For a given initiating event, a system has two hazard barriers, shown below $($note that $x$ is shown with a reliability block diagram while $Y$ has a fault tree$).$ After an initiating event, if barrier $x$ succeeds, the system is safe. If both barriers fail, then an undesirable consequence occurs $(100$ injuries$).$ If barrier X fails, but barrier Y succeeds, the consequence is less severe $(10$ injuries$).$ Draw the event tree for this situation $($label all sequences and consequences$).$ Find the minimum cut sets for each scenario.

For the situation described in problem $1$: if the frequency of the initiating event is $0\mathrm{.}25/$year$,$ calculate the system risk.

Still for the situation described in problem $1$: calculate the Birnbaum, Risk Achievement Worth, Risk Reduction Worth and Fussell$-$Vessely Importance Measures for components A$,$ B$,$ C$,$ and D$.$

Assume a system $($not the system in problem $1!)$ has three components: X$,$ Y$,$ Z$.$ If the rank order uncertainty is given as:

$($:$P(R_x)=1$