11.34. Box and Liu (1999) describe an experiment flying paper helicopters where
ID: 3321042 • Letter: 1
Question
11.34. Box and Liu (1999) describe an experiment flying
paper helicopters where the objective is to maximize flight
time. They used the central composite design shown in Table
P11.11. 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?
11.34. Box and Liu (1999) describe an experiment flying
paper helicopters where the objective is to maximize flight
time. They used the central composite design shown in Table
P11.11. 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?
Explanation / Answer
(a)
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]
P-value
Prob >F
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
Source Sum of squares df Mean square F valueP-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 29Related Questions
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