The article “Application of Analysis of Variance to Wet

Chapter 8, Problem 4E

(choose chapter or problem)

The article “Application of Analysis of Variance to Wet Clutch Engagement” (M. Mansouri, M. Khonsari, et al., Proceedings of the Institution of Mechanical Engineers, 2002:117–125) presents the following fitted model for predicting clutch engagement time in seconds \((y)\) from engagement starting speed in m/s \((x_1)\), maximum drive torque in \(\mathrm {N \cdot m}\) \((x_2)\), system inertia in \(\mathrm {kg \cdot m}^2\) \((x_3)\), and applied force rate in kN/s \((x_4)\):

\(y=-0.83+0.017 x_{1}+0.0895 x_{2}+42.771 x_{3}+0.027 x_{4}-0.0043 x_{2} x_{4}\)

The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was SSE = 0.036310. There were 44 degrees of freedom for error.

a. Predict the clutch engagement time when the starting speed is 20 m/s, the maximum drive torque is 17 \(\mathrm {N \cdot m}\), the system inertia is 0.006 \(\mathrm {kg \cdot m}^2\), and the applied force rate is 10 kN/s.

b. Is it possible to predict the change in engagement time associated with an increase of 2 m/s in starting speed? If so, find the predicted change. If not, explain why not.

c. Is it possible to predict the change in engagement time associated with an increase of 2 \(\mathrm {N \cdot m}\) in maximum drive torque? If so, find the predicted change. If not, explain why not.

d. Compute the coefficient of determination \(R^2\).

e. Compute the F statistic for testing the null hypothesis that all the coefficients are equal to 0. Can this hypothesis be rejected?

Equation Transcription:

Text Transcription:

(y)

(x_1)

N{cdot}m

(x2)

kg{cdot}m^2

(x3)

(x4)

y=-0.83+0.017x_1+0.0895x_2+42.771x_3+0.027x_4-0.0043x_2x_4

kg{cdot}m^2

N{cdot}m

R^2