(BOUNDARY CONDITIONS) SPLIT FRACTIONS (BOUNDARY CONDITIONS)

REASONS FOR FAILURE There are three primary reasons for component failure: Random failure (handled in fault tree) Planned maintenance unavailability (see last time) Lack of needed support (as the result of another failure earlier in the same event tree) Lack of needed support is handled in the event trees: Through the development of different split fractions or boundary conditions The methods are the same as for maintenance 2

BOUNDARY CONDITIONS Consider a system with two motor-driven pumps (MD) and one turbine-driven pump (TD) AFW MD1 MD2 TD3 Alignments: Normal Maint. on MD1 Maint. on MD2 Maint. on TD3 Boundary Condition No power to MD1 Probabilities based on product of maintenance frequency and duration Any one split fraction must consider all possible maintenance alignments: There is no way to know which alignment the plant will be in at the time of an accident! 3

GUARANTEED SUCCESS vs. GUARANTEED FAILURE Boundary conditions can involve either: Guaranteed failure (GF), or Guaranteed success (GS) GF generally means lack of needed support –e.g.: Loss of electric power (EP) Loss of service water GS usually means a system/component is not needed: Due to successes of other systems in the event tree 4

GF EXAMPLE: Start with Maintenance Model Normal Alignment 1∩3 1∩4 2∩3 2∩4 Maintenance on 1 3 4 on 3 1 2 Normal Alignment 1∩3 1∩4 2∩3 2∩4 Maintenance on 1 3 4 on 3 1 2 Normal Alignment 1∩3 1∩4 2∩3 2∩4 Maintenance on 1 3 4 on 3 1 2 Normal Alignment 1∩3 1∩4 2∩3 2∩4 Maintenance on 1 3 4 on 3 1 2 1 2 3 4 (P1P3 + P1P4 + P2P3 + P2P4) P(normal) + (P3 + P4) P(maintenance on 1) + (P1 + P2) P(maintenance on 3) Consider several sets of boundary conditions: GF of 1 GF of 3 GF of 1 and 3 (P3 + P4) [P(normal) + P(maintenance on 1)] + 1 P(maintenance on 3) (P1 + P2) [P(normal) + P(maintenance on 3)] + 1 P(maintenance on 1) 1 [P(normal) + P(maintenance on 1) + P(maintenance on 3)] = 1 5

GUARANTEED SUCCESS vs. GUARANTEED FAILURE Consider a plant in which either main feed water (MFW) or AFW can accomplish the same function Boundary conditions for AFW are: Success (or failure) of MFW (Success or) failure of EP to AFW EP to AFW MFW AFW GS Function is provided by MFW GS Function is provided by MFW (loss of EP to AFW is irrelevant) GF AFW is GF, due to loss of EP 6

GS EXAMPLE: Start with Maintenance Model Normal Alignment 1∩3 1∩4 2∩3 2∩4 Maintenance on 1 3 4 on 3 1 2 Normal Alignment 1∩3 1∩4 2∩3 2∩4 Maintenance on 1 3 4 on 3 1 2 1 2 3 4 (P1P3 + P1P4 + P2P3 + P2P4) P(normal) + (P3 + P4) P(maintenance on 1) + (P1 + P2) P(maintenance on 3) Boundary condition: GS of 2 (P1P3 + P1P4) P(normal) + (P3 + P4) P(maintenance on 1) + P1 P(maintenance on 3) 7

The answer depends on the reasons for GF and GS GS vs. GF What happens if GF due to maintenance combines with GS due to boundary conditions: Or vice versa? The answer depends on the reasons for GF and GS In general, GS will dominate—for example: GF due to maintenance, combined with GS because the function is not needed  GS GS because a valve is locked in desired position, combined with GF due to loss of EP  GS However, GF can dominate in some situations 8