It should be noted that the number of outward transitions in a state is the sum of the frequencies of all transitions that can occur in that state. For example, consider the system shown in Figure 8-2. The frequency of outward transition in state 1 is P1(t)(λ1+λ2).

Similarly, the frequency of inward transitions to a state can be found by summing the frequencies of all inward transitions. This frequency is equivalent to the frequency of visits to a particular state. For the system in Figure 8-2, the frequency of visits of state 4 is P2(t)λ2+P3(t)λ1.

Under steady-state conditions, the frequency of inward transitions is equivalent to the frequency of outward transitions. This information can be used to find steady-state probabilities (also availability) as well as system MTBF.