Consider a production system with 2 machines. When a machine is up and running,

it takes a random amount of time to go down and these random "up times" for each

machine are iid exponentially distributed. Machine A is an old machine. Its mean up

time is 4 hour. Machine

B

is a new machine. Its mean up times is 6 hours. There is

one repairman, John, on standby, who repairs machines one at a time following the

order of breakdown. The repair times for machine

A

are iid exponentially distributed

with mean 2 hours. The repair times for machine

B

are iid exponentially distributed

with mean 1 hours.

Describe a continuous time Markov chain to model the system and give the rate

transition diagram, and the holding time rates and the jump matrix.