T
tatos
Member
Consider 2 machines
Time to break down follows an exponential distribution with rate s
Time to repair also follows an exponential distribution but with rate r
Only one machine can be repaired at a time
the generator matrix is given by
-r r 0
s -(s+r) r
0 2s -2s
My question is: why isn't there a transition rate to describe a movement from 2 machines in working order to 0 machines in working order (entry 3,1 in the matrix above, which is 0)? i.e. Why does it seem like it has to pass through "state 1" en route to zero machines in working order?
I understand how you can go from 0 to 1 only and not from 0 to 2 (because only one machine can be repaired at a time) but I don't understand why you can't go from 2 to 0 immediately (since surely the machines can simultaneously break down?)
Time to break down follows an exponential distribution with rate s
Time to repair also follows an exponential distribution but with rate r
Only one machine can be repaired at a time
the generator matrix is given by
-r r 0
s -(s+r) r
0 2s -2s
My question is: why isn't there a transition rate to describe a movement from 2 machines in working order to 0 machines in working order (entry 3,1 in the matrix above, which is 0)? i.e. Why does it seem like it has to pass through "state 1" en route to zero machines in working order?
I understand how you can go from 0 to 1 only and not from 0 to 2 (because only one machine can be repaired at a time) but I don't understand why you can't go from 2 to 0 immediately (since surely the machines can simultaneously break down?)