Consider a drilling machine in a factory. It could be in one of three different 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 bad part state or it could go to the downstate. The mean time until it leaves the good state is 20 minutes. When it leaves G, it goes to D 90% of the time and it goes to B 10% of the time. After it reaches the bad state, it stays in that state until it produces an average of 30 parts, and then it always goes to D. After the machine enters D, it stays there for a random length of time whose mean is 3 minutes, and then it always goes to G. 

 What are the probabilities of going from each state to each other state in one operation time? 

pGG =

pGB =

pGD =

pBG =

pBB =

pBD =

pDG =

pDB =

pDD =