization Analysis