1.1
|
RunOrder
|
Factors
|
Flight Time
|
?
|
|
A
|
Q
|
L
|
W
|
Fold at Wing tip
|
y1
|
y2
|
y3
|
|
1
|
-1
|
-1
|
-1
|
1
|
-1
|
2.56
|
2.6
|
2.48
|
2.55
|
|
2
|
1
|
1
|
-1
|
-1
|
1
|
2.62
|
2.55
|
2.65
|
2.61
|
|
3
|
-1
|
1
|
1
|
-1
|
1
|
2.39
|
2.45
|
2.42
|
2.42
|
|
4
|
1
|
1
|
1
|
-1
|
-1
|
2.30
|
2.25
|
2.33
|
2.29
|
|
5
|
-1
|
-1
|
1
|
1
|
1
|
2.23
|
2.2
|
2.25
|
2.23
|
|
6
|
-1
|
1
|
-1
|
-1
|
-1
|
2.25
|
2.26
|
2.31
|
2.27
|
|
7
|
-1
|
-1
|
-1
|
-1
|
1
|
2.33
|
2.4
|
2.29
|
2.34
|
|
8
|
-1
|
-1
|
1
|
-1
|
-1
|
2.43
|
2.51
|
2.49
|
2.48
|
|
9
|
1
|
-1
|
1
|
-1
|
1
|
2.55
|
2.41
|
2.6
|
2.52
|
|
10
|
1
|
-1
|
1
|
1
|
-1
|
2.88
|
2.79
|
2.85
|
2.84
|
|
11
|
1
|
1
|
-1
|
1
|
-1
|
2.24
|
2.2
|
2.31
|
2.25
|
|
12
|
1
|
-1
|
-1
|
-1
|
-1
|
2.77
|
2.81
|
2.79
|
2.79
|
|
13
|
1
|
-1
|
-1
|
1
|
1
|
2.29
|
2.25
|
2.21
|
2.25
|
|
14
|
-1
|
1
|
1
|
1
|
-1
|
2.82
|
2.95
|
2.98
|
2.92
|
|
15
|
1
|
1
|
1
|
1
|
1
|
2.78
|
2.65
|
2.71
|
2.71
|
|
16
|
-1
|
1
|
-1
|
1
|
1
|
2.13
|
2.2
|
2.18
|
2.17
|
1.2 Which effects are clear?
1.3 Use the least-squares estimation method to estimate those clear effects.
1.4 Conduct an analysis of variance by completing the corresponding ANOVA table. What conclusion can you make in terms of effects' significance? Is the fold-at-wing-tip helpful (to improve the flight time)?
1.5 Plot a half-normal plot. Do you reach the same conclusion as you did in (1.4)? Convert your model of the coded variable into a model of the natural variables.
1.6 Use a first order model without interactions. Determine the steepest ascent direction. Choose the step size of the factor corresponding to the largest I Qh I to be 0.5 (in coded value). Finish the following table, where the data for the last column (observed 9) is the average of the observations from actual experiments you and your teammate conduct. [Note that the 0.5 step size is an absolute value. In determining Δ you should associate an appropriate plus/minus sign with it.)
|
Design points
|
Coded Variable
|
Natural Variable
|
Predicted y^
|
Observed y¯
|
|
XA
|
XQ
|
XW
|
XL
|
ξA
|
ξQ
|
ξW
|
ξL
|
|
Base (staring point)
|
|
|
|
|
|
|
|
|
|
|
|
Step size (Δ)
|
|
|
|
|
|
|
|
|
|
|
|
Base + Δ
|
|
|
|
|
|
|
|
|
|
|
|
Base +2 Δ
|
|
|
|
|
|
|
|
|
|
|
|
Base +3 Δ
|
|
|
|
|
|
|
|
|
|
|
|
Base +4 Δ
|
|
|
|
|
|
|
|
|
|
|
1.7 Based on the table, at which point you should switch to a second order design? How do you come to this decision?