ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAG
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2^3 Full Factorial Array (Similar to the Taguchi L8 Orthogonal Array)
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CP5070 DOE Tutorial Example 1 on dissolution of lactose
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2 levels of 3 factors with up to 8 reps = (2^3) x 8 = 64 or less data points; Change only yellow boxes
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Factor Assignment
Response Table (Data)
Quick Calculations
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Main Effects
Interactions (i.e. AxB).
Replicates used to normalize the data
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Run#
Run Order
ABC
D=AB
E=AC
F=BC
G=ABC
R1R2R3R4R5R6R7R8Ave.Std.Dev.
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1 1---+++-3.13.1 -
Each run was replicated 8 times (R1, R2, etc)
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2 3+----++3.83.8 -
The response variable is dissolution of lactose (minutes)
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3 2-+--+-+2.82.8 -
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4 6++-+---1.81.8 -
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5 4--++--+0.70.7 -
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6 5+-+-+--1.01.0 -
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7 8-++--+-0.80.8 -
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8 7+++++++0.30.3 -
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Reference Key to Factor Selection
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Factor A = Your factor:
Diameter; B =Microwaving Time; C =Power
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Factor D = Your factor:
Diameter x microwaving Time; E =Diameter x Power; F =Microwaving time x Power; G =AxBxC
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Confounding Column Information (for alternative factor assignment considerations)
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The Taguchi L8 array is very similar to this arrray but has slightly different columns that confound with each other. This
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array does not have confounding columns. Using the L8 array requires an uderstanding of column confounding.
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Calculating the Significance of Main Effects (Solving for Means)
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Factor A
Runs Where A is + :
4 +2 +1 +0 =7 / 4 = Ave=1.6925+ (HIGH)
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Runs Where A is - :
3 +3 +1 +1 =7 / 4 = Ave=1.84- (LOW)
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Total Effect = Difference =
-0.15
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Factor B
Runs Where B is + :
3 +2 +1 +0 =6 / 4 = Ave=1.3925+ (HIGH)
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Runs Where B is - :
3 +4 +1 +1 =9 / 4 = Ave=2.14- (LOW)
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Total Effect = Difference =
-0.75
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Factor C
Runs Where C is + :
1 +1 +1 +0 =3 / 4 = Ave=0.69+ (HIGH)
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Runs Where C is - :
3 +4 +3 +2 =11 / 4 = Ave=2.84- (LOW)
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Total Effect = Difference =
-2.15
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Calc. the Sig. of 2nd Order Interaction Effects or Aliased Effects (Solving for Means)
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Factor D (AB)
Runs Where D is + :
3 +2 +1 +0 =6 / 4 = Ave=1.4825+ (HIGH)
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Runs Where D is - :
4 +3 +1 +1 =8 / 4 = Ave=2.05- (LOW)
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Total Effect = Difference =
-0.57
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Factor E (AC)
Runs Where E is + :
3 +3 +1 +0 =7 / 4 = Ave=1.785+ (HIGH)
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Runs Where E is - :
4 +2 +1 +1 =7 / 4 = Ave=1.75- (LOW)
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Total Effect = Difference =
0.04
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Factor F (BC)
Runs Where F is + :
3 +4 +1 +0 =8 / 4 = Ave=1.985+ (HIGH)
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Runs Where F is - :
3 +2 +1 +1 =6 / 4 = Ave=1.55- (LOW)
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Total Effect = Difference =
0.44
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Calc. the Sig. of 3rd Order Interaction Effects, Error, or Aliased Effects (Solving for Means)
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Factor G (ABC)
Runs Where G is + :
4 +3 +1 +0 =8 / 4 = Ave=1.89
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Runs Where G is - :
3 +2 +1 +1 =7 / 4 = Ave=1.64
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Total Effect = Difference =
0.25
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