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    om om Presentation Transcript

    • TAGUCHI TECHNIQUES AND APPLICATIONS
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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.
    • 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
      • 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
    • 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
    • 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
      • 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
    • 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
      • 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.
    • 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
      • 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
    • 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