4.3 Repairable Hierarchical System
For HSs with components subject to independent repair, a separable approach similar to that in Section 4.2 is combined with the Markov method for the system availability analysis [2] .
The possible states for each component A located at layer i of a repairable HS include: operational state (AiO), covered failure state (AiC), layer i UF state (AiUi), layer (i + 1) UF state (

Figure 4.7 CTMC for component A at layer i [2] .
Solving the CTMC of Figure 4.7 , the state occupation probability for each state P(AiO), P(AiC), P(AiUi), P(AiUi + 1), ..., P(AiUL) can be obtained. The separable approach presented in Section 4.2 can then be similarly applied to separate the consideration of layer i UF from the combinatorics of the solution to evaluating the unavailability of a...