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Planning for a Successful Design of Experiment Jim Akers SIU ASQ Spring Conference 2013

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Jim Akers 2 Topics we will cover This presentation will provide a process for planning a successful design of experiment. We will cover the basics of DOE creating a charter choosing an appropriate design The participants will take away a DOE charter template and a flowchart for simple design selection. The major focus is asking and answering the right questions to create an appropriate experiment.

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Jim Akers THE BASICS OF DOE 3

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Jim Akers Will help you gain knowledge in: – Improving performance characteristics – Understand relationships between process variables – Reducing costs – Understand how to optimize processes Creates the ultimate process knowledge to make your product/process Better Faster Cheaper Objectives in Using DOE 4

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Jim Akers Let’s Start with an Example: Plot a histogram and calculate the average and standard deviation Fuel Economy to <66 to <1212 to <1818 to <2424 to <3030 to <3636 to <4242 to <4848 to <5454 to <=60 mgp Number of Cars 5

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Jim Akers What Might Explain the Variation? DOE is about discovering and quantifying the magnitude of cause and effect relationships. We need DOE because intuition can be misleading.... but we’ll get to that in a minute. Regression can be used to explain how we can model data experimentally. MOTHERNATURE 6

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Jim Akers Mileage Data with Vehicle Weight: Let’s take a look at the mileage data and see if there’s a factor that might explain some of the variation. Draw a scatter diagram for the following data: Y=f(X) XY 7

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Jim Akers Plot the data on a scatter chart and draw a best fit line Determine the equation for that line, – you now have a ‘model’ for the data Regression Analysis Y=f(X) ~21 We have now experimented with one factor, but that does not explain all of the variation.

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Jim Akers There are a few basic ways to understand a process you are working on. We will talk about two of them. Classical 1FAT experiments – One factor at a time (1FAT) focuses on one variable at two or three levels and attempts to hold everything else constant (which is impossible to do in a complicated process). DOE – When properly constructed, it can focus on a wide range of key input factors and will determine the optimum levels of each of the factors. Each have their advantages and disadvantages. Experimenting with a System 9

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Jim Akers Let’s consider how two known (based on years of experience) factors affect gas mileage, tire size (T) and fuel type (F). 1FAT Example Fuel TypeTire size F1F1 T1T1 F2F2 T2T2 Y=f(X) T( 1,2 ) Y F( 1,2 ) 10

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Jim Akers Step 1: Select two levels of tire size and two kinds of fuels. Step 2: Holding fuel type constant (and everything else), test the car at both tire sizes. 1FAT Design Fuel TypeTire sizeMpg F1F1 T1T1 20 F1F1 T2T

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Jim Akers Since we want to maximize mpg the more desirable response happened with T 2 Step 3: Holding tire size at T 2, test the car at both fuel types. 1FAT Design Fuel TypeTire sizeMpg F1F1 T2T2 30 F2F2 T2T

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Jim Akers Looks like the ideal setting is F 2 and T 2 at 40mpg. This is a common experimental method. 1FAT Design Fuel TypeTire sizeMpg F1F1 T2T2 30 F2F2 T2T2 40 What about the possible interaction effect of tire size and fuel type? F 2 T 1 13

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Jim Akers Suppose that the untested combination F 2 T 1 would produce the results below. There is a different slope so there appears to be an interaction. A more appropriate design would be to test all four combinations. – That is called a full factorial 1FAT Design 14

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Jim Akers We need a way to – investigate the relationship(s) between variables – distinguish the effects of variables from each other (and maybe tell if they interact with each other) – quantify the effects......So we can predict, control, and optimize processes. What About Other Factors – and Noise? 15

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Jim Akers DOE to the Rescue!! Y=f(X) DOE uses purposeful changes of the inputs (factors) in order to observe corresponding changes to the outputs (response). Remember the IPO’s we did – they are real important here. 16

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Jim Akers To ‘design’ an experiment, means to pick the points that you’ll use to understand the design space. The Basics RunAB In tabular form, it would look like: High (+) Low (-) Factor B Settings Factor A Settings High (+)Low (-) (-,+) (+,-) (+,+) (-,-) Y A B X1X1 X2X2 17 Design Space AB

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Jim Akers A full factorial is an experimental design which contains all levels of all factors. No possible treatments are omitted. – The preferred (ultimate) design – Best for modeling (Response Surface Methods) A fractional factorial is a balanced experimental design which contains fewer than all combinations of all levels of all factors. – The preferred design when a full factorial cannot be performed due to lack of resources – Okay for some modeling – Good for screening Full vs. Fractional Factorial 18

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Jim Akers Full factorial – 2 level – 3 factors – 8 runs – Balanced (orthogonal) Fractional factorial – 2 level – 3 factors – 4 runs - half fraction – Balanced (orthogonal) 2 Level Designs 19

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Jim Akers Full factorial – 3 level – 3 factors – 27 runs – Balanced (orthogonal) – Used when it is expected the response is non-linear 3 Level Designs 20

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Jim Akers Average Y when A was set ‘high’ Average Y when A was set ‘low’ The difference in the average Y when A was ‘high’ from the average Y when A was ‘low’ is the ‘factor effect’ The differences are calculated for every factor in the experiment Measuring An “Effect” 21

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Jim Akers When the effect of one factor changes due to the effect of another factor, the two factors are said to ‘interact.’ more than two factors can interact at the same time, but it is rare outside of chemical reactions. Response - Y Factor A LowHigh B = High B = Low Slight Response - Y Factor A LowHigh B = HighB = Low Strong Looking For Interactions Response - Y LowHigh B = High B = Low None 22 Factor A

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Jim Akers Too much variation in the response Measurement error Poor experimental discipline Aliases (confounded) effects Inadequate model Something changed - And: - Reasons Why a Model Might Not Confirm: There may not be a true cause-and-effect relationship. There may not be a true cause-and-effect relationship. 23

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Jim Akers Proof – Storks do bring babies! A plot of the population of Oldenburg, Germany at the end of each year against the number of storks observed in that year, Source: “Statistics for Experimenters” by Box, Hunter, and Hunter. (1978) 24

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Jim Akers Useful to see how factors effect the response and to determine what other settings provide the same response Response Surface Method - 2D Contour Plot 25

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Jim Akers Helpful in reaching the optimal result Response Surface Method - 3D Response Surface Plot 26

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Jim Akers CREATING A CHARTER 27

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Jim Akers Planning - DOE Steps Set objectives - create a Charter – Comparative Determine what factor is significant – Screening Determine what factors will be studied – Model – Response Surface Method Determine interactions and optimize Select factors (process variables from C&E) and levels you will test Select an experimental design Execute the experiment CONFIRM the model!! Verify the data is consistent with the experimental assumptions Analyze and interpret the results Use/present the results 28

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Jim Akers I. STATEMENT OF THE PROBLEM: __________________________________________ __________________________________________ (During this step you should estimate your current level of quality by way of Cpk, dpm, or total loss. This estimate will then be compared with improvements found after Step XII.) II. OBJECTIVE OF THE EXPERIMENT: __________________________________________ __________________________________________ III. START DATE: ________ END DATE: ________ Planning - Charter 29

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Jim Akers IV. SELECT MEASUREABLE QUALITY CHARACTERISTICS (also known as responses, dependent variables, or output variables). These characteristics should be related to customer needs and expectations. Planning - Charter 30

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Jim Akers V. COMPLETE A LITERATURE REVIEW, PROCESS FLOW DIAGRAM, AND CAUSE & EFFECT DIAGRAM. FROM THE CAUSE & EFFECT DIAGRAM SELECT FACTORS (also known as parameters or input variables) which are anticipated to have an effect on the response. Write Standard Operating Procedures for all variables that are to be held constant. Planning - Charter 31

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Jim Akers VI. DETERMINE THE NUMBER OF RESOURCES TO BE USED IN THE EXPERIMENT. Consider the desired number, the cost per resource, time per experimental trial, the maximum allowable number of resources. VII. WHICH DESIGN TYPES AND ANALYSIS STRATEGIES ARE APPROPRIATE? Discuss advantages and disadvantages of each. VIII. SELECT THE BEST DESIGN TYPE AND ANALYSIS STRATEGY TO SUIT YOUR NEEDS. Planning - Charter 32

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Jim Akers IX. CAN ALL THE RUNS BE RANDOMIZED? ____________________________________________ ________________________________________ WHICH FACTORS ARE MOST DIFFICULT TO RANDOMIZE?________________________________ ________________________________________ X. CONDUCT THE EXPERIMENT AND RECORD THE DATA. (Monitor both of these events for accuracy.) XI. ANALYZE THE DATA, DRAW CONCLUSIONS, MAKE PREDICTIONS, AND PERFORM CONFIRMATION TESTS. Planning - Charter 33

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Jim Akers XII. ASSESS RESULTS, MAKE DECISIONS, AND DOCUMENT YOUR RESULTS. (Evaluate your new state of quality and compare with the quality level prior to the improvement effort. Estimate your return on investment. If necessary, conduct more experimentation.) Planning - Charter 34 MS Word Template available at:

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Jim Akers CHOOSING AN APPROPRIATE DESIGN 35

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Jim Akers 36 Choosing an Appropriate Design Source: Understanding Industrial Designed Experiments – ISBN

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Jim Akers 2-Level Design Summary 37 Source: Understanding Industrial Designed Experiments – ISBN

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Thank you Jim Akers

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