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?

Transcribed Image Text:

Std. Run Wing Wing Base order order area ratio width Base length Avg. flight time Std. Dev flight time -23456TOOD 9 -1 -1 3.67 0.052 21 3.69 0.052 14 3.74 0.055 4 3.7 0.062 2 -1 3.72 0.052 19 1 3.55 0.065 7 22 3.97 0.052 8 25 3.77 0.098 9 27 3.5 0.079 10 13 1 3.73 0.072 11 20 1 3.58 0.083 12 6 1 3.63 0.132 13 12 -1 1 3.44 0.058 14 17 1 3.55 0.049 15 26 1 3.7 0.081 16 1 1 3.62 0.051 17 8 0 0 3.61 0.129 18 15 2 0 0 0 3.64 0.085 19 7 0 -2 0 0 3.55 0.1 20 5 0 2 0 0 3.73 0.063 21 29 0 0 -2 22 28 0 0 23 16 0 0 24 18 0 0 25 24 0 0 26 10 0 0 27 23 0 0 28 11 0 0 29 3 0 0 30 30 0 0 NNOOOo o . o o 0 3.61 0.051 2 0 3.6 0.095 0 -2 3.8 0.049 0 2 3.6 0.055 0 0 3.77 0.032 0 0 3.75 0.055 0 3.7 0.072 0 0 3.68 0.055 0 0 3.69 0.078 0 3.66 0.058