Consider a drilling machine in a factory. It could be in one of three dierent states: G, in which it is working normally (making good parts); B in which it is working but producing bad parts; or D, in which it is under repair (\down") and not making parts. Transitions can occur at times 0, 30 seconds, 60 seconds, etc. Assume that all transitions are governed by Bernoulli distributions. That is, each time at which a transition can occur it occurs with a probability determined by the origin and destination state, and not dependent on how long the system was in the origin state. When it is working or making bad parts, the machine performs an operation in exactly 30 seconds. Assume that when it is in one of these states and it changes state, it changes state before it makes the next part, and that the change takes no time. That is, when it goes from G to B, it makes one bad part; and when it goes from G to D, it does not make a part. When the machine is making good parts, it could go to the the bad part state or it could go to