Question

"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 is functioning, so it is a number 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 reliability equals [$1760+ $11007*(In R)], which will be paid immediately. Maintenance on the actuator will occur in year 6 and in year 12. In each year the maintenance cost as a function of reliability R is [$1350/ln(1.45R)]. Assume the interest rate is 10%.
What is the optimal torque design (a number between 0.1 and 3.5 rounded to the nearest tenth) of the actuator that minimizes the discounted lifecycle costs of the actuator? (You do not need to calculate annual equivalent cost, but you do need to calculate the present value of the costs.)"

Answer 1

Solution :

Approach: Used excel to minimize the total cost ( installation cost + maintenance cost (in present value)

Step 1: Assumed T=2.5

Step 2: Calculated reliability R as given in excel

Step 3: Calculated cost of installation based on this R

Step 4: Calculated maintenance cost for year 6 and 12 and then discounted it with 10%

Step 5: Add maintenance and installation to get total lifecycle cost

Step 6: Open solver in excel, and set the minimization objective for cell B10 (total cost)

• By changing variable torque given in B2
• Set constraints B2 can have min .1 and max of 3.5 value

Step 7: after setting all the constraints hit enter to get the minimum value of cost as 4915.185 when torque value is 1.9205.

Ans: T = 1.9205