ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAF
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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 8---+++-3.123.123.123.123.123.123.123.123.120.00
Each run was replicated 8 times (R1, R2, etc)
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2 1+----++3.523.523.523.523.523.523.523.523.520.00
The response variable is dissolution of lactose (minutes)
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3 2-+--+-+2.522.522.522.522.522.522.522.522.520.00
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4 4++-+---1.521.521.521.521.521.521.521.521.520.00
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5 3--++--+0.740.740.740.740.740.740.740.740.740.00
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6 5+-+-+--0.950.950.950.950.950.950.950.950.950.00
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7 7-++--+-0.520.520.520.520.520.520.520.520.520.00
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8 6+++++++0.320.320.320.320.320.320.320.320.320.00FactorLowHigh
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Factor A1.811.6575
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Reference Key to Factor Selection
Factor B2.121.34
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Factor A = Your factor:
Diameter; B =Microwaving Time; C =PowerFactor C2.790.6725
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Factor D = Your factor:
Diamter 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 =6 / 4 = Ave=1.5775+ (HIGH)
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Runs Where A is - :
3 +3 +1 +1 =7 / 4 = Ave=1.73- (LOW)
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Total Effect = Difference =
-0.15
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Factor B
Runs Where B is + :
3 +2 +1 +0 =5 / 4 = Ave=1.22+ (HIGH)
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Runs Where B is - :
3 +4 +1 +1 =8 / 4 = Ave=2.08- (LOW)
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Total Effect = Difference =
-0.86
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Factor C
Runs Where C is + :
1 +1 +1 +0 =3 / 4 = Ave=0.6325+ (HIGH)
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Runs Where C is - :
3 +4 +3 +2 =11 / 4 = Ave=2.67- (LOW)
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Total Effect = Difference =
-2.04
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Calc. the Sig. of 2nd Order Interaction Effects or Aliased Effects (Solving for Means)
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At Low B
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A x B Interaction
Runs Where A is + :
3.52++0.95+=4.47 / 2 = Ave=2.24+ (HIGH)
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Runs Where A is - :
+0.74++3.12=3.86 / 2 = Ave=1.93- (LOW)
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Total Effect = Difference =
0.31
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At High B
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Runs Where A is + :
+1.52++0.32=1.84 / 2 = Ave=0.92+ (HIGH)
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Runs Where A is - :
2.52++0.52+=3.04 / 2 = Ave=1.52- (LOW)
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Total Effect = Difference =
-0.60
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A x C Interaction
At Low C
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Runs Where A is + :
3.52++1.52+=5.04 / 2 = Ave=2.52+ (HIGH)
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Runs Where A is - :
+2.52++3.12=5.64 / 2 = Ave=2.82- (LOW)
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Total Effect = Difference =
-0.30
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At High C
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Runs Where A is + :
+0.95++0.32=1.27 / 2 = Ave=0.64+ (HIGH)
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Runs Where A is - :
0.74++0.52+=1.26 / 2 = Ave=0.63- (LOW)
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Total Effect = Difference =
0.01
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B x C Interaction
At Low C
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Runs Where B is + :
3.52++1.52+=5.04 / 2 = Ave=2.52+ (HIGH)
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Runs Where B is - :
+3.52++3.12=6.64 / 2 = Ave=3.32- (LOW)
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Total Effect = Difference =
-0.80
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At High C
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Runs Where B is + :
+0.32++0.52=0.84 / 2 = Ave=0.42+ (HIGH)
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Runs Where B is - :
0.74++0.95+=1.69 / 2 = Ave=0.85- (LOW)
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Total Effect = Difference =
-0.43
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