Integrating 2K Factorial DOE and General Linear Model (GLM)
2K factorial DOE ( Design Of Experiment ) is a popular tools to either modeling your process or optimizing your process . Speaking about optimizing your process , a process owner of a process might ask you question like “ From your 2K result , can you tell me the percentage of contribution of each factor to the process output ? “ .
To answer this question , we cannot directly know the percentage of each factor contribution to the process output because in 2K result , it does not show the value of SEQ SUM SQUARE as shown in regression or General Full Factorial . Thus you need to integrate the result of 2K with GLM .
Let’s have a look at below case study :
Let say you executed 2K DOE in order to maximize your process output by working on 3 factors as below with 2 replicates ( total 16 runs ):
Factor low (-1) level High (+1) level
A 195 205
B Vtech PolyAll
C Smooth Ribbed
Your task is to find the optimum setting for each factor that can mazimize your process output and you also need to report the contribution of each term ( factor and interaction ) towards the process output .
Proceeding with 2K DOE analyze, you will get the final model as below :
Factorial Fit: Y versus A, B, C
Estimated Effects and Coefficients for Y (coded units)
Term Effect Coef SE Coef T P
Constant 78.463 0.8050 97.47 0.000
A -11.300 -5.650 0.8050 -7.02 0.000
B -9.150 -4.575 0.8050 -5.68 0.000
C 3.350 1.675 0.8050 2.08 0.062
B*C -3.525 -1.763 0.8050 -2.19 0.050
S = 3.22004 PRESS = 241.306
R-Sq = 89.18% R-Sq(pred) = 77.11% R-Sq(adj) = 85.25%
Analysis of Variance for Y (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 3 890.54 890.54 296.847 28.63 0.000
2-Way Interactions 1 49.70 49.70 49.703 4.79 0.050
Residual Error 11 114.06 114.06 10.369
Lack of Fit 3 12.25 12.25 4.082 0.32 0.810
Pure Error 8 101.81 101.81 12.726
Total 15 1054.30
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