while trying to draw the transition diagram for part iii0 of the ques. I consider 3 discrete states- 0- no machine working 1-one machine out of two working 2-both machines workin we have a transition from state 0 to state 1 with rate (rho) from state 1 to 0 with rate (sigma) from state 1 to state 2 with rate (rho) FROM STATE 2 TO STATE 1 WITH RATE (2*sigma) i have a doubt in last transition. why transition from state 2 to state 1 has rate (2*sigma) instead of sigma only. If we think about it as there are two choices for repairing the machine-- machine 1 working and 2 not working machine 2 working and 1 not working Then i got the point that why the rate is (2*sigma)---(A) But if my thought process in point A is correct then why we dont consider the 2 options for repairing of machines i.e- repairing 1 and 2 still broken reparing 2 and 1 still broken so by this logic the force of transition from state 0 to state 1 should be (2*rho) instead of (rho). But this is not the case. Please clarify!
When both machines are working (state 2), either of them could break at any moment. So the first machine could break (with rate sigma) or the second machine could break (with rate sigma). So the overall rate of breaking in state 2 (ie the rate of moving from state 2 to state 1) is 2*sigma. When both machines are broken (state 0), there is only one repair team, so only one machine could be fixed at any moment. So the rate of repair (ie the rate of moving from state 0 to state 1) is rho.
