CDOIF Guidance

139 / 648

Safety and environmental standards for fuel storage sites
Final report
137
Annex 3 PFD(avg) calculation and influence of loop architecture
39 In these examples assumptions and failure rate data used in this annex are fictitious and any
similarity to values used in industry is coincidental, thus the values used should not be taken from
this guide and used for PFD calculations. The values used are to demonstrate the use of the
example calculation method.
Average probability of failure on demand (for a low demand mode of operation)
40 The following is one example of how the average probability of failure on demand of a safety
function for a given system may be derived and is based upon Annex B in BS EN 61508-6.
41 The average probability of failure on demand of a safety function for a given system is
determined by calculating and combining the average probability of failure on demand for all the
subsystems which together provide the safety function. Since the probabilities are likely to be
small, this can be expressed by the following:
Where is the average probability of failure on demand of the system
is the average probability of failure on demand of the sensor
is the average probability of failure on demand of the logic solver
is the average probability of failure on demand of the final element
42 If the safety function depends on more than one voted group of sensors or actuators, the
combined average probability of failure on demand of the sensor or final element subsystem,
PFDs or PFDFE, is given in the following equations, where PFDGi and PFDgj is the average
probability of failure on demand for each voted group of sensors and final elements respectively:
1oo1 architecture
43 For the example given in Figure 37 (1oo1 architecture) it can be shown that the average
probability of failure on demand for a system with a very low failure rate is:
∑
=
i
S PFD Gi PFD
∑
=
j
FE PFD Gj PFD
( ) CE DD DU oo G t PFD λ λ + =
)11(
CE D t
× = λ
MTTR MTTR T
DD DU × + + = λ λ
2
1
MTTR MTTR T t
D
DD
D
DU
CE × + + = λ
λ
λ
λ
2
1
FE LS S SYS PFD PFD PFD PFD + + =
FE LS S SYS PFD PFD PFD PFD
FE LS S SYS PFD PFD PFD PFD + + =
FE LS S SYS PFD PFD PFD PFD
FE LS S SYS PFD PFD PFD D + + =
FE LS S SYS PFD PFD PFD D
FE LS PFD PFD + +
FE LS S PFD PFD FD
FE LS S SYS PFD PFD PFD PFD + + =
FE LS S SYS PFD PFD PFD PFD