L > Moving to another question will save this respone ||d Question 8 of 92! 3 po
ID: 3145901 • Letter: L
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L > Moving to another question will save this respone ||d Question 8 of 92! 3 points Save Answer Question 8 An aircraft control actuator is part of the flight control system that enables an airplane to fly It is important that the actuators are reliable. Reliability can be defined as the probability a system i s functioning, so it is a numb ber between 0 and 1. One way to increase reliability of the actuator is to increase the torque. The reliability R as a function of the maximum torque T (in Newton-meters) is given by R(T)-0.91'exp(0.027T) where torque T is between 0.1 and 3.5. The development and installation cost as a function of r Maintenance on the actuator will occur in year 5 and in year 7. In each year the maintenance cost as a function of reliability R eliability equals [$1820+ $12690 (In R)], which will be paid immediately is [$1430/ln(1.45R)] Assume the interest rate is 11% What is the optimal torque design (a number between 0.1 and 3.5 rounded to the nearest tenth) of the actuator that (You do not need to calculate annual equivalent cost, but you do need to calculate the present value of minimizes the discounted ifecycle costs of the actuator? the costs )" Question 8 of 9 Moving to another question will save this response 1038 PM ^ dx 10/18/2017Explanation / Answer
The discounted lifecycle cost as a function of reliability is
1820+12690 ln R + 1430/[ln(1.45R)*1.115] + 1430/[ln(1.45R)*1.117]
Substituting T for R, we write discounted LCC as a function of torque
1820 + 12690 [ln 0.91 + .027T] + 1430/([ln(1.45*.91) + .027T]*1.115) + 1430([ln(1.45*.91) + .027T]*1.117)
= 1820 + 12690 [ln 0.91 + .027T] + 1430/[ln(1.45*.91) + .027T]*(1/1.115 + 1/1.117)
Take the first derivative with respect to T and setting it equal to 0
dLCC/dT = 12690*.027 – 1430*.027/[ln(1.45*.91)+.027T]2 * (1/1.115 + 1/1.117) = 0
342.63 – 41.3127 / [.277253+.027T]2 = 0
0.12062 = [.277253+.027T]2
0.34730-0.277253=0.27T
T = 2.59
R = .091*exp(.027*2.59)
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