Reference no: EM132856683

A machine with two components is subject to a series of shocks that occur deterministically at the beginning of each day. When the machine is working, a shock can cause failure of component 1 alone with probability 0.03, component 2 alone with probability 0.03, both components with probability 0.04, or no failures with probability 0.9. When a failure occurs, the machine is shut down and no more failures occur until the machine is repaired. The repair time in days of component i (i = 1,2), is a geometric random variable with parameter ri, with r1 = 0.85 and r2 = 0.8. Assume that there is a single repair person and all repair times are independent. If both components fail simultaneously, the repair person repairs component one first, followed by component two.

If the machine is up at the beginning of Monday, what is the distribution over the possible states at the beginning of Thursday?