Introduction To Taguchi Method

Introduction to Taguchi Methods By Ramon Balisnomo September 5, 2008

Who is Dr. Genichi Taguchi? Born in 1924 in the town of Tokamachi, Japan Studied Textile Engineering and earned his doctorate from Kyushu University (Japan) in 1962 Developed much of his thinking in isolation from the school of Ronald Fisher (Factorial DOE), only coming into direct contact in 1954. Pioneered his method with Dr. Yuin Wu in 1966 while consulting with Bell Labs

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 Only the main effects and two factor interactions are considered. Higher-order interactions are assumed to be non-existent. Experimenters are asked to identify which interactions might be significant before conducting the experiment, through their knowledge of the subject matter. Taguchi’s orthogonal arrays are not randomly generated; they are based on judgmental sampling. Traditional DOE’s treat noise as a nuisance (blocking), but Taguchi makes it the focal point of his analysis.

Three-step Procedure for Experimental Design Find the total degree of freedom (DOF). Select a standard orthogonal array using the following two rules: The number of runs in the orthogonal design  total DOF The selected orthogonal array should be able to accommodate the factor level combinations in the experiment Assign factors to appropriate columns using the following rules: Assign interactions according to the linear graph and interaction table Keep some columns empty if not all columns can be assigned

Degree-of-freedom (DOF) Rules The overall mean always uses 1 degree of freedom. For each factor, A , B ,…; if the number of levels are n A , n B ,…, for each factor, the degree of freedom = number of levels – 1 ; for example, the degree of freedom for factor A = n A – 1 and B = n B – 1 . For any two factor interaction, for example, AB interaction, the degree of freedom = ( n A -1 )( n B -1 )

Find the Total Degree of Freedom Example: In an experiment, there is 1 two-level factor, A, and 6 three-level factors, B,C,D,E,F,G, and 1 two-factor interaction, AB. What is the total degree of freedom (DOF)? Answer: 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 A B C D E F 6 Three-Level Factors AB AC BC 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 L8 8 7 7 L9 9 4 4 L12 12 11 11 L16 16 15 15 L'16 16 5 5 L18 18 8 1 7 L25 25 6 6 L27 27 13 13 L32 32 31 31 L'32 32 10 1 9 L36 36 23 11 12 L'36 36 16 3 13 L50 50 12 1 11 L54 54 26 1 25 L64 64 63 63 L'64 64 21 21 L81 81 40 40

Assign Factors to Appropriate Columns 9 Two-Level Factors A B C D E F G H I Significant Interactions AB AC AD AF 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 6 Three-Level Factors A B C D E F Significant Interactions AB AC BC 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 Primary Goal : Find factor settings (inputs, X) that minimize response variation (outputs, Y), while adjusting or keeping the process on target. Adjust design parameters to maximize the S/N ratio A product designed with this goal will deliver more consistent performance regardless of the environment in which it is used.

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 – Output Variable

Pre-experimental Planning: You need to decide what are the control factors you can optimize. These go into the INNER ARRAY (I/A). Noise factors go in the OUTER ARRAY (O/A). While you cannot control noise factors during product use, you need to be able to control noise factors for experimental purposes. In Taguchi designs, responses (Y’s) are measured at selected combinations of the control factor levels. The experiment is carried out by running the complete set of noise factor settings at each combination of control factor settings (at each run).

Parameter Design for Nominal-the-Best Characteristics Select an appropriate output quality characteristic to be optimized. Select control factors and their levels, identifying their possible interactions Select noise factors and their levels; if there are many noise factors use compound noise factors to form two or three compounded noise combinations Select adequate inner and outer arrays; assign control factors to the inner array, and noise factors to the outer array Perform the experiment Perform statistical analysis and the two-step optimization procedure: Select control factors levels to maximize S/N Select mean adjusting factor(s) to target value Predict optimal output performance level based on an optimal control factor level combination, and conduct a confirmation experiment to verify the result.

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 Select an appropriate output quality characteristic to be optimized. Select control factors and their levels, identifying their possible interactions Select noise factors and their levels 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: Select an appropriate output quality characteristic to be optimized. Select control factors and their levels, identifying their possible interactions Select noise factors and their levels Pieces Per Minute Raw rubber compound Production Rate

Select adequate inner and outer arrays; assign control factors to the inner array, and noise factors to the outer array. Stat  DOE  Taguchi  Create Taguchi Design…

Select adequate inner and outer arrays; assign control factors to the inner array, and noise factors to the outer array. 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

Select adequate inner and outer arrays; assign control factors to the inner array, and noise factors to the outer array. DOF = 1 + ( #factors x ( #levels -1)) = 1 + ( 7 x (2-1)) = 8 Calculate the DOF for a 3-Level 4-Factor experiment:

Select adequate inner and outer arrays; assign control factors to the inner array, and noise factors to the outer array. Choose the L8 Taguchi Design because number of runs in orthogonal array ≥ DOF

Select adequate inner and outer arrays; assign control factors to the inner array, and noise factors to the outer array. Fill-in the dialog box as shown: Then click OK until you see the worksheet.

Select adequate inner and outer arrays; assign control factors to the inner array, and noise factors to the outer array. This box is called your Inner Array

The Outer Array are Controlled Noise Variables Response Variable Temp. & Humidity Y1 50 ° @ 15% Y2 50 ° @ 50% Y3 60 ° @ 15% Y4 60 ° @ 50% Y5 70 ° @ 15% Y6 70 ° @ 50% Y7 80 ° @ 15% Y8 80 ° @ 50% Y9 90 ° @ 15% Y10 90 ° @ 50%

Select adequate inner and outer arrays; assign control factors to the inner array, and noise factors to the outer array. Prepare the Outer Array which corresponds to the Noise Factor (enter Y1, Y2, Y3,… 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

Perform statistical analysis and the two-step optimization procedure: (a) Select control factors levels to maximize S/N; (b) Select mean adjusting factor(s) to target value Stat  DOE  Taguchi  Analyze Taguchi Design…

Perform statistical analysis and the two-step optimization procedure: (a) Select control factors levels to maximize S/N; (b) Select mean adjusting factor(s) to target value

Perform statistical analysis and the two-step optimization procedure: (a) Select control factors levels to maximize S/N; (b) Select mean adjusting factor(s) to target value This is probably the most important option you’ll choose

Perform statistical analysis and the two-step optimization procedure: (a) Select control factors levels to maximize S/N; (b) Select mean adjusting factor(s) to target value Questions: Which control factor has the most impact on the SN ratio? Which control factor has the least impact on the SN ratio? Hint: notice the rankings in the bottom row

Perform statistical analysis and the two-step optimization procedure: (a) Select control factors levels to maximize S/N; (b) Select mean adjusting factor(s) to target value Factor G has very little influence on the S/N ratio (see Figure 1), but it has the biggest impact changing the mean production rate (see Figure 2). Because G has an insignificant effect on S/N but a very significant effect on the output itself, it is the perfect choice for the mean adjust factor. The main effects chart (Figure 2) indicates that shifting G to a higher level will increase production output but not affect S/N, and a higher production level will certainly increase the throughput. The optimal setting for G should be 2.

Predict optimal output performance level based on an optimal control factor level combination, and conduct a confirmation experiment to verify the result. Stat  DOE  Taguchi  Predict Taguchi Results…

Predict optimal output performance level based on an optimal control factor level combination, and conduct a confirmation experiment to verify the result.

Class Exercise: Seal Strength You are evaluating the factors that affect the seal strength of plastic bags used to ship your products. You’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 ± 2 lbs.

Questions for Class Exercise: Seal Strength 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? What do you predict are the values for S/N ratio, mean, standard deviation at the optimal settings?

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: Taguchi’s Orthogonal Arrays L4, L8, L9, L12, L16, & L18

Introduction To Taguchi Method

Introduction To Taguchi Method

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Introduction To Taguchi Method