Safety analysis on a Markov graph Consider the graph in Figure 7.22. From the initial state 1 which represents a behavior without fault, the system degrades with the appearance of faults; it evolves towards the states 2, 3 and 4 which are failing states. On the contrary, protective and repair mechanisms are going to make the system evolve towards better states, for example the state 3 towards the state I! The arcs between states indicate the hourly rate of evolution (probabilities): pI, p2, p3, p4 for the degradations and rI, r2 for the corrections and repairs.

Study the evolution of the graph from state 1 towards state 4 which is here supposed to be catastrophic.

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p1 3 1 rl p2 r2 2 p4 13 p3 4 Figure 7.22. Markov graph