L.%20Goch%20

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DOE Design Analysis Using Minitab

• L. Goch February 2011

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Agenda

• DOE Design
• DOE Pitfalls Types of Designs
• Screen Design Example
• Characterization Design Example
• Optimization Design Example
• DOE Analysis
• Response Surface Design

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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 Repetitions within Each Run
• Studying a local event and believing it applies
  to everything
• Same as sample size selection.
• Solution Replication of Runs within the DOE or
  as a Confirmation DOE

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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 (lt3 Factors)
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• Screening Designs
• Plackett-Burman example (2 Level DOE)
• Stat gt Doe gt Factorial gt Create Factorial Design
• Check Plackett-Burman design
• Will review during training
• L16 L18 are also Good Screening Designs (2 3
  Level Mixed DOE)
• Stat gt Doe gt Taguchi gt Create Taguchi Design
• Check Mixed Level Design
• Review on own

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Lets use Minitab to Generate the Matrix
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Design Matrix
Enter Factors most likely to have Interactions
FIRST!
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Design Matrix OutputStandard Order Screening
Experiment
Minitabs default is to display the runs in
Random Order.
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• Characterization Designs
• Full Factorial Doe
• Stat gt Doe gt Factorial gt Create Factorial Design
• Check General Full Factorial Design
• Review on own
• Fractional Factorial Doe
• Stat gt Doe gt Factorial gt Create Factorial Design
• Check 2-Level Factorial (default generators)
• Will review during training

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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 doesnt?

Survey Says These variable greatly effect MPG
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Lets use Minitab to Generate the Matrix
WHAT DESIGN SHOULD YOU CHOOSE?
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Lets use Minitab to Generate the Matrix
WHAT DESIGN SHOULD YOU CHOOSE?
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Design Matrix
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Design Matrix
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Design Matrix OutputStandard Order for Full
Factorial
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• Optimization Designs
• Box Behnken Central Composite Designs
• Stat gt Doe gt Response Surface gt Create Response
  Surface Design
• Check Box Behnken or Central Composite

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Lets use Minitab to Generate the Matrix
WHAT DESIGN SHOULD YOU CHOOSE?
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Design Matrix
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Design Matrix OutputRandom Order for Central
Composite Design
Axial Points are the Actual Max Min Points of
the Design.
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• Analyzing Data
• Full Fractional Factorial Doe
• Stat gt Doe gt Factorial gt Define Custom Factorial
  Design
• Analyze factorial design
• Review on own
• Response Surface Doe
• Stat gt Doe gt Response Surface gt Define custom
  response surface Design
• Analyze response surface design
• Review on own

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Minitab Procedures Data Analysis with Multiple
Inputs (Xs) 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 (Xs)
• 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
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Roadmap for Analyzing Multiple Inputs (Xs)

• Step 1 Identify inputs (Xs) vs outputs (Ys).
•  
• 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

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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 its non-numeric
4-levels.
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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.
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Analyze the Data
Step 2) Plot the data
Does there appear to be any patterns in the data?
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Analyze the Data
Step 3) Find Best Equation Based on P-values
Define Inputs in MINITAB
Select Inputs
Click OK
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Analyze the Data
Step 3) Find Best Equation Based on P-values
Define Inputs in MINITAB
Inputs Defined in MINITAB
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Analyze the Data
Step 3) Find Best Equation Based on P-values
Analyze Data
Select Terms Click OK
Select Output
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Analysis
Step 3) continued
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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
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Term Elimination
Step 3) continued
Press ltCtrlgt e
Click Terms
Double Click on Terms to Eliminate
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Finding the Best Model
Step 3) continued
One at a time remove any two input terms with
pgt0.10
Continue reducing the model by removing the 2
item terms that are significantly above our alpha
value of 0.10
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Finding the Best Model
Step 3) continued
One at a time remove any main effect terms with
pgt0.10 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
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Finding the Best Model
Step 3) continued
Evaluate any terms with pgt0.05 if they are NOT in
a 2 input term.
Evaluate any term with an alpha value of gt0.05.
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.
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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 lt 0.05.
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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)
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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
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How Accurate is the Model?
Step 5) Determine Model Accuracy
Equation can predict to within /- 2 Stdevs
Model can Predict Quality to within /- 3.4 with
a 95 Confidence Level
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Analyze the Residuals
Step 6) Check Residuals
Press ltCtrlgt e
Click Graphs
Check Four in One
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Analyze the Residuals
Step 6) Check Residuals
Looking for Normal Distribution
Looking for Random Pattern
Residual Plots Use if n gt 25
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Plot the Results
Step 7a) Make 3-D Plots
Select
Check Surface Plot Click Setup
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Plot the Results
Step 7a) Make 3-D Plots
Best Quality at Low Temp High Time. Robust at
350-425o 33-38 minutes.
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Evaluate the Results
Step 8) Does the Results Make Sense

• EXPERIMENTAL RESULTS
• Numbers results matched up with original plotted
  data.
• Operator didnt 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?

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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).

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Confirm Results!
Step 9) Confirm Results Determine Optimal
Settings
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Step 9) Confirm Results (cont.) Determine
Optimal Settings
Select Output Variable
Enter Specifications
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Plot the Results
Step 7b) Make Optimization Plot
Click Drag Red lines to see changes in Output
Relationships Run confirmation at 350o for 38
minutes for maximum Quality.
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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