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This example validates the robust design inner array with a two level factorial design and an out array with a general full factorial design in Weibull++.


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The data are from the example on page 1252 in the book ''Applied linear Statistical Models'' by Michael H.K, Christopher J.N, John N. William. Li, Fifth Edition, McGraw-Hill, 2005.


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{| {{Table}}
!rowspan="2" | Run
!rowspan="2" | A
!rowspan="2" | B
!rowspan="2" | C
!colspan="4" | Noise Factor
|-
!style="background:#f0f0f0;"|60°F
!style="background:#f0f0f0;"|70°F
!style="background:#f0f0f0;"|80°F
!style="background:#f0f0f0;"|90°F
|-
| 1||1||1||1||48||49||56||63
|-
| 2||1||-1||-1||50||52||55||63
|-
| 3||-1||1||1||70||72||77||84
|-
| 4||-1||-1||-1||42||65||70||73
|-
| 5||-1||1||-1||61||70||78||79
|-
| 6||-1||-1||1||65||74||74||77
|-
| 7||1||-1||1||40||59||63||66
|-
| 8||1||1||-1||48||51||55||60
 
|}
.


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From the book the results are:
 
{| {{Table}}
 
!Predictor
!Coef
|-
| Constant||62.781
|-
| A||-7.906
|-
| B||1.031
|-
| C||2.031
|-
| AB||-2.156
|-
| AC||-1.406
|-
| BC||-0.969
|-
| ABC||0.594
|-
 
|}
 


{{Reference_Example_Heading4|DOE++}}
{{Reference_Example_Heading4|DOE++}}
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The software results match the book results. The ANOVA table is:
 
[[Image:robust_design_anova.png|center]]
 
The final equation in terms of the actual factors is:
 
[[Image:robust_design_equation.png|center]]

Latest revision as of 21:09, 18 September 2023

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Robust Design

This example validates the robust design inner array with a two level factorial design and an out array with a general full factorial design in Weibull++.

Reference Case

The data are from the example on page 1252 in the book Applied linear Statistical Models by Michael H.K, Christopher J.N, John N. William. Li, Fifth Edition, McGraw-Hill, 2005.

Data

Run A B C Noise Factor
60°F 70°F 80°F 90°F
1 1 1 1 48 49 56 63
2 1 -1 -1 50 52 55 63
3 -1 1 1 70 72 77 84
4 -1 -1 -1 42 65 70 73
5 -1 1 -1 61 70 78 79
6 -1 -1 1 65 74 74 77
7 1 -1 1 40 59 63 66
8 1 1 -1 48 51 55 60

.

Result

From the book the results are:

Predictor Coef
Constant 62.781
A -7.906
B 1.031
C 2.031
AB -2.156
AC -1.406
BC -0.969
ABC 0.594


Results in DOE++

The software results match the book results. The ANOVA table is:

Robust design anova.png

The final equation in terms of the actual factors is:

Robust design equation.png
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