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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 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 InputOutput Process Controllable factors Uncontrollable factors Lotfi K. Gaafar 2004

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Introduction to DOE 3 © 2003 QA Publishing, LLC 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

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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 2 Trial 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 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.

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Introduction to DOE 7 © 2003 QA Publishing, LLC 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

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Introduction to DOE 8 © 2003 QA Publishing, LLC 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

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Introduction to DOE 9 © 2003 QA Publishing, LLC By Paul A. Keller DOE: Applications in Process Development Improve process yield Reduce variability Reduce development time Reduce overall costs Lotfi K. Gaafar 2004

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Introduction to DOE 10 © 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 Lotfi K. Gaafar 2004

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Introduction to DOE 11 © 2003 QA Publishing, LLC By Paul A. Keller DOE: Basic Principles Replication – Error estimation – Accuracy Blocking – Unimportant significant factor – Precision Randomization – Independence – Even out uncontrollable factors Lotfi K. Gaafar 2004

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Introduction to DOE 12 © 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 Lotfi K. Gaafar 2004

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Introduction to DOE 13 © 2003 QA Publishing, LLC 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 Lotfi K. Gaafar 2004

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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 Matrix – Hold 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 may be statistically insignificant Moving off current operating points presents a risk. – Probing techniques: Response Surface Analysis – Evolutionary 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 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;

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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): ) 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

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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): ) 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 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

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Introduction to DOE 20 © 2003 QA Publishing, LLC 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.

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Introduction to DOE 21 © 2003 QA Publishing, LLC 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.

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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-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

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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 other – If sum of factors’ columns in standard format equal 0, then design is orthogonal Some writers lump balance as part of orthogonality.

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Introduction to DOE 24 © 2003 QA Publishing, LLC 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

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Introduction to DOE 25 © 2003 QA Publishing, LLC By Paul A. Keller Sample Designs Box Behnken Plackett Burman 2 k designs (fractional, confounding, fold over, projection) 3 k designs Mixed level designs Latin Squares Central Composite (with axial points) John’s ¾ Lotfi K. Gaafar 2004

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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 Lotfi K. Gaafar 2004

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

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

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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 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 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 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). 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, different machines, raw materials and so on. Lotfi K. Gaafar 2004 From:http://www.qualityamerica.com/knowledgecente/articles/ANTONYdoe1.htm

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Introduction to DOE 33 © 2003 QA Publishing, LLC By Paul A. Keller 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 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. Lotfi K. Gaafar 2004 From:http://www.qualityamerica.com/knowledgecente/articles/ANTONYdoe1.htm

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