QUESTION 5 

Consider two identical constant failure rate components with λ=0.02 failures/day and a repair rate of μ=0.1 repairs/day. Your organisation's current policy is to have two spare parts in inventory and a single repair person. You have been tasked with determining if the addition of a spare to the inventory is cost effective. The time to install a component is considered negligible, i.e. if there is a spare available, the repair time is zero. 

a. Draw a Markov diagram to model the situation of having two spares.

b. Determine the steady-state probability of having both components working. 

c. Repeat a) and b) for the case of three spares. 

d. The cost of down time is $30,000 per component per day while the cost of maintaining an item in inventory is $1000 per component per day. Is it economical to add the third spare?