5因子的部分因子实验设计-全模型下残差非正态，删减模型下正态，结果可信吗？

Fractional Factorial Design

Factors: 5 Base Design: 5, 16 Resolution: V
Runs: 19 Replicates: 1 Fraction: 1/2
Blocks: 1 Center pts (total): 3

Design Generators: E = ABCD Factor High level Low level
HP Press (kgf) 30 18
Alias Structure HP Temp (°C) 115 95
I + ABCDE HP Time (s) 420 300
A + BCDE AN Temp (°C) 125 100
B + ACDE AN Time (hrs) 3 1
C + ABDE
D + ABCE
E + ABCD
AB + CDE BD + ACE
AC + BDE BE + ACD
AD + BCE CD + ABE
AE + BCD CE + ABD
BC + ADE DE + ABC

实验设计表：

StdOrder RunOrder CenterPt Blocks HP Press HP Temp HP Time AN Temp AN Time Hardness
18 1 0 1 24 105 360 112.5 2 38.95
3 2 1 1 18 115 300 100 1 34.99
7 3 1 1 18 115 420 100 3 41.00
2 4 1 1 30 95 300 100 1 31.74
8 5 1 1 30 115 420 100 1 37.00
16 6 1 1 30 115 420 125 3 42.78
10 7 1 1 30 95 300 125 3 48.46
19 8 0 1 24 105 360 112.5 2 37.33
5 9 1 1 18 95 420 100 1 27.59
1 10 1 1 18 95 300 100 3 29.46
13 11 1 1 18 95 420 125 3 37.66
6 12 1 1 30 95 420 100 3 30.47
4 13 1 1 30 115 300 100 3 39.96
14 14 1 1 30 95 420 125 1 45.24
12 15 1 1 30 115 300 125 1 42.48
11 16 1 1 18 115 300 125 3 41.21
9 17 1 1 18 95 300 125 1 30.88
17 18 0 1 24 105 360 112.5 2 36.66
15 19 1 1 18 115 420 125 1 42.19

Minitab 实验分析：
1） 全模型
Factorial Fit: Hardness versus HP Press, HP Temp, ...

Estimated Effects and Coefficients for Hardness (coded units)

Term Effect Coef SE Coef T P
Constant 37.686 0.2212 170.39 0.000
HP Press 4.143 2.072 0.2410 8.60 0.003
HP Temp 5.014 2.507 0.2410 10.40 0.002
HP Time 0.596 0.298 0.2410 1.24 0.304
AN Temp 7.336 3.668 0.2410 15.22 0.001
AN Time 2.361 1.180 0.2410 4.90 0.016
HP Press*HP Temp -3.439 -1.719 0.2410 -7.13 0.006
HP Press*HP Time -2.381 -1.191 0.2410 -4.94 0.016
HP Press*AN Temp 2.611 1.306 0.2410 5.42 0.012
HP Press*AN Time -1.060 -0.530 0.2410 -2.20 0.115
HP Temp*HP Time 0.487 0.244 0.2410 1.01 0.387
HP Temp*AN Temp -3.410 -1.705 0.2410 -7.07 0.006
HP Temp*AN Time -0.289 -0.144 0.2410 -0.60 0.591
HP Time*AN Temp 0.615 0.307 0.2410 1.28 0.292
HP Time*AN Time -2.387 -1.194 0.2410 -4.95 0.016
AN Temp*AN Time -0.032 -0.016 0.2410 -0.07 0.952


S = 0.964063 PRESS = 12.8592
R-Sq = 99.52% R-Sq(pred) = 97.80% R-Sq(adj) = 97.14%


Analysis of Variance for Hardness (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 5 408.180 408.180 81.6359 87.84 0.002
2-Way Interactions 10 173.842 173.842 17.3842 18.70 0.017
Residual Error 3 2.788 2.788 0.9294
Curvature 1 0.006 0.006 0.0060 0.00 0.954
Pure Error 2 2.782 2.782 1.3911
Total 18 584.810




2）删减模型
Factorial Fit: Hardness versus HP Press, HP Temp, ...

Estimated Effects and Coefficients for Hardness (coded units)

Term Effect Coef SE Coef T P
Constant 37.686 0.2575 146.33 0.000
HP Press 4.143 2.072 0.2806 7.38 0.000
HP Temp 5.014 2.507 0.2806 8.93 0.000
HP Time 0.596 0.298 0.2806 1.06 0.319
AN Temp 7.336 3.668 0.2806 13.07 0.000
AN Time 2.361 1.180 0.2806 4.21 0.003
HP Press*HP Temp -3.439 -1.719 0.2806 -6.13 0.000
HP Press*HP Time -2.381 -1.191 0.2806 -4.24 0.003
HP Press*AN Temp 2.611 1.306 0.2806 4.65 0.002
HP Temp*AN Temp -3.410 -1.705 0.2806 -6.07 0.000
HP Time*AN Time -2.387 -1.194 0.2806 -4.25 0.003


S = 1.12260 PRESS = 73.2980
R-Sq = 98.28% R-Sq(pred) = 87.47% R-Sq(adj) = 96.12%


Analysis of Variance for Hardness (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 5 408.180 408.180 81.6359 64.78 0.000
2-Way Interactions 5 166.548 166.548 33.3097 26.43 0.000
Residual Error 8 10.082 10.082 1.2602
Curvature 1 0.006 0.006 0.0060 0.00 0.950
Lack of Fit 5 7.294 7.294 1.4587 1.05 0.554
Pure Error 2 2.782 2.782 1.3911
Total 18 584.810