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Introduction to DOE 1 2003 QA Publishing, LLC
By Paul A. Keller
Introduction to Design of Experiments
Lotfi K. Gaafar 2004
Lotfi K. Gaafar 2004 This presentation uses information from Paul A. Keller of QA Publishing, LLC.
Dr. Lotfi K. Gaafar
The American University in Cairo
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Introduction to DOE 2 2003 QA Publishing, LLC
By Paul A. Keller
Overview
Input OutputProcess
Controllable factors
Uncontrollable factors
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Introduction to DOE 3
2003 QA Publishing, LLC
By Paul A. Keller
Designed Experiment Terminology
Response:Mfg: Yield of a ProcessService: Customer Satisfaction
Controlled Factors: set to predefined levels for DOE
Mfg: Furnace Temp., Fill Pressure, Material MoistureService: Process Design, Follow-up
Uncontrollable Factors: factors that cannot becontrolled in actual operations, but may be controlledduring experimentation.
Mfg: Humidity, air pollution
Service:Arrival rate, efficiency
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Introduction to DOE 4
2003 QA Publishing, LLC
By Paul A. Keller
Designed vs. Traditional Experiments
Traditional: vary one factor at a time
Factor Response is deviation from base
How do you maximize the result?What is Effect of each Factor?
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Introduction to DOE 5
2003 QA Publishing, LLC
By Paul A. Keller
One factor at a time
Ignores effect of Interaction
Trial 2Trial 3
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Introduction to DOE 6
2003 QA Publishing, LLC
By Paul A. Keller
Implications of Interaction
We may think a factor is unimportant if
we dont vary other factors at the same
time.
We may improve the process, but it onlyworks if other factors remain constant.
We may be able to reduce the effect of a
factor by minimizing variation of another.
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2003 QA Publishing, LLC
By Paul A. Keller
Designed Experiments Vs.
Historical Data
DesignedDesigned to detect specific factors and
interactions (orthogonal)
Relatively short period of timeCasual Factors observed and/or controlledRecorded anomalies
Historical
May be incapable of detecting interactionsMay lack range to detect factor significanceUnrecognized biasesChanging environment
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2003 QA Publishing, LLC
By Paul A. Keller
DOE: Objectives
Determine influential variables (factors)
Determine where to set influential factorsto optimize response
Determine where to set influential factorsto minimize response variability
Determine where to set influential factors
to minimize the effect of the uncontrollablefactors
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2003 QA Publishing, LLC
By Paul A. Keller
DOE: Applications in Process Development
Improve process yield
Reduce variability
Reduce development time Reduce overall costs
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2003 QA Publishing, LLC
By Paul A. Keller
DOE: Applications in Design
Evaluate and compare alternatives
Evaluate material alternatives
Product robustness Determine key design parameters
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2003 QA Publishing, LLC
By Paul A. Keller
DOE: Basic Principles
Replication
Error estimationAccuracy
Blocking
Unimportant significant factorPrecision
RandomizationIndependenceEven out uncontrollable factors
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2003 QA Publishing, LLC
By Paul A. Keller
DOE Steps
Problem statement
Choice of factors, levels, and ranges
Choice of response variable(s)
Choice of experimental design
Performing the experiment
Statistical analysis Conclusions and recommendations
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Introduction to DOE 13
2003 QA Publishing, LLC
By Paul A. Keller
Resource Allocation
Dont commit all resources to one design
Start with Screening designOnly 25% of resources on any one experiment
Learn from each design
What did you do wrong? Excluded factors, wrong conditions, etc.
What to do next? Sometimes next stage of improvement isnt worth the
cost of another experiment
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Introduction to DOE 14
2003 QA Publishing, LLC
By Paul A. Keller
Selecting Factors
For each response, brainstorm likely factors
For screening, if more than 5-7 factors:
Reduce factor list through ranking
Nominal Group Technique, Prioritization MatrixHold some factors constant
ex: raw material type/supplier
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Introduction to DOE 15
2003 QA Publishing, LLC
By Paul A. Keller
Selecting Factor Level Values
Spanning entire region likely to yield the
most understanding.
If factor's levels are close, measured effect maybe statistically insignificant
Moving off current operating points
presents a risk.
Probing techniques: Response Surface AnalysisEvolutionary Operation (EVOP): converge on
best solution
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Introduction to DOE 16
2003 QA Publishing, LLC
By Paul A. Keller
Effects of Aliasing: Confounding
Aliased parameters are CONFOUNDED
Cannot be estimated independently of oneanother
Estimates are linear combination of confoundedparameters
Aliasing creates other confounded pairs
If ABC = D, then A = BCD; B = ACD; C = ABD;AB = CD; AC = BD; AD = BC;
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Introduction to DOE 17
2003 QA Publishing, LLC
By Paul A. Keller
Desirable Designs(ref: Box, G.E.P. and N.R. Draper. Robust Designs. Biometrika 62 (1975):347-352)
Provide sufficient distribution of
information throughout region of interest
Provide model that predicts the response,
as close as possible to true response, at allpoints w/in region of interest
Provide ability to detect model lack of fit
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Introduction to DOE 18
2003 QA Publishing, LLC
By Paul A. Keller
Desirable Designs (cont.)(ref: Box, G.E.P. and N.R. Draper. Robust Designs. Biometrika 62 (1975):347-352)
Allow blocking
Allow sequential buildup of design
Provides internal estimate of error
variance
Provide simple means of calculating
estimates of coefficients
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Introduction to DOE 19
2003 QA Publishing, LLC
By Paul A. Keller
Design Performance
Considerations
Number of Runsminimal best
Design Resolution
indicates which, if any, interactions can beindependently estimated Minimum Detectable Effect
Orthogonality & Balance Other: D-Optimal, A-Optimal & G-Optimal
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Introduction to DOE 20
2003 QA Publishing, LLC
By Paul A. Keller
Design Resolution
Resolution IIIEstimates of Main factor effects only; all
interactions may be confounded with oneanother and MF may be confounded with
interactions.
Resolution IV
Estimates of MF are not confounded with 2-
factor interactions but may be confounded withhigher order interactions. Two factorinteractions may be confounded with oneanother and with higher order interactions.
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Introduction to DOE 21
2003 QA Publishing, LLC
By Paul A. Keller
Design Resolution (continued)
Resolution VEstimates of MF and 2-factor effects are not
confounded with one another but may beconfounded with higher-order interactions.
Three-factor and higher interactions may beconfounded.
Resolution VI
Estimates of MF and 2-factor effects are notconfounded with each other or with 3-factorinteractions. Three-factor and higherinteractions may be confounded with one another.
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Introduction to DOE 22
2003 QA Publishing, LLC
By Paul A. Keller
Design Resolution (continued)
Resolution VII
Estimates of MF, 2-factor and 3-factoreffects are not confounded with one another
but may be confounded with higher orderinteractions. Four-factor and higher
interactions may be confounded.
Resolution vs. Number of Trials
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Introduction to DOE 23
2003 QA Publishing, LLC
By Paul A. Keller
Orthogonality
Orthogonality refers to the property of a
design that assures that all specified
parameters may be estimated
independently of any otherIf sum of factors columns in standard
format equal 0, then design is orthogonal
Some writers lump balanceas part oforthogonality.
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Introduction to DOE 24
2003 QA Publishing, LLC
By Paul A. Keller
Balance
Balance implies data is properly distributed overdesign space.
uniform physical distributionan equal number of levels of each factor.
Some designs sacrifice balance to achieve better
distribution of variance or predicted error
Ex: Central Composite.
Balance may be sacrificed by avoiding extremecombinations of factors
Ex: Box-Behnken
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Introduction to DOE 25
2003 QA Publishing, LLC
By Paul A. Keller
Sample Designs
Box Behnken
Plackett Burman
2kdesigns (fractional, confounding, fold over,
projection) 3kdesigns
Mixed level designs
Latin Squares
Central Composite (with axial points)
Johns
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Introduction to DOE 26
2003 QA Publishing, LLC
By Paul A. Keller
Sample Designs
Nested Designs
Split Plots
Simplex lattice design
Simplex centroid design
D- Optimal
A- Optimal
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Introduction to DOE 27
2003 QA Publishing, LLC
By Paul A. Keller
General Guidelines
1. Good understanding of the problem
Research has shown that one of the key reasons for an
industrial experiment to be unsuccessful is due to lack of
understanding of the problem itself. The success of any
industrially designed experiment will heavily rely on thenature of the problem at hand. The success of the experiment
also requires team effort.
Lotfi K. Gaafar 2004 From:http://www.qualityamerica.com/knowledgecente/articles/ANTONYdoe1.htm
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Introduction to DOE 28
2003 QA Publishing, LLC
By Paul A. Keller
General Guidelines
2. Conduct a thorough and in-depth Brainstorming Session
The successful application of DOE requires a mixture of
statistical, planning, engineering, communication and teamwork
skills. Brainstorming must be treated as an integral part in the
design of effective experiments. It is advised to consider thefollowing key issues while conducting brainstorming session:
Identification of the process variables, the number of levels of each process variable
and other relevant information about the experiment
Development of team spirit and positive attitude in order to assure greater participationof the team members.
How well does the experiment simulate users environment?
Who will do what and how?
How quickly does the experimenter need to provide the results to management?
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Introduction to DOE 29
2003 QA Publishing, LLC
By Paul A. Keller
General Guidelines
3. Select the appropriate response or quality characteristic
A response is the performance characteristic of a product which is
most critical to customers and often reflects the product quality. It
is important to choose and measure an appropriate response for
the experiment. The following tips may be useful to engineers inselecting the quality characteristics for industrial experiments.
Use responses that can be measured accurately.
Use responses which are directly related to the energy transfer associated with the
fundamental mechanism of the product or the process.Use responses which are complete, i.e., they should cover the input-output relationship
for the product or the process.
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Introduction to DOE 30
2003 QA Publishing, LLC
By Paul A. Keller
General Guidelines
4. Choose a suitable design for the experiment
The choice of an experimental design will be dependent upon the
following factors:
Number of factors and interactions (if any) to be studiedComplexity of using each design
Statistical validity and effectiveness of each design
Ease of understanding and implementation
Nature of the problem
Cost and time constraints
Lotfi K. Gaafar 2004 From:http://www.qualityamerica.com/knowledgecente/articles/ANTONYdoe1.htm
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Introduction to DOE 31
2003 QA Publishing, LLC
By Paul A. Keller
General Guidelines
5. Perform a screening experiment
A screening experiment is useful to reduce the number of process
variables to a manageable number and thereby reduce the number
of experimental runs and costs associated with the entire
experimentation process. For example, one may be able to studyseven factors using just eight experimental trials. It is advisable
not to invest more than 25% of the experimental budget in the first
phase of any experimentation such as screening. Having identified
the key factors, the interactions among them can be studied usingfull or fractional factorial experiments (Box et al., 1978).
Lotfi K. Gaafar 2004 From:http://www.qualityamerica.com/knowledgecente/articles/ANTONYdoe1.htm
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Introduction to DOE 32
2003 QA Publishing, LLC
By Paul A. Keller
General Guidelines
6. Use Blocking Strategy to increase the efficiency of
experimentation
Blocking can be used to minimize experimental results being
influenced by variations from shift-to-shift, day-to-day or machine-
to-machine. The blocks can be batches of different shifts, differentmachines, raw materials and so on.
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d i O 33
2003 QA Publishing, LLC
General Guidelines
7. Perform Confirmatory trials/experiments
It is necessary to perform a confirmatory experiment/trial to verify
the results from the statistical analysis. Some of the possible
causes for not achieving the objective of the experiment are:
wrong choice of design for the experimentinappropriate choice of response for the experiment
failure to identify the key process variables which affect the
response
inadequate measurement system for making measurementslack of statistical skills, and so on.
Lotfi K Gaafar 2004 From:http://wwwqualityamerica com/knowledgecente/articles/ANTONYdoe1 htm