Problem $2$

An event tree in a probabilistic risk assessment model for a nuclear power plant is given in Figure $1.$

The initiating event in the event tree is a transient event. Speciffcally, it is a n u nscheduled turbine

trip. The engineered safety features needed to respond to this initiating event include the reactor protection

system, the main feedwater system, and the auxiliary feedwater system. The frequency of this initiating

event is $p_1=\frac{0\mathrm{.}1}{?}$ year. The probability of the failure of main feedwater system is $p_3=1{10}^{-2}.$ The

probabilities of the failures of the reactor protection system and the auxiliary feedwater system $($i$.$e$,$ p$2$

and $p_4,$ respectively$)$ are calculated using fault tree. The fault trees for the failures of these two engineered

safety features $($i$.$e$.,$ reactor protection system and auxiliary feedwater pump$)$ are shown in Figures $2$ and $3,$

respectively.

${?}^1$ Link to The Seattie Times news article.

${?}^2$ Link to the Wikipedia page.

Figure $1$: The event tree used in homework assignment $1.$

$T_1$ : The reactor protection

system fails to trip the reactor

$$

The probabilities of the events in the fault tree for the failure of the reactor protection system are:

$P(C_1)=1{10}^{-3},P(D_1)=2{10}^{-4},$ and $P(E_1)=1{10}^{-2}.$ Assuming independence between events, we

have

$p_2=P(T_1)=P(A_1{B}_1)=P((C_1{D}_1)(E_1{D}_1))$

$=P((C_1{E}_1)(C_1{D}_1)(D_1{E}_1)D_1)$

$=P((C_1{E}_1)D_1)$

$=P(C_1{E}_1)+P(D_1)-P(C_1{E}_1{D}_1)$

$=P(C_1)P(E_1)+P(D_1)-P(C_1)P(E_1)P(D_1)$

The probabilities of the events in the fault tree for the failure of the auxiliary feedwater system are:

$P(A_2)=1{10}^{-4},P(B_2)=1{10}^{-4},$ and $P(C_2)=2{10}^{-3}.$ Assuming independence between events, we

have

$p_4=P(T_2)=P(A_2{B}_2{C}_2)$

$=P(A_2)+P(B_2)+P(C_2)-P(A_2)P(B_2)-P(A_2)P(C_2)-P(B_2)P(C_2)+P(A_2)P(B_2)P(C_2).$

Question $2-1$: Given the information above, calculate the risk corresponding to the tran$-$

Figure $3$: The fault tree for the failure of the auxiliary feedwater system.

sient event $($i$.$e$.,$ turbine trip$)$ in terms of the frequency of CD $($i$.$e$.,$ core damage$)P(CD).$

Question $2-2$ : In the probabilistic risk assessment model, there are two human errors or human failure

events: $E_1($in the fault tree for the failure of the reactor protection system$)$ and $C_2($in the fault tree for the

failure of the auxiliary feedwater system$).$ For each of the two human errors, calculate its contribution to the

system risk in terms of the difference $\frac{?}{{?}_{\frac{?}{?}}P(CD)}$ between the system risk when the nominal probability of that

human error is used and the system risk when that human error does not occur $($i$.$e$.,$ the probability of that

single human error is $0).$ This calculation should be done separately for $E_1$ and $C_2.$