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Introduction to Taguchi Methods By Ramon Balisnomo September 5, 2008
Who is Dr. Genichi Taguchi? ,[object Object],[object Object],[object Object],[object Object]
Robust Design A  B  C Control Factors Productor Process LSL USL defects defects Input Output
Robust Design Noise factor(s) A  B  C Control Factors Product or Process LSL USL defects defects Input Output
Robust Design Noise factor(s) A  B  C Control Factors Product or Process LSL USL Input Output
Taguchi Experimental Design Versus Traditional Design of Experiments ,[object Object],[object Object],[object Object],[object Object]
Three-step Procedure for Experimental Design ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Degree-of-freedom (DOF) Rules ,[object Object],[object Object],[object Object]
Find the Total Degree of Freedom ,[object Object],[object Object],[object Object],Factors Degree of freedom Overall mean 1 A 2-1=1 B,C,D,E,F,G 6 x (3-1)=12 AB (2-1)x(3-1)=2 Total DOF 16
Find the Total Degree of Freedom ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Significant Interactio ns DOF = ___________ Factors Degree of freedom Overall mean 1 3-level factors: A,B,C,D,E,F 6 x (3-1)=12 Interactions: AB, AC, BC 3 x (3-1)x(3-1)=12 Total DOF 1 + 12 + 12 = 25
Select a Taguchi Orthogonal Arrays Based on DOF Orthogonal Array No. Runs Max. Factors Max. of columns at these levels 2-level 3-level 4-level 5-level L4 4 3 3 Ā  Ā  Ā  L8 8 7 7 Ā  Ā  Ā  L9 9 4 Ā  4 Ā  Ā  L12 12 11 11 Ā  Ā  Ā  L16 16 15 15 Ā  Ā  Ā  L'16 16 5 Ā  Ā  5 Ā  L18 18 8 1 7 Ā  Ā  L25 25 6 Ā  Ā  Ā  6 L27 27 13 Ā  13 Ā  Ā  L32 32 31 31 Ā  Ā  Ā  L'32 32 10 1 Ā  9 Ā  L36 36 23 11 12 Ā  Ā  L'36 36 16 3 13 Ā  Ā  L50 50 12 1 Ā  Ā  11 L54 54 26 1 25 Ā  Ā  L64 64 63 63 Ā  Ā  Ā  L'64 64 21 Ā  Ā  21 Ā  L81 81 40 Ā  40 Ā  Ā 
Assign Factors to Appropriate Columns ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Linear Graph for L16 6 7 1 13 12 3 10 9 8 2 4 11 5 15 14 A C D B F E H G I
Assign Factors to Appropriate Columns ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Linear Graph for L27 1 13 9 3,4 8,11 6,7 5 2 10 12 A D B C E F
Robust Parameter Design ,[object Object],[object Object],[object Object]
What is the Signal-to-Noise Ratio? = mean or average = standard deviation or natural variation = signal to noise ratio S/N 1   >   S/N 2  >  S/N 3
What is the Signal-to-Noise Ratio? Input Variable X Mean Signal-to-Noise (S/N) Ratio ā€“ Output Variable
Pre-experimental Planning: ,[object Object],[object Object],[object Object]
Parameter Design for Nominal-the-Best Characteristics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
In the rubber industry an extruder is used to mold the raw rubber compound into the desired shapes.  Variation in output from the extruder directly affects the dimensions of the weather strip as the flow of rubber increases or decreases. Find the right settings for a consistent rubber extruder output (number of units produced per minute).
Parameter Diagram ,[object Object],[object Object],[object Object],Control Factors Level 1 Level 2 A Same Different B Same Different C Cool Hot D Current Level Additional Material E Low High F Low High G Normal Range Higher Range
Parameter Diagram Noise factor: 10 different combinations of temperature & humidity (e.g. 70 degrees @ 15% humidity) A  B  C  D  E  F  G Control Factors: ,[object Object],[object Object],[object Object],Pieces Per Minute Raw rubber compound Production Rate
[object Object],Stat  ļƒØ DOE  ļƒØ Taguchi  ļƒØ Create Taguchi Designā€¦
[object Object],This is a 2-Level 7-Factor experiment (2 7 ). Control Factors Level 1 Level 2 A Same Different B Same Different C Cool Hot D Current Level Add. Material E Low High F Low High G Normal Range Higher Range
[object Object],DOF = 1 + (  #factors  x (  #levels  -1)) = 1 + ( 7 x (2-1)) =  8 Calculate the DOF for a 3-Level 4-Factor experiment:
[object Object],Choose the L8 Taguchi Design because number of runs in orthogonal array ā‰„ DOF
[object Object],Fill-in the dialog box as shown: Then click OK until you see the worksheet.
[object Object],This  box  is called your  Inner Array
The Outer Array are Controlled Noise Variables  Response Variable Temp. & Humidity Y1 50 Ā° @  15% Y2 50 Ā° @  50% Y3 60 Ā° @  15% Y4 60 Ā° @  50% Y5 70 Ā° @  15% Y6 70 Ā° @  50% Y7 80 Ā° @  15% Y8 80 Ā° @  50% Y9 90 Ā° @  15% Y10 90 Ā° @  50%
[object Object],Prepare the  Outer Array  which corresponds to the Noise Factor (enter Y1, Y2, Y3,ā€¦ Y10).  We will be running 10 different noise levels. The Outer Array is where you will enter the results of the experiment. To see the results, open the Excel file named:  This  box  is called your  Outer Array
5.  Perform the experiment. Open & paste the results from the Excel file named: Inner Array Outer Array
[object Object],Stat  ļƒØ DOE  ļƒØ Taguchi  ļƒØ Analyze Taguchi Designā€¦
[object Object]
[object Object]
[object Object]
[object Object]
[object Object],This is probably the most  important option youā€™ll choose
[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object]
[object Object]
[object Object]
[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
[object Object],Stat  ļƒØ DOE  ļƒØ Taguchi  ļƒØ Predict Taguchi Resultsā€¦
[object Object]
[object Object]
[object Object]
[object Object]
Class Exercise: Seal Strength You are evaluating the factors that affect the seal strength of plastic bags used to ship your products.  Youā€™ve identified three controllable factors ( Temperature ,  Pressure , and  Thickness ) and two noise conditions ( Noise1  and  Noise2 ) that may affect seal strength.  Open the Minitab Project: You want to ensure that seal strength meets specifications.  If seal strength is too weak, it may break, contaminating the product.  If seal strength is too strong, customers may have difficulty opening the bag.  The specification is 18 Ā± 2 lbs.
Questions for Class Exercise: Seal Strength ,[object Object],[object Object],[object Object]
Which one of the three control factors influence the robustness of the product (S/N ratio) the most?
What are the optimal settings for the most consistent seal strength? Temperature = 60 Pressure = 36 Thickness = 1.25
What do you predict are the values for S/N ratio, mean, standard deviation at the optimal settings?
Appendix: Taguchiā€™s Orthogonal Arrays L4, L8, L9, L12, L16, & L18
Introduction To Taguchi Method
Introduction To Taguchi Method
Introduction To Taguchi Method
Introduction To Taguchi Method
Introduction To Taguchi Method

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Introduction To Taguchi Method

  • 1. Introduction to Taguchi Methods By Ramon Balisnomo September 5, 2008
  • 2.
  • 3. Robust Design A B C Control Factors Productor Process LSL USL defects defects Input Output
  • 4. Robust Design Noise factor(s) A B C Control Factors Product or Process LSL USL defects defects Input Output
  • 5. Robust Design Noise factor(s) A B C Control Factors Product or Process LSL USL Input Output
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11. Select a Taguchi Orthogonal Arrays Based on DOF Orthogonal Array No. Runs Max. Factors Max. of columns at these levels 2-level 3-level 4-level 5-level L4 4 3 3 Ā  Ā  Ā  L8 8 7 7 Ā  Ā  Ā  L9 9 4 Ā  4 Ā  Ā  L12 12 11 11 Ā  Ā  Ā  L16 16 15 15 Ā  Ā  Ā  L'16 16 5 Ā  Ā  5 Ā  L18 18 8 1 7 Ā  Ā  L25 25 6 Ā  Ā  Ā  6 L27 27 13 Ā  13 Ā  Ā  L32 32 31 31 Ā  Ā  Ā  L'32 32 10 1 Ā  9 Ā  L36 36 23 11 12 Ā  Ā  L'36 36 16 3 13 Ā  Ā  L50 50 12 1 Ā  Ā  11 L54 54 26 1 25 Ā  Ā  L64 64 63 63 Ā  Ā  Ā  L'64 64 21 Ā  Ā  21 Ā  L81 81 40 Ā  40 Ā  Ā 
  • 12.
  • 13.
  • 14.
  • 15. What is the Signal-to-Noise Ratio? = mean or average = standard deviation or natural variation = signal to noise ratio S/N 1 > S/N 2 > S/N 3
  • 16. What is the Signal-to-Noise Ratio? Input Variable X Mean Signal-to-Noise (S/N) Ratio ā€“ Output Variable
  • 17.
  • 18.
  • 19. In the rubber industry an extruder is used to mold the raw rubber compound into the desired shapes. Variation in output from the extruder directly affects the dimensions of the weather strip as the flow of rubber increases or decreases. Find the right settings for a consistent rubber extruder output (number of units produced per minute).
  • 20.
  • 21.
  • 22.
  • 23.
  • 24.
  • 25.
  • 26.
  • 27.
  • 28. The Outer Array are Controlled Noise Variables Response Variable Temp. & Humidity Y1 50 Ā° @ 15% Y2 50 Ā° @ 50% Y3 60 Ā° @ 15% Y4 60 Ā° @ 50% Y5 70 Ā° @ 15% Y6 70 Ā° @ 50% Y7 80 Ā° @ 15% Y8 80 Ā° @ 50% Y9 90 Ā° @ 15% Y10 90 Ā° @ 50%
  • 29.
  • 30. 5. Perform the experiment. Open & paste the results from the Excel file named: Inner Array Outer Array
  • 31.
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • 40.
  • 41.
  • 42.
  • 43.
  • 44.
  • 45.
  • 46.
  • 47.
  • 48. Class Exercise: Seal Strength You are evaluating the factors that affect the seal strength of plastic bags used to ship your products. Youā€™ve identified three controllable factors ( Temperature , Pressure , and Thickness ) and two noise conditions ( Noise1 and Noise2 ) that may affect seal strength. Open the Minitab Project: You want to ensure that seal strength meets specifications. If seal strength is too weak, it may break, contaminating the product. If seal strength is too strong, customers may have difficulty opening the bag. The specification is 18 Ā± 2 lbs.
  • 49.
  • 50. Which one of the three control factors influence the robustness of the product (S/N ratio) the most?
  • 51. What are the optimal settings for the most consistent seal strength? Temperature = 60 Pressure = 36 Thickness = 1.25
  • 52. What do you predict are the values for S/N ratio, mean, standard deviation at the optimal settings?
  • 53. Appendix: Taguchiā€™s Orthogonal Arrays L4, L8, L9, L12, L16, & L18