Problem 1 A company has two machines. During any day, each machine that is worki

Question

Problem 1 A company has two machines. During any day, each machine that is working at the beginning of the day has a chance of breaking down. If a machine breaks down during the day, it is sent to a repair facility and will be working two days after it breaks down. (Thus, if a machine breaks down during day 3, it will be working at the beginning of day 5.). Letting the state of the system be the number of machines working at the beginning of the day formulate a transition probability matrix for this situation.

Explanation / Answer

A machine working on a particular day has a probability of 1/3 of breaking down during the day. So, the probability of working on the next day is 1-1/3 = 2/3

Further, if a machine is down for repairs at the beginning of a day, then the probability of that machine working at the beginning of the next day is 1.

The transition matrix is as follows

Tomorrow Today Working Not working Working 2/3 1/3 Not working 1     0    

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