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### Transcript

• 1. TAGUCHI TECHNIQUES AND APPLICATIONS
• 2. CONCEPTS OF TAGUCHI PHILOSOPHY
• Quality should be designed into the product and not inspected into it
• Quality is best achieved by minimizing the deviation from a target. The product design should be such that it is immune to uncontrollable factors
• The cost of quality should be measured as a function of deviation from the standard
• 3. TAGUCHI TECHNIQUES
• Off-line QA Techniques
• Ensures Quality of design of process and products
• Robust design is the procedure used
• Makes use of “Orthogonal Arrays” for designing experiments
• 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. STEPS IN EXPERIMENTATION
• State the problem
• Determine the objective
• Determine the measurement method
• Identify the factors influencing the performance characteristic
• Separate the factors into control and noise factors
• Determine the number of levels and values for all factors
• Identify control factors that may interact
• 6. STEPS CONTD…
• Select the orthogonal arrays and the required linear graph
• Assign factors and interactions to columns
• Conduct the experiment
• Analyze the data
• Interpret the results
• Select optimum levels of significant factors
• Predict expected results
• Run a conformation experiment
• 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. L 8 (2 7 ) ORTHOGONAL ARRAY NOTE :
• Eight experimental runs and Balanced number of 1s and 2s
• Any pair of columns have only four combinations (1,1); (1,2); (2,1); (2,2)
• If the same number of combinations occur, then the columns are orthogonal
• In the L 8 , any pair of columns is orthogonal
• L 8 can be applied to 7 or less factors
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. LOCATION OF INTERACTIONS
• LINEAR GRAPHS
• Taguchi devised this technique
• Graphic representation of Interaction information in a matrix experiment
• Helps to assign main factors and interactions to the different columns of an OA
• TRIANGULAR TABLES
• Each OA has a set of linear graphs and a triangular table associated with it
• 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. 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. SELECTION OF OA
• Determine the df. Required
• Note the levels of each factor and decide the type of OA (2-level or 3-level)
• Select the particular OA which satisfies the following conditions
• df(OA) >= df required for the experiment
• Interactions possible (OA) > the interactions required
• 13.
• Draw the required graph
• Compare with the standard linear graph of the chosen OA
• Superimpose the required LG on the standard LG to find the location of factor columns and interaction columns
• The remaining columns (if any) are left out
• Draw the layout indicating the assignment of factors and interactions
• The rows will indicate the no of experiments (trials) to be executed
• 14. COMPUTATION OF DEGREES OF FREEDOM
• DEGREES OF FREEDOM
• Maximum no of independent pair wise comparison
• Df. for each factor with ‘a’ levels = a-1
• Df. of an interaction = product of df of interacting factors
• for factor ‘A’ with ‘a’ levels and factor ‘B’ with ‘b’ levels
• Df. for an experimental design = sum of df’s of factors and interaction
• Df. available in an OA = no of trials-1
• for a L 8 OA df = 8-1 = 7
• 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
• DEGREES OF FREEDOM
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.
• Levels of factors – All at 2-levels
• therefore choose 2-level OA
• Selection of required OA
• The OA which satisfies the required df is OA, L 8
• Interactions required = 3
• Interactions possible in L 8 = 3
• Therefore the best would be L 8
• Required linear graph
A B C D
• 17. 5. Standard LGS for L 8 OA
• Superimpose the required LG with the standard LG
• Linear Graph (B) is similar to the required LG
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.
• DESIGN LAYOUT
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. CONDUCTING THE EXPERIMENT
• Test sheet
• Randomization
• The order of performing the tests should be random
• Randomization protects the experiment from any unknown and uncontrolled factors that may vary during the entire experiment and which influence the result
• Two methods of randomization
• COMPLETE RANDOMIZATION
• SIMPLE REPETITION
• 20.
• COMPLETE RANDOMIZATION
• Trials are selected randomly
• For repetition, each trial is selected randomly in each repetition
• Used when change of test setup is inexpensive and easy
• SIMPLE REPETITION
• Trials are selected randomly and is repeated for required nos.
• Used when test setup changes are costly
• 21. CONCLUSIONS
• Vary one factor at a time experiment, do not consider interactions
• Statistically designed experiments is the only SOUND and SEIENTIFIC approach available
• OAs enable the designer to run a minimum no of experiments and obtain maximum information
• Taguchi methods leads to Robust Design
• Taguchi’s Robust Design makes use of OAs and additive models rather than full-factorial designs