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2222 Will help you gain knowledge in: ◦ Improving performance characteristics ◦ Reducing costs ◦ Understand regression analysis ◦ Understand relationships between variables ◦ Understand correlation ◦ Understand how to optimize processes So you can: ◦ Recognize opportunities ◦ Understand terminology ◦ Know when to get help X-2

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3333 Plot a histogram and calculate the average and standard deviation Fuel Economy 0 2 4 6 8 10 12 14 16 0 to <66 to <1212 to <1818 to <2424 to <3030 to <3636 to <4242 to <4848 to <5454 to <=60 mgp Number of Cars X-2

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4444 Experimental design (a.k.a. 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. METHOD MOTHER NATURE MEASUREMENT MANPOWERMACHINE MATERIAL X-2

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5555 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 X-2

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6666 If you draw a best fit line and figure out an equation for that line, you would have a ‘model’ that represents the data. Y=f(X) X-2

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7777 There are basically three ways to understand a process you are working on. 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). Mathematical model ◦ Express the system with a mathematical equation. 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. We’ll talk about each. X-2

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8888 Let’s consider how two known (based on years of experience) factors affect gas mileage, tire size (T) and fuel type (F). Fuel TypeTire size F1F1 T1T1 F2F2 T2T2 Y=f(X) T( 1,2 ) Y F( 1,2 ) X-2

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9999 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. Fuel TypeTire sizeMpg F1F1 T1T1 20 F1F1 T2T2 30 X-2

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10 Since we want to maximize mpg the more desirable response happened with T2 Step 3: Holding tire size at T2, test the car at both fuel types. Fuel TypeTire sizeMpg F1F1 T2T2 30 F2F2 T2T2 40 X-2

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11 Looks like the ideal setting is F2 and T2 at 40mpg. This is a common experimental method. 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 X-2

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12 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. X-2

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13 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. X-2

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14 We can see some problems with 1FAT. Now let’s go back and talk about the statapult. We can do a mathematical model or we could do a DOE. DOE will build a ‘model’ - a mathematical representation of the behavior of measurements. or… You could build a “mathematical model” without DOE and it might look something like... X-2

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15 X-2

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16 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. X-3

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17 Set objectives (Charter) ◦ Comparative Determine what factor is significant ◦ Screening Determine what factors will be studied ◦ Model – response surface method Determine interactions and optimize Select process variables (C&E) and levels you will test at Select an experimental design Execute the design CONFIRM the model!! Check that the data are consistent with the experimental assumptions Analyze and interpret the results Use/present the results X-4

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18 X-8

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19 http://jimakers.com/downloads/DOE_Setup.docxjimakers.com/downloads/DOE_Setup.docx X-8

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20 To ‘design’ an experiment, means to pick the points that you’ll use for a scatter diagram. See DOE terms X-9 through X-15 RunAB 1-- 2-+ 3+- 4++ In tabular form, it would look like: High (+) Low (-) Factor B Settings Factor A Settings High (+)Low (-) (-,+) (+,-) (+,+) (-,-) Y A B X1X1 X2X2 X-9

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21 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 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 X-16

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22 Full factorial ◦ 2 level ◦ 3 factors ◦ 8 runs ◦ Balanced (orthogonal) Fractional factorial ◦ 2 level ◦ 3 factors ◦ 4 runs - Half fraction ◦ Balanced (orthogonal) X-16

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23 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 X-16

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24 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 thought to be rare outside of chemical reactions. Response - Y Factor A LowHigh B = High B = Low Slight Response - Y Factor A LowHigh B = HighB = Low Strong Response - Y Factor A LowHigh B = High B = Low None X-16

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25 Using the statapult, we will experiment with some factors to “model” the process. We will perform a confirmation run to determine if the model will help us predict the proper settings required to achieve a desired output. What design should we use? Y A B X1X1 X2X2 C D X3X3 X4X4 Y=f(X 1, X 2, X 3, X 4 ) X-17

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26 Too much variation in the response Measurement error Poor experimental discipline Aliases (confounded) effects Inadequate model Something changed - And: - There may not be a true cause-and-effect relationship. There may not be a true cause-and-effect relationship. X-17

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28 FactorABCDResponse #1 Row #A -B -C -D -Y1Y2Y3 1 2 1 3 1 4 11 5 1 6 1 1 7 11 8 111 91 101 1 1111 12111 1311 14111 15111 161111 X-17 Confirmation runs

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33 Full factorial ◦ 3 level ◦ 3 factors ◦ 27 runs ◦ Balanced (orthogonal) ◦ Used when it is expected the response in non-linear X-18

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34 Useful to see how factors effect the response and to determine what other settings provide the same response X-30

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35 Helpful in reaching the optimal result X-30

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Section 4.2. Correlation and Regression Describe only linear relationship. Strongly influenced by extremes in data. Always plot data first. Extrapolation.

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