Consider a system, the operation of which obeys the following reliability block diagram: Give - in the most efficient way - the expression of the system availability A(t) as a function of the individual availabilities Ai(t),i=1..9, of the components, which are assumed to be independent. Pivot method: if E7 working, bridge system with bottom-right component replaced by E4//E6, in series with E8//E9; if E7 failed: - E5 failed: bridge system again with E1-E3 as top-left component and E6-E9 as bottomright component - E5 working: E1//E2 in series with a block with two parallel lines: (E3//E4)-E8 and E6-E9 What does this assumption of independence imply, both for the operation of the system and from a logistic standpoint? Using the previous calculation, derive the minimal cutsets and minimal paths of this system. Based on those two sets: Give two alternative equivalent reliability block diagrams. Give the Esary-Proschan bounds on the system availability. Explain why one of them is an upper bound, and why the other one is a lower bound