Nuclear Engineering Problem Please Help Probability during

Nuclear Engineering Problem, Please Help! : Probability during station blackout:

In a station blackout (SBO), all AC power is lost. In such an event, Catawba Nuclear Station has a Standby Shutdown Facility (SSF) that has a small auxiliary diesel generator that can power minimal instrumentation and controls, such that hot standby conditions can be maintained for 72 hours with operator actions to allow for restoration of AC power either from offsite power or from emergency diesel generators. Under SBO conditions, what is the probability of core damage, given the following assumptions? Probability of proper startup and operation of the SSF diesel generator is 0.9. Probability of proper startup and operation of the standby makeup pump for the \"feed\" portion of RCS feed-and-bleed operation is 0.95. Probability of proper operation of the reactor vessel head vents for the \"bleed\" portion of RCS feed-and-bleed operation is 0.99. Probability of proper operation of the turbine-driven auxiliary feed water pump for the input portion of maintenance of secondary heat sink is 0.85. Probability of proper operation of the main steam safety valves for the output portion of maintenance of secondary heat sink is 0.995.

Solution

Under SBC conditions, the core gets damaged only when all the startups and operations of the auxiliary equipment fail to happen.

Hence the probability that the core does not get damaged = Probability of proper startup and operation of all the auxiliary equipment

Let us suppose the assumptions given in the problem are represented by events A, B, C, D, E

Then Probability that all the 5 events take place simultaneosly = P_A * P_B * P_C * P_D * P_E

= 0.9 * 0.95 * 0.99 * 0.85 * 0.995

= 0.716

The probability that these events won\'t happen simultaneously = 1 - 0.716 = 0.284