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L. Goch – February 2011

DOE Design & Analysis Using Minitab. L. Goch – February 2011. Agenda. DOE Design DOE Pitfalls & Types of Designs Screen Design Example Characterization Design Example Optimization Design Example DOE Analysis Response Surface Design. Experiments Pitfalls.

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L. Goch – February 2011

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  1. DOE Design & Analysis Using Minitab L. Goch – February 2011

  2. Agenda • DOE Design • DOE Pitfalls & Types of Designs • Screen Design Example • Characterization Design Example • Optimization Design Example • DOE Analysis • Response Surface Design

  3. Experiments Pitfalls • Having an unknown or unaccounted for input variable be the real reason your Y changed • These are called Noise Variables • Number of storks correlating to human births… • Solution: Randomization • Having too little data in too short a time period • Murphy at work again…. • Solution: Repetitionswithin Each Run • Studying a local event and believing it applies to everything • Same as sample size selection…. • Solution: Replicationof Runs within the DOE or as a Confirmation DOE

  4. High Level Map Of Experiments Screening Designs (6-11 Factors) Plackett-Burman DOE L16 & L18 DOEs Fractional Factorial & Full Factorial DOEs Response Surface DOEs Characterization Designs (3-5 Factors) Optimization Designs (<3 Factors)

  5. Screening Designs • Plackett-Burman example (2 Level DOE) • Stat > Doe > Factorial > Create Factorial Design • Check ‘Plackett-Burman design’ • Will review during training • L16 & L18 are also Good Screening Designs (2 & 3 Level Mixed DOE) • Stat > Doe > Taguchi > Create Taguchi Design • Check ‘Mixed Level Design’ • Review on own

  6. 2. Choose factors 1. Choose design 3. Choose the final design NOTE: MINITAB will always default to the Exp. with the fewest runs Let’s use Minitab to Generate the Matrix

  7. 4. Define the Factors and their levels 5. Hit “OK” after you have named all your factors and their levels. Levels can be alphanumeric unless when center points are used. Design Matrix Enter Factors most likely to have Interactions FIRST!

  8. Design Matrix OutputStandard Order Screening Experiment Minitab’s default is to display the runs in Random Order.

  9. Characterization Designs • Full Factorial Doe • Stat > Doe > Factorial > Create Factorial Design • Check ‘General Full Factorial Design’ • Review on own • Fractional Factorial Doe • Stat > Doe > Factorial > Create Factorial Design • Check ‘2-Level Factorial (default generators)’ • Will review during training

  10. DOE Example • Problem: Current Car gas mileage is 30 mpg. Would like to get 40 mpg. • We might try: • Change brand of gas • Change octane rating • Drive Slower • Tune-up Car • Wash and wax car • Buy new tires • Change Tire Pressure • What if it works? • What if it doesn’t? “Survey Says” These variable greatly effect MPG

  11. 1. Choose design type 2. Choose # factors Let’s use Minitab to Generate the Matrix WHAT DESIGN SHOULD YOU CHOOSE?

  12. 1. Choose design 2. Choose factors 3. Choose the final design Let’s use Minitab to Generate the Matrix WHAT DESIGN SHOULD YOU CHOOSE?

  13. 4. Define the Factors and their levels 5. Hit “OK” after you have named all your factors and their levels. Levels can be alphanumeric except when centerpoints are used. Design Matrix

  14. 6. Click on the Options button so we can de-select something for this exercise... 7. Turn off the Randomization option for this exercise only Design Matrix

  15. Design Matrix OutputStandard Orderfor Full Factorial

  16. Optimization Designs • Box Behnken & Central Composite Designs • Stat > Doe > Response Surface > Create Response Surface Design • Check ‘Box Behnken’ or ‘Central Composite’

  17. 1. Choose design 2. Choose factors 3. Choose the final design Let’s use Minitab to Generate the Matrix WHAT DESIGN SHOULD YOU CHOOSE?

  18. 4. Define the Factors and their levels 5. Hit “OK” after you have named all your factors and their levels. Factors MUST be numeric. Choose Cube or Axial Points Design Matrix

  19. Design Matrix OutputRandom Order for Central Composite Design Axial Points are the Actual Max & Min Points of the Design.

  20. Analyzing Data • Full & Fractional Factorial Doe • Stat > Doe > Factorial > Define Custom Factorial Design • Analyze factorial design • Review on own • Response Surface Doe • Stat > Doe > Response Surface > Define custom response surface Design • Analyze response surface design • Review on own

  21. Minitab Procedures: Data Analysis with Multiple Inputs (X’s) and One Output (Y) • We can use the Analyze Response Surface Design feature under DOE to analyze any type of data collection with multiple inputs (X’s) • Used for 2k Full & 2k-n Fractional Factorials or other Characterization or Optimization designs • Used for Plackett-Burman or other screening designs • Used for Passively Collected data • Used for Historically Collected data • Can NOT be used when an Input is Non-Numeric and has more than 3 levels (e.g. 3+ Machines, 3+ Cavities) Remember CAUSATION can only be determined thru experimentally designed and collected data

  22. Roadmap for Analyzing Multiple Inputs (X’s): Step 1: Identify inputs (X’s) vs outputs (Y’s). Step 2: Plot your data Step 3: Find Best Equation based on P-Values Step 4: Check R-squared and Adj. R-squared Step 5: Determine how well your model (i.e. equation) can predict. Step 6: Check Residuals Step 7: Make 3-D plots Step 8: Do the Results Make Sense? Step 9: Confirm Results or begin next Experiment

  23. Step 1) Identify Inputs & Outputs Analyze the Data Open worksheet Carpet.mtw Inputs: Carpet Composition Output: Durability Step 1b) Composition can be coded from text to numeric since it has only 2-levels. Carpet Type can NOT be coded since it’s non-numeric & 4-levels.

  24. Step 1) Identify Inputs & Outputs Analyze the Data Open worksheet Reheat.mtw Inputs: Operator Temp Time Output: Durability Step 1b) Operator can be coded from text to numeric since it has only 2-levels.

  25. Analyze the Data Step 2) Plot the data Does there appear to be any patterns in the data?

  26. Analyze the Data Step 3) Find Best Equation Based on P-values * Define Inputs in MINITAB Select Inputs Click OK

  27. Analyze the Data Step 3) Find Best Equation Based on P-values * Define Inputs in MINITAB Inputs Defined in MINITAB

  28. Step 3) Find Best Equation Based on P-values * Analyze Data Analyze the Data Select Terms & Click OK Select Output

  29. MINITAB tells you there is not enough information to get p-value on these terms. P-Values! Analysis Step 3) continued

  30. Remove term from Equation Terms One at a time remove highest P-value >0.10 until all <0.10 Finding the Best Model Step 3) continued Now we can reduce the model more by removing the 2 input terms that are significantly above our alpha value of 0.10

  31. Term Elimination Step 3) continued Press <Ctrl> e Click Terms Double Click on Terms to Eliminate

  32. Finding the Best Model Step 3) continued One at a time remove any two input terms with p>0.10 Continue reducing the model by removing the 2 item terms that are significantly above our alpha value of 0.10

  33. Finding the Best Model Step 3) continued One at a time remove any main effect terms with p>0.10 if they are NOT in a 2 input term. Continue reducing the model by removing the main effect terms that are significantly above our alpha value of 0.10

  34. Finding the Best Model Step 3) continued Evaluate any terms with p>0.05 if they are NOT in a 2 input term. Evaluate any term with an alpha value of >0.05. These are marginally significant terms. Only leave in if 1) that are contained in a significant 2 input term OR 2) they make sense per theory/prior testing.

  35. Find the Best Model Step 3) completed • This is our best equation to describe our Quality level based on the p-values All Terms in the Regression Equation are Significant The p-values are < 0.05.

  36. Find the Best Model Step 3) completed Frozen Food Quality = -180.963 + (0.43070 * Temp) + (5.79598 * Time) - (0.000318 * Temp2) - (0.05181 * Time2) - (0.00521 * Temp * Time)

  37. Analyze the R-squared(s) Step 4) Check R-squared and Adj. R-squared If more than ~4% apart eliminate term with highest p-value Temp & Time explain 71.5% of the variability in Quality

  38. How Accurate is the Model? Step 5) Determine Model Accuracy Equation can predict to within +/- 2 Stdev’s Model can Predict Quality to within +/- 3.4 with a 95% Confidence Level

  39. Analyze the Residuals Step 6) Check Residuals Press <Ctrl> e Click Graphs Check Four in One

  40. Analyze the Residuals Step 6) Check Residuals Looking for Normal Distribution Looking for Random Pattern Residual Plots: Use if n > 25

  41. Plot the Results Step 7a) Make 3-D Plots Select Check Surface Plot & Click Setup

  42. Plot the Results Step 7a) Make 3-D Plots Best Quality at Low Temp & High Time. Robust at ~350-425o & ~33-38 minutes.

  43. Evaluate the Results Step 8) Does the Results Make Sense • EXPERIMENTAL RESULTS: • Numbers results matched up with original plotted data. • Operator didn’t matter to the results. • Lower oven temps & longer times result in the highest, most robust quality levels. • Are the results what you would have expected? • Are some statistically significant items not PRACTICALLY significant? • Looking at the 3-D plot, do the changes in Temp & Time have a big enough effect on Quality to be useful?

  44. Confirm Results! Step 9) Confirm Results or begin Next Experiment • ALWAYS, ALWAYS run a confirmation run at the optimal settings or a small confirmation experiment. This is critical to ensure that your results are accurate!!!! • If your data was historical or collected passively, you will need to run an experiment to show that your inputs CAUSED the changes to happen in your output. • At this point you may decide to eliminate factors from your experimentation process or add new factors to your experimentation. • Be careful to set up your next experiment so that the results can be compared to your previous experiment(s).

  45. Confirm Results! Step 9) Confirm Results * Determine Optimal Settings

  46. Step 9) Confirm Results (cont.) * Determine Optimal Settings Select Output Variable Enter Specifications

  47. Step 7b) Make Optimization Plot Plot the Results Click & Drag Red lines to see changes in Output & Relationships Run confirmation at 350o for 38 minutes for maximum Quality.

  48. Summary • The goal of DOE design is to get the most information from the fewest amount of runs. Thus, DOE design is based on specific combinations of • the # of Factors to be tested • the # of Levels for each of the factors • The goal of DOE analysis is to achieve reliable, predictable results. For this to happen, four items must be evaluated as part of the analysis • P-values: Significance of Terms in Equation • R-Square: Relationship of Inputs to Outputs • +/- 2 * S: Predictability of Equation • Residuals: Violation of Analysis Assumptions

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