Problem $4$

Consider the sequential series system in Figure $2.$ When a condition I $($initiating event$)$ exists, $x$ is activated

first, followed by $Y,$ and then $Z.$ When this exact sequence successfully occurs, the sequential system properly

responds to the initiating condition; otherwise, the system may be considered failed.

Figut $2.$ Dequenial seItes system.

a$)$ Draw an event tree $($events I,$x,Y,Z)$ that depicts the minimum number of scenarios possible. $(2$p$)$

b$)$ If blocks $x,Y,$ and $Z$ are represented by the reliability block diagrams in Figure $3,$ determine a Boolean

representation of each event scenario in $($a$)$ in terms of $A,B,C,D,$ and $E.(2$p$)$

Y

Figure $3$: Reliability block diagrams for blocks $x,Y$ and $Z.$

c$)$ Let component unavailabilities be $P(A)=P(B)=P(C)=0\mathrm{.}01,$ and $P(D)=P(E)=0\mathrm{.}005.$ Quantify

the system unavailability. You can use the rare event approximation if appropriate. Basic events

$A,B,C,D,$ and $E$ are assumed independent. $(2$p$)$