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<Function> <Process Name> Planning for a Successful Design of Experiment Jim Akers SIU ASQ Spring Conference 2013 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. Jim Akers 2 THE BASICS OF DOE Jim Akers 3 Objectives in Using DOE • 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 Jim Akers 4 Let’s Start with an Example: Data 18 32 31 21 23 16 26 27 19 20 30 16 23 25 22 29 24 38 22 19 28 27 33 17 21 21 17 14 12 14 17 17 13 21 45 41 33 26 21 15 8 19 11 25 24 17 18 28 26 34 Fuel Economy of 50 automobiles (in mpg) Plot a histogram and calculate the average and standard deviation Fuel Economy 16 X 22.88 S 7.7266 14 Number of Cars 12 10 8 6 4 2 0 0 to <6 6 to <12 12 to <18 18 to <24 24 to <30 30 to <36 36 to <42 42 to <48 48 to <54 54 to <=60 mgp Jim Akers 5 What Might Explain the Variation? MANPOWER METHOD MACHINE EFFECT Effect MEASUREMENT MOTHERNATURE MATERIAL • 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. Jim Akers 6 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: X Observation 1 2 3 4 5 6 7 8 9 10 Jim Akers X - Weight (lbs) 3000 2800 2100 2900 2400 3300 2700 3500 2500 3200 Y=f(X) Y Y - Mileage(mpg) 18 21 32 17 31 14 21 12 23 14 7 Regression Analysis • 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 Y=f(X) mpg Scatter Chart (Weight vs mpg) 35 30 25 ~21 20 15 10 5 0 1900 Jim Akers y = -0.0152x + 63.507 R² = 0.9191 2400 2800 2900 Weight We have now experimented with one factor, but that does not explain all of the variation. 3400 3900 8 Experimenting with a System 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. Jim Akers 9 1FAT Example • Let’s consider how two known (based on years of experience) factors affect gas mileage, tire size (T) and fuel type (F). T(1,2) F(1,2) Jim Akers Y=f(X) Y Fuel Type Tire size F1 T1 F2 T2 10 1FAT Design 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. Jim Akers Fuel Type Tire size Mpg F1 T1 20 F1 T2 30 11 1FAT Design 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. Jim Akers Fuel Type Tire size Mpg F1 T2 30 F2 T2 40 12 1FAT Design • Looks like the ideal setting is F2 and T2 at 40mpg. • This is a common experimental method. What about the possible interaction effect of tire size and fuel type? F2T1 Jim Akers Fuel Type Tire size Mpg F1 T2 30 F2 T2 40 13 1FAT Design • Suppose that the untested combination F2T1 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 70 60 F2 mpg 50 40 30 F1 20 10 0 T1 T2 Tire Size Jim Akers 14 What About Other Factors – and Noise? • 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. Jim Akers 15 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. Run X1 X2 X3 X4 1 + + + + + + + + + + + + + + + + 2 3 4 5 6 7 8 Jim Akers Y1 Y2 Y3 Y-bar SY 16 The Basics • To ‘design’ an experiment, means to pick the points that you’ll use to understand the design space. X1 A B (-,+) Design Space Y (+,+) High (+) Factor B Settings In tabular form, it would look like: Low (-) (-,-) Low (-) Jim Akers X2 (+,-) Factor A Settings Run A B AB 1 2 3 4 + + + + + + High (+) 17 Full vs. Fractional Factorial • 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. – – – Jim Akers The preferred design when a full factorial cannot be performed due to lack of resources Okay for some modeling Good for screening 18 2k r runs 2 Level Designs k number of factors • Full factorial – – – – 2 level 3 factors 8 runs Balanced (orthogonal) 23 8 runs • Fractional factorial – – – 231 4 runs Jim Akers – 2 level 3 factors 4 runs - half fraction Balanced (orthogonal) 19 3k r runs 3 Level Designs k number of factors • Full factorial – – – – – Jim Akers 3 level 3 factors 27 runs Balanced (orthogonal) 33 27 runs Used when it is expected the response is non-linear 20 Measuring An “Effect” Response - Y Average Y when A was set ‘high’ Average Y when A was set ‘low’ Low High Factor A • 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 Jim Akers 21 Looking For Interactions B = High B = Low Strong Slight Low -Y Response B = Low B = High Low Factor A High High Factor A Jim Akers Response - Y Response - Y When the effect of one factor changes due to the effect of another factor, the two factors are said to ‘interact.’ None B = Low more than two factors can interact at the same time, but it is rare outside of chemical reactions. B = High Low Factor A High 22 Reasons Why a Model Might Not Confirm: • • • • • • 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. Jim Akers 23 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, 1930-1936. Source: “Statistics for Experimenters” by Box, Hunter, and Hunter. (1978) Jim Akers 24 Response Surface Method - 2D Contour Plot • Useful to see how factors effect the response and to determine what other settings provide the same response Jim Akers 25 Response Surface Method - 3D Response Surface Plot • Helpful in reaching the optimal result Jim Akers 26 CREATING A CHARTER Jim Akers 27 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 Jim Akers 28 Planning - Charter • 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: ________ Jim Akers 29 Planning - Charter • IV. SELECT MEASUREABLE QUALITY CHARACTERISTICS (also known as responses, dependent variables, or output variables). These characteristics should be related to customer needs and expectations. Jim Akers 30 Planning - Charter • 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. Jim Akers 31 Planning - Charter • 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. Jim Akers 32 Planning - Charter • 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. Jim Akers 33 Planning - Charter • 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.) MS Word Template available at: http://jimakers.com/downloads/DOE_Setup.docx Jim Akers 34 CHOOSING AN APPROPRIATE DESIGN Jim Akers 35 Choosing an Appropriate Design Jim Akers Source: Understanding Industrial Designed Experiments – ISBN 1-880156-03-2 36 2-Level Design Summary Jim Akers Source: Understanding Industrial Designed Experiments – ISBN 1-880156-03-2 37 <Function> <Process Name> Thank you Jim Akers