1. (BOUNDARY CONDITIONS)
SPLIT FRACTIONS
(BOUNDARY CONDITIONS)

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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