Robust Design:
Experiments for Better Products


       Taguchi Techniques




                            MITSloan
Robust Design and Quality in the
     Product Development Process


              Concept    System-Level    Detail    Tes...
Goalpost vs Taguchi View




                       COST $
COST $




           Nominal              Nominal
            ...
General Loss Function
              Product & Process Engineer (a priori)

                     Manufacturing (daily)

   ...
Who is the better target shooter?




     Pat                                                       Drew
      Adapted fr...
Exploiting Non-Linearities


 YB


 YA




                       XA                                          XB
      Sou...
Goals for Designed Experiments

 Understanding relationships between
 design parameters and product
 performance
 Understa...
Robust Designs
A Robust Product or Process performs correctly,
  even in the presence of noise factors.

  Outer Noise
  E...
Parameter Design

         Procedure




                     MITSloan
Step 1: P-Diagram
Step 1: Select appropriate controls,
 response, and noise factors to explore
 experimentally.
 controlla...
The “P” Diagram

  Uncontrollable
  Noise Factors



                      Measurable
    Product or
     Product or      ...
Example: Brownie Mix

Controllable Input Parameters
  Recipe Ingredients (quantity of eggs, flour, chocolate)
  Recipe Dir...
Step 2: Objective Function
Step 2: Define an objective function (of
 the response) to optimize.
 maximize desired performa...
Types of Objective Functions

Larger-the-Better   Smaller-the-Better
e.g. performance      e.g. variance
     ƒ(y) = y2   ...
Step 3: Plan the Experiment
Elicit desired effects:

  Use full or fractional factorial designs to
  identify interactions...
Experiment Design: Full Factorial

Consider k factors, n levels each.
Test all combinations of the factors.
The number of ...
Experiment Design: Full Factorial


Expt # Param A Param B   2 factors, 3 levels each:
  1      A1      B1
  2      A1    ...
Experiment Design:
 One Factor at a Time

Consider k factors, n levels each.
Test all levels of each factor while
freezing...
Experiment Design:
One Factor at a Time
Expt # Param A Param B Param C Param D
  1      A2      B2      C2      D2
  2    ...
Experiment Design:
  Orthogonal Array

Consider k factors, n levels each.
Test all levels of each factor in a balanced
way...
Experiment Design:
Orthogonal Array
 Expt # Param A Param B Param C Param D
   1      A1      B1      C1      D1
   2     ...
Using Inner and Outer Arrays
 Induce the same noise factor levels for each
 combination of controls in a balanced manner
 ...
Step 4: Run the Experiment

Step 4: Conduct the experiment.
 Vary the input and noise parameters
 Record the output respon...
Paper Airplane Experiment

Expt # Weight Winglet Nose   Wing   Trials   Mean Std Dev S/N
 1      A1     B1      C1    D1
 ...
Step 5: Conduct Analysis
Step 5: Perform analysis of means.
 Compute the mean value of the
 objective function for each pa...
Parameter Design Procedure
 Step 6: Select Setpoints
Parameters can effect
  Average and Variation (tune S/N)
  Variation ...
Parameter Design Procedure
 Step 6: Advanced Use

Conduct confirming experiments.
Set scaling parameters to tune
response....
Confounding Interactions

Generally the main effects dominate the
response. BUT sometimes interactions are
important. This...
Confounding Interactions
S/N




                     A1
                     A2
                     A3




      B1   B2...
Key Concepts of Robust Design
Variation causes quality loss
Parameter Design to reduce Variation
Matrix experiments (ortho...
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Robust Design - Experiments For Better Products - Taguchi Techniques

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Robust Design - Experiments For Better Products - Taguchi Techniques

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Robust Design - Experiments For Better Products - Taguchi Techniques

  1. 1. Robust Design: Experiments for Better Products Taguchi Techniques MITSloan
  2. 2. Robust Design and Quality in the Product Development Process Concept System-Level Detail Testing and Production Concept System-Level Detail Testing and Production Planning Planning Development Design Design Refinement Ramp-Up Development Design Design Refinement Ramp-Up Robust Concept Robust Quality efforts are and System Parameter & typically made here, Design Tolerance when it is too late. Design MITSloan
  3. 3. Goalpost vs Taguchi View COST $ COST $ Nominal Nominal Value Value MITSloan
  4. 4. General Loss Function Product & Process Engineer (a priori) Manufacturing (daily) [ ] k ⋅ σ + (µ − m ) 2 2 Nominal Value Average Value Variance Cost Factor MITSloan
  5. 5. Who is the better target shooter? Pat Drew Adapted from: Clausing, Don, and Genichi Taquchi. “Robust Quality.” Boston, MA: Harvard Business Review, 1990. Reprint No. 90114. MITSloan
  6. 6. Exploiting Non-Linearities YB YA XA XB Source: Ross, Phillip J. “Taguchi Techniques for Quality Engineering (2nd Edition).” New York, NY: McGraw Hill, 1996. MITSloan
  7. 7. Goals for Designed Experiments Understanding relationships between design parameters and product performance Understanding effects of noise factors Reducing product or process variations MITSloan
  8. 8. Robust Designs A Robust Product or Process performs correctly, even in the presence of noise factors. Outer Noise Environmental changes, Operating conditions, People Inner Noise Function & Time related (Wear, Deterioration) Product Noise Part-to-Part Variations MITSloan
  9. 9. Parameter Design Procedure MITSloan
  10. 10. Step 1: P-Diagram Step 1: Select appropriate controls, response, and noise factors to explore experimentally. controllable input parameters measurable performance response uncontrollable noise factors MITSloan
  11. 11. The “P” Diagram Uncontrollable Noise Factors Measurable Product or Product or Performance Process Process Response Controllable Input Parameters MITSloan
  12. 12. Example: Brownie Mix Controllable Input Parameters Recipe Ingredients (quantity of eggs, flour, chocolate) Recipe Directions (mixing, baking, cooling) Equipment (bowls, pans, oven) Uncontrollable Noise Factors Quality of Ingredients (size of eggs, type of oil) Following Directions (stirring time, measuring) Equipment Variations (pan shape, oven temp) Measurable Performance Response Taste Testing by Customers Sweetness, Moisture, Density MITSloan
  13. 13. Step 2: Objective Function Step 2: Define an objective function (of the response) to optimize. maximize desired performance minimize variations quadratic loss signal-to-noise ratio MITSloan
  14. 14. Types of Objective Functions Larger-the-Better Smaller-the-Better e.g. performance e.g. variance ƒ(y) = y2 ƒ(y) = 1/y2 Nominal-the-Best Signal-to-Noise e.g. target e.g. trade-off ƒ(y) = 1/(y–t)2 ƒ(y) = 10log[µ2/σ2] MITSloan
  15. 15. Step 3: Plan the Experiment Elicit desired effects: Use full or fractional factorial designs to identify interactions. Use an orthogonal array to identify main effects with minimum of trials. Use inner and outer arrays to see the effects of noise factors. MITSloan
  16. 16. Experiment Design: Full Factorial Consider k factors, n levels each. Test all combinations of the factors. The number of experiments is nk . Generally this is too many experiments, but we are able to reveal all of the interactions. MITSloan
  17. 17. Experiment Design: Full Factorial Expt # Param A Param B 2 factors, 3 levels each: 1 A1 B1 2 A1 B2 nk = 32 = 9 trials 3 A1 B3 4 A2 B1 5 A2 B2 6 A2 B3 4 factors, 3 levels each: 7 A3 B1 nk = 34 = 81 trials 8 A3 B2 9 A3 B3 MITSloan
  18. 18. Experiment Design: One Factor at a Time Consider k factors, n levels each. Test all levels of each factor while freezing the others at nominal level. The number of experiments is 1+k(n-1). BUT this is an unbalanced experiment design. MITSloan
  19. 19. Experiment Design: One Factor at a Time Expt # Param A Param B Param C Param D 1 A2 B2 C2 D2 2 A1 B2 C2 D2 3 A3 B2 C2 D2 4 A2 B1 C2 D2 5 A2 B3 C2 D2 6 A2 B2 C1 D2 7 A2 B2 C3 D2 8 A2 B2 C2 D1 9 A2 B2 C2 D3 4 factors, 3 levels each: 1+k(n-1) = 1+4(3-1) = 9 trials MITSloan
  20. 20. Experiment Design: Orthogonal Array Consider k factors, n levels each. Test all levels of each factor in a balanced way. The number of experiments is n(k-1). This is the smallest balanced experiment design. BUT main effects and interactions are confounded. MITSloan
  21. 21. Experiment Design: Orthogonal Array Expt # Param A Param B Param C Param D 1 A1 B1 C1 D1 2 A1 B2 C2 D2 3 A1 B3 C3 D3 4 A2 B1 C2 D3 5 A2 B2 C3 D1 6 A2 B3 C1 D2 7 A3 B1 C3 D2 8 A3 B2 C1 D3 9 A3 B3 C2 D1 4 factors, 3 levels each: n(k-1) = 3(4-1) = 9 trials MITSloan
  22. 22. Using Inner and Outer Arrays Induce the same noise factor levels for each combination of controls in a balanced manner 3 factors, 2 levels each: 4 factors, 3 levels each: L4 outer array for noise L9 inner array for controls E1 E1 E2 E2 F1 F2 F1 F2 G2 G1 G2 G1 A1 B1 C1 D1 A1 B2 C2 D2 inner x outer = A1 B3 C3 D3 A2 B1 C2 D3 L9 x L4 = A2 B2 C3 D1 A2 B3 C1 D2 A3 B1 C3 D2 36 trials A3 B2 C1 D3 A3 B3 C2 D1 MITSloan
  23. 23. Step 4: Run the Experiment Step 4: Conduct the experiment. Vary the input and noise parameters Record the output response Compute the objective function MITSloan
  24. 24. Paper Airplane Experiment Expt # Weight Winglet Nose Wing Trials Mean Std Dev S/N 1 A1 B1 C1 D1 2 A1 B2 C2 D2 3 A1 B3 C3 D3 4 A2 B1 C2 D3 5 A2 B2 C3 D1 6 A2 B3 C1 D2 7 A3 B1 C3 D2 8 A3 B2 C1 D3 9 A3 B3 C2 D1 MITSloan
  25. 25. Step 5: Conduct Analysis Step 5: Perform analysis of means. Compute the mean value of the objective function for each parameter setting. Identify which parameters reduce the effects of noise and which ones can be used to scale the response. (2-Step Optimization) MITSloan
  26. 26. Parameter Design Procedure Step 6: Select Setpoints Parameters can effect Average and Variation (tune S/N) Variation only (tune noise) Average only (tune performance) Neither (reduce costs) MITSloan
  27. 27. Parameter Design Procedure Step 6: Advanced Use Conduct confirming experiments. Set scaling parameters to tune response. Iterate to find optimal point. Use higher fractions to find interaction effects. Test additional control and noise factors. MITSloan
  28. 28. Confounding Interactions Generally the main effects dominate the response. BUT sometimes interactions are important. This is generally the case when the confirming trial fails. To explore interactions, use a fractional factorial experiment design. MITSloan
  29. 29. Confounding Interactions S/N A1 A2 A3 B1 B2 B3 MITSloan
  30. 30. Key Concepts of Robust Design Variation causes quality loss Parameter Design to reduce Variation Matrix experiments (orthogonal arrays) Two-step optimization Inducing noise (outer array or repetition) Data analysis and prediction Interactions and confirmation MITSloan

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