ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAH
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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
ABCR1R2R3R4R5R6R7R8Ave.Std.Dev.
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1 1+--3.5 -
Each run was replicated 8 times (R1, R2, etc)
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2 3-+-1.6 -
The response variable is dissolution of lactose (minutes)
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3 2--+0.7 -
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4 6++-1.2 -
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5 4+-+0.7 -
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6 5+++0.3 -
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7 8-++0.5 -
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8 7---3.1 -
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Reference Key to Factor Selection
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Factor A = Your factor:
diameter (cm)
; B =
microving time(mins)
; C =
power(%)
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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 + :
2 +1 +0 +3 =6 / 4 = Ave=1.55+
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Runs Where A is - :
4 +1 +1 +1 =5 / 4 = Ave=1.35-
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Total Effect = Difference =
0.20ABC
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-1.351.531.75
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Factor B
Runs Where B is + :
1 +1 +1 +3 =6 / 4 = Ave=1.375++1.551.3751.15
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Runs Where B is - :
4 +2 +1 +0 =6 / 4 = Ave=1.53-
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Total Effect = Difference =
-0.15
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Factor C
Runs Where C is + :
1 +0 +1 +3 =5 / 4 = Ave=1.15+
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Runs Where C is - :
4 +2 +1 +1 =7 / 4 = Ave=1.75-
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Total Effect = Difference =
-0.60
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Calc. the Sig. of 2nd Order Interaction Effects or Aliased Effects (Solving for Means)
LOW BHIGH B
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LOW A1.91.05
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Factor D (AB)
Runs Where D is + :
4 +1 +1 +3 =9 / 4 = Ave=2.125+HIGH A2.10.75
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Runs Where D is - :
2 +1 +0 +1 =3 / 4 = Ave=0.78-
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Total Effect = Difference =
1.35
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Factor E (AC)
Runs Where E is + :
4 +1 +0 +3 =8 / 4 = Ave=1.9+
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Runs Where E is - :
2 +1 +1 +1 =4 / 4 = Ave=1.00-
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Total Effect = Difference =
0.90
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Factor F (BC)
Runs Where F is + :
4 +2 +1 +3 =9 / 4 = Ave=2.175+
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Runs Where F is - :
1 +1 +1 +0 =3 / 4 = Ave=0.73-
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Total Effect = Difference =
1.45
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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 + :
2 +1 +1 +3 =6 / 4 = Ave=1.525
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Runs Where G is - :
4 +1 +0 +1 =6 / 4 = Ave=1.38
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Total Effect = Difference =
0.15LOW CHIGH C
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LOW A2.350.6
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HIGH A2.350.5
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ABC
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1.150.71.4
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0.951.40.7
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LOW CHIGH C
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LOW B3.30.6
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HIGH B1.40.5
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LOW BHIGH B
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LOW A0.71.6
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HIGH A0.71.2
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LOW CHIGH C
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LOW A1.60.7
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HIGH A1.20.7
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