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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