DOE Intorduction

7/28/2019 DOE Intorduction

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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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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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By Paul A. Keller

One factor at a time

Ignores effect of Interaction

Trial 2Trial 3


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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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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




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





By Paul A. Keller

DOE: Applications in Process Development

Improve process yield

Reduce variability

Reduce development time Reduce overall costs





By Paul A. Keller

DOE: Applications in Design

Evaluate and compare alternatives

Evaluate material alternatives

Product robustness Determine key design parameters





By Paul A. Keller

DOE: Basic Principles

Replication

Error estimationAccuracy

Blocking

Unimportant significant factorPrecision

RandomizationIndependenceEven out uncontrollable factors





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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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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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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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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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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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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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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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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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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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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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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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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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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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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Sample Designs

Nested Designs

Split Plots

Simplex lattice design

Simplex centroid design

D- Optimal

A- Optimal



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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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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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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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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



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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).



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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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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

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DOE Intorduction