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In: Statistics and Probability

the subject is Design of an experiment use mini-tab to slove the question Box and Liu...

the subject is Design of an experiment
use mini-tab to slove the question


Box and Liu describe an experiment flying paper helicopters where the objective is to maximize flight
time. They used the central composite design shown in Table below. Each run involved a single helicopter made to the following specifications: x1 = wing area (in2), -1 = 11.80 and +1 = 13.00; x2 = wing-length to width ratio, -1 = 2.25 and +1 = 2.78; x3 = base width (in), -1 = 1.00 and +1 = 1.50; and x4 = base length (in), -1 = 1.50 and +1 = 2.50. Each helicopter was flown four times and the average flight time and the standard deviation of flight time was recorded.
(a) Fit a second-order model to the average flight time response.
(b) Fit a second-order model to the standard deviation of flight time response.
(c) Analyze the residuals for both models from parts (a) and (b). Are transformations on the response(s) necessary? If so, fit the appropriate models.
(d) What design would you recommend to maximize the flight time?
(e) What design would you recommend to maximize the flight time while simultaneously minimizing the standard deviation of flight time?

Solutions

Expert Solution

Sol:

Sol:

Design Expert Output

Response 1                        Avg Fit Time

ANOVA for response surface reduced quadartic model

Analysis of variance table [Partial sum of squares - Type III]

Source Sum of squares df Mean square F value

P-value

Prob >F

Model 0.28 11 0.025 15.78 <0.0001 significance
A-wing area 1.67E005 1 1.667E005 0.010 0.9198
B length width 0.062 1 0.062 38.83 <0.0001
Cbase width 1.500E004 1 1.500E004 0.094 0.7628
Dbase width 0.089 1 0.089 55.61 <0.0001
AB 0.013 1 0.013 8.28 0.0100
AC 0.023 1 0.023 14.09 0.0015
AD 0.031 1 0.031 19.17 0.0004
BC 0.034 1 0.034 21.43 0.0002
CD 7.225E003 1 7.22E003 4.52 0.0475
A2 7.511E003 1 7.51E003 4.70 0.0438
C2 0.013 1 0.013 8.04 0.0110
Residual 0.029 18 1.597E003
LACK OF FIT 0.020 13 1.513E003 0.83 0.6382
PURE ERROR 9.083E003 5
COR TOTAL 0.31 29

Std. dev 0.040           R squared    0.9060

mean   3.66                Adj R-squared 0.8486

c.v% 1.09                    Pred R squared 0.7581

press 0.074                   Adeq predision   19.913

Factor Coefficient Estimate df Standard Error 95%CI Low 95%CI High VIF
INTERCEPT 370 1 0.012 367 372 1.00
a wing area 8.33E004 1 8.158E003 0.018 0.016 1.00
B length width 0.051 1 8.158E003 0.034 0.068 1.00
C Base width 2.500E003 1 8.158E003 0.015 0.020 1.00
D base width 0.061 1 8.158E003 0.078 0.054 1.00
AB 0.029 1 9.991E003 0.050 7.75E003 1.00
AC 0.037 1 9.991E003 0.058 0.017 1.00
AD 0.044 1 9.991E003 0.023 0.065 1.00
BC 0.045 1 9.991E003 0.025 0.067 1.00
CD 0.021 1 9.991E003 0.042 2.590E004 1.00
A2 0.016 1 7.491E003 0.032 5.060E004 1.01
C2 0.021 1 1.491E003 0.037 5.507E003

1.01

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