ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAIAJAKALAMANAOAPAQARASATAUAVAW
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2^3 Full Factorial Array (Similar to the Taguchi L8 Orthogonal Array)
At LOW B
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CP5070 DOE Tutorial Example 1 on dissolution of lactose
Average of Low A:1.9Low BHigh B
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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
Average of High A:2.1at -A (10cm)1.91.1
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Total effect of A:0.2at +A (15cm)2.10.8
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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
At HIGH B
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Run#
Run Order
ABC
D=AB
E=AC
F=BC
G=ABC
R1R2R3R4R5R6R7R8Ave.Std.Dev.Average of Low A:1.05
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1 1---+++-3.1 -
Each run was replicated 8 times (R1, R2, etc)
Average of High A:0.75
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2 3+----++3.5 -
The response variable is dissolution of lactose (seconds)
Total effect of A:-0.3
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3 2-+--+-+1.6 -
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4 6++-+---1.2 -
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5 4--++--+0.7 -
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6 5+-+-+--0.7 -
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7 8-++--+-0.5 -
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8 7+++++++0.3 -
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Reference Key to Factor Selection
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Factor A = Your factor:
Diamater of Bowl
; B =
Microwaving Time
; C =
Power
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Factor D = Your factor:
Diamater x Microwaving
; 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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-+Low CHigh C
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Factor A
Runs Where A is + :
4 +1 +1 +0 =6 / 4 = Ave=1.425+Factor A1.4751.425at LOW Cat -A (10cm)2.350.6
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Runs Where A is - :
3 +2 +1 +1 =6 / 4 = Ave=1.475-Factor B20.9Average of Low A:2.35at +A (15cm)2.350.5
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Total Effect = Difference =
-0.05Factor C2.350.55Average of High A:2.35
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at LOW C, total effect of A:0
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Factor B
Runs Where B is + :
2 +1 +1 +0 =4 / 4 = Ave=0.90+
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Runs Where B is - :
3 +4 +1 +1 =8 / 4 = Ave=2.00-at HIGH C
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Total Effect = Difference =
-1.10Average of Low A:0.6
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Average of High A:0.5
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Factor C
Runs Where C is + :
1 +1 +1 +0 =2 / 4 = Ave=0.55+at HIGH C, total effect of A:-0.1
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Runs Where C is - :
3 +4 +2 +1 =9 / 4 = Ave=2.35-
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Total Effect = Difference =
-1.80
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Calc. the Sig. of 2nd Order Interaction Effects or Aliased Effects (Solving for Means)
at LOW CLow CHigh C
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Average of Low B:3.3at -B3.30.7
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Factor D (AB)
Runs Where D is + :
3 +1 +1 +0 =5 / 4 = Ave=1.325+Average of High B:1.4at +B1.40.4
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Runs Where D is - :
4 +2 +1 +1 =6 / 4 = Ave=1.58-at LOW C, total effect on B:-1.9
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Total Effect = Difference =
-0.25
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at HIGH C
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Factor E (AC)
Runs Where E is + :
3 +2 +1 +0 =6 / 4 = Ave=1.425+Average of Low B:0.7
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Runs Where E is - :
4 +1 +1 +1 =6 / 4 = Ave=1.48-Average of High B:0.4
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Total Effect = Difference =
-0.05at HIGH C, total effect on B:-0.3
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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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TotalAverage
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Calc. the Sig. of 3rd Order Interaction Effects, Error, or Aliased Effects (Solving for Means)
Factor A
Runs where A is +:
3.5 +0.3 =3.81.9
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Runs where A is -:
1.6 +0.7 =2.31.15Difference:0.75
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Factor G (ABC)
Runs Where G is + :
4 +2 +1 +0 =6 / 4 = Ave=1.525Factor B
Runs where B is +:
1.6 +0.3 =1.90.95
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Runs Where G is - :
3 +1 +1 +1 =6 / 4 = Ave=1.38
Runs where B is -:
3.5 +0.7 =4.22.1Difference:-1.15
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Total Effect = Difference =
0.15Factor C
Runs where C is +:
0.7 +0.3 =1.00.5
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Runs where C is -:
3.5 +1.6 =5.12.55Difference:-2.05
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-+
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Factor A1.151.9
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Factor B2.10.95
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Factor C2.550.5
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