Question

Economic 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. The development and installation cost as a function of reliability equals [$1690+ $11220*(In R)], which will be paid immediately. Maintenance on the actuator will occur in year 4 and in year 11. In each year the maintenance cost as a function of reliability R is [$1320/ln(1.45R)]. These equations are only valid for reliability R > 0.7. Assume the interest rate is 13%.
What is the optimal reliability (a decimal between 0.7 and 1, rounded to the nearest hundredth) of the actuator that minimizes the discounted lifecycle costs of the actuator? (You do not need to calculate the annual equivalent cost, but you do need to calculate the present value of the costs.)"

Answer 1

Development and Intsallation Cost = 1690 + 11220 x ln R =C1

Discount Rate =13%

Maintenance Cost in Year 7= 1320/ln1.45R

PV of Maintenance Cost in Year 4 = C2 = [1320/(ln1.45R*(1.13)^(4))]

Maintenance Cost in Year 11 = $ 1320/ln1.45R

PV of Maintenance Cost in Year 11 = C3 = [1320/(ln1.45R*(1.13)^(11))]

Total Cost = C1 + C2 + C3 = 1690 + 11220 x lnR + [1320 x 0.6133 / ln1.45R] + [1320 x 0.2607 /ln1.45R]

Differemtiating cost function with respect to R, you can use mathematical tools for it.

Solving the above equation using EXCEL Function SOLVER we get R = 0.9504 and Minimal Cost = $ 4716.69