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 the 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 e^(0.027 * T)

The development and installation cost as a function of reliability equals

$1,950 + $10,026 * ln(R), which will be paid immediately.

Maintenance on the actuator will occur in year 5 and in year 10. In each year, the maintenance cost is

$1,400 / Ln(1.45*R)

Assume the interest rate is 15%.

What is the optimal torque design in order to minimize the discounted lifecycle cost of the actuator? What is the reliability of the actuator? (You do not need to calculate annual equivalent cost, but you do need to calculate the present value of the costs.)

Assume the airplane manufacturer has a requirement of at least 0.99 reliability. Does your answer in part a achieve that reliability? If not, what torque would you recommend that meets this requirement and keeps the discounted lifecycle cost as low as possible?

What is the difference in discounted lifecycle costs between parts a and b? Note: A decision maker who is responsible for determining what the reliability should be for the actuator can consider whether increasing the reliability is worth the additional cost.