I am trying to understand the steps in constructing a transition
probabililty matrix for a pump system. I am particularly interested in
the detail of the method to convert the transistion data into the
probabilities to populate the matrix.

The system comprises two pumps, A & B arranged in parallel. Pump A has
a MTBF of 900hr and a MTTR of 100hr. Pump B has a MTBF of 800hr and a
MTTR of 200hr.
There are 4 potential states:
State 1 - A & B Operating.
State 2 - A failed and being repaired, B running.
State 3 - A running, B failed and being repaired.
State 4 - Both A & B failed.
It assumed there are no transitions between states 2 & 3.

Can anyone help?