introduction to doe 1 © 2003 qa publishing, llc by paul a. keller introduction to design of...

Introduction to DOE 1

© 2003 QA Publishing, LLC

By Paul A. Keller

Introduction to Design of Experiments

Lotfi K. Gaafar 2004Lotfi K. Gaafar 2004

This presentation uses information from Paul A. Keller of QA Publishing, LLC.

Dr. Lotfi K. Gaafar

The American University in Cairo



By Paul A. Keller

Overview

Input OutputProcess

Controllable factors

Uncontrollable factorsLotfi K. Gaafar 2004



By Paul A. Keller

Designed Experiment Terminology• Response:

– Mfg: Yield of a Process

– Service: Customer Satisfaction

• Controlled Factors: set to predefined levels for DOE– Mfg: Furnace Temp., Fill Pressure, Material Moisture

– Service: Process Design, Follow-up

• Uncontrollable Factors: factors that cannot be controlled in actual operations, but may be controlled during experimentation. Mfg: Humidity, air pollution

Service: Arrival rate, efficiency



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?



By Paul A. Keller

One factor at a time •Ignores effect of Interaction

Trial 2

Trial 3



By Paul A. Keller

Implications of Interaction

• We may think a factor is unimportant if we don’t vary other factors at the same time.

• We may improve the process, but it only works if other factors remain constant.

• We may be able to reduce the effect of a factor by minimizing variation of another.



By Paul A. Keller

Designed Experiments Vs. Historical Data• Designed

–Designed to detect specific factors and interactions (orthogonal)

–Relatively short period of time–Casual Factors observed and/or controlled–Recorded anomalies

• Historical–May be incapable of detecting interactions –May lack range to detect factor significance–Unrecognized biases–Changing environment



By Paul A. Keller

DOE: Objectives

• Determine influential variables (factors)• Determine where to set influential factors

to optimize response• Determine where to set influential factors

to minimize response variability• Determine where to set influential factors

to minimize the effect of the uncontrollable factors

Lotfi K. Gaafar 2004



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 estimation

– Accuracy

• Blocking– Unimportant significant factor

– Precision

• Randomization– Independence

– Even 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




By Paul A. Keller

Resource Allocation

• Don’t commit all resources to one design

–Start with Screening design

–Only 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 isn’t worth the

cost of another experiment




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 Matrix

–Hold some factors constant• ex: raw material type/supplier



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 may be statistically insignificant

• Moving off current operating points presents a risk.

–Probing techniques: Response Surface Analysis

–Evolutionary Operation (EVOP): converge on best solution



By Paul A. Keller

Effects of Aliasing: Confounding

• Aliased parameters are CONFOUNDED

–Cannot be estimated independently of one another

–Estimates are linear combination of confounded parameters

• Aliasing creates other confounded pairs

–If ABC = D, then A = BCD; B = ACD; C = ABD; AB = CD; AC = BD; AD = BC;



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 all points w/in region of interest

• Provide ability to detect model lack of fit



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



By Paul A. Keller

Design Performance Considerations

• Number of Runs–minimal best

• Design Resolution–indicates which, if any, interactions can be

independently estimated

• Minimum Detectable Effect• Orthogonality & Balance• Other: D-Optimal, A-Optimal & G-Optimal



By Paul A. Keller

Design Resolution • Resolution III

–Estimates of Main factor effects only; all interactions may be confounded with one another and MF may be confounded with interactions.

• Resolution IV–Estimates of MF are not confounded with 2-

factor interactions but may be confounded with higher order interactions. Two factor interactions may be confounded with one another and with higher order interactions.



By Paul A. Keller

Design Resolution (continued)• Resolution V

–Estimates of MF and 2-factor effects are not confounded with one another but may be confounded with higher-order interactions. Three-factor and higher interactions may be confounded.

• Resolution VI–Estimates of MF and 2-factor effects are not

confounded with each other or with 3-factor interactions. Three-factor and higher interactions may be confounded with one another.



By Paul A. Keller

Design Resolution (continued)

• Resolution VII

–Estimates of MF, 2-factor and 3-factor effects are not confounded with one another but may be confounded with higher order interactions. Four-factor and higher interactions may be confounded.

• Resolution vs. Number of Trials



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 other

–If sum of factors’ columns in standard format equal 0, then design is orthogonal

• Some writers lump balance as part of orthogonality.



By Paul A. Keller

Balance• Balance implies data is properly distributed over

design space. – uniform physical distribution

– an 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 extreme combinations of factors– Ex: Box-Behnken



By Paul A. Keller

Sample Designs• Box Behnken• Plackett Burman• 2k designs (fractional, confounding, fold over,

projection)• 3k designs • Mixed level designs • Latin Squares • Central Composite (with axial points)• John’s ¾




By Paul A. Keller

Sample Designs

• Nested Designs

• Split Plots

• Simplex lattice design

• Simplex centroid design

• D- Optimal

• A- Optimal




By Paul A. Keller

General Guidelines

1. Good understanding of the problemResearch 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 the nature of the problem at hand. The success of the experiment also requires team effort.

Lotfi K. Gaafar 2004From:http://www.qualityamerica.com/knowledgecente/articles/ANTONYdoe1.htm



By Paul A. Keller

General Guidelines

2. Conduct a thorough and in-depth Brainstorming SessionThe 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 the following 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 participation of 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?




By Paul A. Keller

General Guidelines

3. Select the appropriate response or quality characteristicA 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 in selecting 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.




By Paul A. Keller

General Guidelines

4. Choose a suitable design for the experimentThe choice of an experimental design will be dependent upon the following factors:

•Number of factors and interactions (if any) to be studied •Complexity of using each design •Statistical validity and effectiveness of each design •Ease of understanding and implementation •Nature of the problem •Cost and time constraints




By Paul A. Keller

General Guidelines

5. Perform a screening experimentA 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 study seven 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 using full or fractional factorial experiments (Box et al., 1978).




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, different machines, raw materials and so on.




By Paul A. Keller

General Guidelines

7. Perform Confirmatory trials/experimentsIt 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 experiment inappropriate choice of response for the experiment failure to identify the key process variables which affect the response inadequate measurement system for making measurements lack of statistical skills, and so on.


introduction to doe 1 © 2003 qa publishing, llc by paul a. keller introduction to design of...

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