ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAIAJAKALAMANAOAPAQ
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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+----++3.53.5 -
The response variable is dissolution of lactose (minutes)
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3 2-+--+-+1.61.6 -
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4 6++-+---1.21.2 -
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5 4--++--+0.70.7 -
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6 5+-+-+--0.70.7 -
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7 8-++--+-0.50.5 -
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8 7+++++++0.30.3 -Run OrderABCBullets 
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2 -+-1.6
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Reference Key to Factor Selection
6 ++-1.2
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Factor A = Your factor:
Diameter
; B =
Microwaving Time
; C =
Power
4 --+0.7
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Factor D = Your factor:
; E =; F =; G =AxBxC5 +-+0.7
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Confounding Column Information (for alternative factor assignment considerations)
Factor A — Runs Where A is + : (1.2 +0.7)/2 = 0.95
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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
Factor A — Runs Where A is - : (1.6 +0.7)/2 = 1.15
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array does not have confounding columns. Using the L8 array requires an uderstanding of column confounding.
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Factor B — Runs Where B is + : (1.6+1.2)/2 = 1.4
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Calculating the Significance of Main Effects (Solving for Means)
Factor B — Runs Where B is - : (0.7 +0.7)/2 = 0.7
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Factor A
Runs Where A is + :
4 +1 +1 +0 =6 / 4 = Ave=1.425+
Factor C — Runs Where C is + : (0.7+0.7)/2 = 0.7
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Runs Where A is - :
3 +2 +1 +1 =6 / 4 = Ave=1.48-
Factor C — Runs Where C is - : (1.6 +1.2)/2 = 1.4
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Total Effect = Difference =
-0.05ABC
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-1.150.71.4
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Factor B
Runs Where B is + :
2 +1 +1 +0 =4 / 4 = Ave=0.9++0.951.40.7
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Runs Where B is - :
3 +4 +1 +1 =8 / 4 = Ave=2.00-
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Total Effect = Difference =
-1.10
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Factor C
Runs Where C is + :
1 +1 +1 +0 =2 / 4 = Ave=0.55+Blow Ahigh AClow Bhigh B
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Runs Where C is - :
3 +4 +2 +1 =9 / 4 = Ave=2.35--1.92.1-3.31.4
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Total Effect = Difference =
-1.80+1.050.75+0.60.4
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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 +1 +1 +0 =5 / 4 = Ave=1.325+
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Runs Where D is - :
4 +2 +1 +1 =6 / 4 = Ave=1.58-
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Total Effect = Difference =
-0.25
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Factor E (AC)
Runs Where E is + :
3 +2 +1 +0 =6 / 4 = Ave=1.425+
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Runs Where E is - :
4 +1 +1 +1 =6 / 4 = Ave=1.48-
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Total Effect = Difference =
-0.05
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Factor F (BC)
Runs Where F is + :
3 +4 +1 +0 =7 / 4 = Ave=1.85+
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Runs Where F is - :
2 +1 +1 +1 =4 / 4 = Ave=1.05-
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Total Effect = Difference =
0.80
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Clow Ahigh A
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-2.352.35
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Calc. the Sig. of 3rd Order Interaction Effects, Error, or Aliased Effects (Solving for Means)
+0.60.5
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Factor G (ABC)
Runs Where G is + :
4 +2 +1 +0 =6 / 4 = Ave=1.525
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Runs Where G is - :
3 +1 +1 +1 =6 / 4 = Ave=1.38
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Total Effect = Difference =
0.15
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