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
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
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.
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
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.
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
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