om

2,486 views

Published on

Published in: Technology
0 Comments
2 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
2,486
On SlideShare
0
From Embeds
0
Number of Embeds
45
Actions
Shares
0
Downloads
0
Comments
0
Likes
2
Embeds 0
No embeds

No notes for slide

om

  1. 1. TAGUCHI TECHNIQUES AND APPLICATIONS
  2. 2. CONCEPTS OF TAGUCHI PHILOSOPHY <ul><li>Quality should be designed into the product and not inspected into it </li></ul><ul><li>Quality is best achieved by minimizing the deviation from a target. The product design should be such that it is immune to uncontrollable factors </li></ul><ul><li>The cost of quality should be measured as a function of deviation from the standard </li></ul>
  3. 3. TAGUCHI TECHNIQUES <ul><li>Off-line QA Techniques </li></ul><ul><li>Ensures Quality of design of process and products </li></ul><ul><li>Robust design is the procedure used </li></ul><ul><li>Makes use of “Orthogonal Arrays” for designing experiments </li></ul>
  4. 4. RESOURCE DIFFERENCES OF TRADITIONAL AND TAGUCHI EXPERIMENTS 27 1,594,323 3 13 9 81 3 4 16 32,768 2 15 8 128 2 7 4 8 2 3 NO OF EXPERIMENTS FULL FACTORIAL TAGUCHI NO OF LEVELS NO OF FACTORS
  5. 5. STEPS IN EXPERIMENTATION <ul><li>State the problem </li></ul><ul><li>Determine the objective </li></ul><ul><li>Determine the measurement method </li></ul><ul><li>Identify the factors influencing the performance characteristic </li></ul><ul><li>Separate the factors into control and noise factors </li></ul><ul><li>Determine the number of levels and values for all factors </li></ul><ul><li>Identify control factors that may interact </li></ul>
  6. 6. STEPS CONTD… <ul><li>Select the orthogonal arrays and the required linear graph </li></ul><ul><li>Assign factors and interactions to columns </li></ul><ul><li>Conduct the experiment </li></ul><ul><li>Analyze the data </li></ul><ul><li>Interpret the results </li></ul><ul><li>Select optimum levels of significant factors </li></ul><ul><li>Predict expected results </li></ul><ul><li>Run a conformation experiment </li></ul>
  7. 7. NOMENCLATURE OF ARRAYS L - Latin square a - no of rows b - no of levels c - no of columns (Factors) Degrees of freedom- a-1 L a (b c ) *Interactions cannot be studied **Can study 1 interaction between the 2-level factor and one 3-level factor - - - L 32 (2 31 ) - - L 16 (2 15 ) - L 81 (3 40 ) **L 12 (2 11 ) L 36 (2 11 ,3 12 ) or L 36 (2 3 ,3 13 ) L 64 (4 21 ) L 27 (3 13 ) L 8 (2 7 ) *L 18 (2 1 ,3 7 ) L 15 (4 5 ) L 9 (3 4 ) L 4 (2 3) Mixed -level 4 -level series 3 -level series 2-level series
  8. 8. L 8 (2 7 ) ORTHOGONAL ARRAY NOTE : <ul><li>Eight experimental runs and Balanced number of 1s and 2s </li></ul><ul><li>Any pair of columns have only four combinations (1,1); (1,2); (2,1); (2,2) </li></ul><ul><li>If the same number of combinations occur, then the columns are orthogonal </li></ul><ul><li>In the L 8 , any pair of columns is orthogonal </li></ul><ul><li>L 8 can be applied to 7 or less factors </li></ul>COLUMNS 2 1 1 2 1 2 2 8 1 2 2 1 1 2 2 7 1 2 1 2 2 1 2 6 2 1 2 1 2 1 2 5 1 1 2 2 2 2 1 4 2 2 1 1 2 2 1 3 2 2 2 2 1 1 1 2 1 1 1 1 1 1 1 1 7 6 5 4 3 2 1 EXPT
  9. 9. LOCATION OF INTERACTIONS <ul><li>LINEAR GRAPHS </li></ul><ul><ul><li>Taguchi devised this technique </li></ul></ul><ul><ul><li>Graphic representation of Interaction information in a matrix experiment </li></ul></ul><ul><ul><li>Helps to assign main factors and interactions to the different columns of an OA </li></ul></ul><ul><li>TRIANGULAR TABLES </li></ul><ul><ul><li>Each OA has a set of linear graphs and a triangular table associated with it </li></ul></ul>
  10. 10. EXAMPLE: LINEAR GRAPH OF THE L 8 OA A B C 1 4 2 5 6 3 Main factors A,B,C, and D are assigned to columns 1,2,4 and 7 Interactions AB, AC and BC should be assigned to columns 3, 5 and 6
  11. 11. TRIANGULAR TABLE These tables give all the possible interacting column relationships that exist for a given OA L 8 TRIANGULAR TABLE 1 6 2 3 5 3 2 1 4 4 5 6 7 3 5 4 7 6 1 2 6 7 4 5 2 3 1 7 6 5 4 3 2 Column no.
  12. 12. SELECTION OF OA <ul><li>Determine the df. Required </li></ul><ul><li>Note the levels of each factor and decide the type of OA (2-level or 3-level) </li></ul><ul><li>Select the particular OA which satisfies the following conditions </li></ul><ul><ul><li>df(OA) >= df required for the experiment </li></ul></ul><ul><ul><li>Interactions possible (OA) > the interactions required </li></ul></ul>
  13. 13. <ul><li>Draw the required graph </li></ul><ul><li>Compare with the standard linear graph of the chosen OA </li></ul><ul><li>Superimpose the required LG on the standard LG to find the location of factor columns and interaction columns </li></ul><ul><li>The remaining columns (if any) are left out </li></ul><ul><li>Draw the layout indicating the assignment of factors and interactions </li></ul><ul><li>The rows will indicate the no of experiments (trials) to be executed </li></ul>
  14. 14. COMPUTATION OF DEGREES OF FREEDOM <ul><li>DEGREES OF FREEDOM </li></ul><ul><li>Maximum no of independent pair wise comparison </li></ul><ul><li>Df. for each factor with ‘a’ levels = a-1 </li></ul><ul><li>Df. of an interaction = product of df of interacting factors </li></ul><ul><li>for factor ‘A’ with ‘a’ levels and factor ‘B’ with ‘b’ levels </li></ul><ul><li>Df. for an experimental design = sum of df’s of factors and interaction </li></ul><ul><li>Df. available in an OA = no of trials-1 </li></ul><ul><li>for a L 8 OA df = 8-1 = 7 </li></ul>
  15. 15. SELECTION OF OA-AN EXAMPLE An experiment has to be conducted with 4 factors (A,B,C and D) each of two levels. Also, the interactions AB, AC and AD are to be satisfied <ul><li>DEGREES OF FREEDOM </li></ul>TOTAL Df. = 7 (2-1) (2-1) = 1 AD (2-1) (2-1) = 1 AC (2-1) (2-1) = 1 AB 2-1 = 1 2 D 2-1 = 1 2 C 2-1 = 1 2 B 2-1 = 1 2 A DF. LEVELS FACTOR
  16. 16. <ul><li>Levels of factors – All at 2-levels </li></ul><ul><li>therefore choose 2-level OA </li></ul><ul><li>Selection of required OA </li></ul><ul><ul><li>The OA which satisfies the required df is OA, L 8 </li></ul></ul><ul><ul><li>Interactions required = 3 </li></ul></ul><ul><ul><li>Interactions possible in L 8 = 3 </li></ul></ul><ul><ul><li>Therefore the best would be L 8 </li></ul></ul><ul><li>Required linear graph </li></ul>A B C D
  17. 17. 5. Standard LGS for L 8 OA <ul><li>Superimpose the required LG with the standard LG </li></ul><ul><li>Linear Graph (B) is similar to the required LG </li></ul>1 3 2 4 5 6 (A) 7 1 4 2 3 5 6 (B) A 1 B2 C4 D7 3 AB AC 5 6 AD
  18. 18. <ul><li>DESIGN LAYOUT </li></ul>For conducting the experiment test sheet may be prepared without the interacting columns Interactions are dependent on the main factors and hence cannot be controlled during experimentation X X 2 1 1 2 1 2 2 8 X X 1 2 2 1 1 2 2 7 X X 1 2 1 2 2 1 2 6 X X 2 1 2 1 2 1 2 5 X X 1 1 2 2 2 2 1 4 X X 2 2 1 1 2 2 1 3 X X 2 2 2 2 1 1 1 2 X X 1 1 1 1 1 1 1 1 7 6 5 4 3 2 1 D AD AC C AB B A RESPECTIVE Y FACTORS TRIAL NO.
  19. 19. CONDUCTING THE EXPERIMENT <ul><li>Test sheet </li></ul><ul><li>Randomization </li></ul><ul><ul><li>The order of performing the tests should be random </li></ul></ul><ul><ul><li>Randomization protects the experiment from any unknown and uncontrolled factors that may vary during the entire experiment and which influence the result </li></ul></ul><ul><ul><li>Two methods of randomization </li></ul></ul><ul><ul><ul><li>COMPLETE RANDOMIZATION </li></ul></ul></ul><ul><ul><ul><li>SIMPLE REPETITION </li></ul></ul></ul>
  20. 20. <ul><li>COMPLETE RANDOMIZATION </li></ul><ul><li>Trials are selected randomly </li></ul><ul><li>For repetition, each trial is selected randomly in each repetition </li></ul><ul><li>Used when change of test setup is inexpensive and easy </li></ul><ul><li>SIMPLE REPETITION </li></ul><ul><li>Trials are selected randomly and is repeated for required nos. </li></ul><ul><li>Used when test setup changes are costly </li></ul>
  21. 21. CONCLUSIONS <ul><li>Vary one factor at a time experiment, do not consider interactions </li></ul><ul><li>Statistically designed experiments is the only SOUND and SEIENTIFIC approach available </li></ul><ul><li>OAs enable the designer to run a minimum no of experiments and obtain maximum information </li></ul><ul><li>Taguchi methods leads to Robust Design </li></ul><ul><li>Taguchi’s Robust Design makes use of OAs and additive models rather than full-factorial designs </li></ul>

×