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Rockwell Automation Publication 1715-UM001J-EN-P - December 2020
Appendix D PFD and PFH Calculations for a SIL 2 System
•
PFDde = Probability of failure on demand for de-energize to action
systems
•
PFDe = Probability of failure on demand for energize to action systems
•
SFFde = Safe failure fraction for de-energize to action systems
•
SFFe = Safe failure fraction for energize to action systems
•
PFHde = Probability of failure per hour for de-energize to action systems
•
PFHe = Probability of failure per hour for energize to action systems
PFD and PFH values in this manual are calculated with formulas explained in
IEC 61508, Part 6, Annex B. See IEC 61508, Part 6, for more information about
calculating PFD values for your system.
PFD Calculations with 24-hour MTTR
The PFD calculations in
are calculated for a 20-year mission time and
are specific to1715 I/O components in ControlLogix® systems.
Common Terms
λ
= failure rate = 1/MTBF
λ
s
= rate of safe failures
λ
d
= rate of dangerous failures = (
λ
du
+
λ
dd
)
λ
dd
= dangerous, detected failure rate =
λ
d
x DC
λ
du
= dangerous, undetected failure rate =
λ
d
x (1-DC)
SFF = safe failure fraction =(
λ
s
+
λ
dd
)/(
λ
s
+
λ
du
+
λ
dd
)
T
CE1oo1
= channel equivalent down time =
λ
du
/
λ
d
x (T
1
/2 + MRT) + (
λ
dd
/
λ
d
x MTTR)
DC = diagnostic coverage
1oo2 Configuration (For energize to action: Dual 1715-OB8DE or 1715-OF8I)
STR
1oo2
= Spurious Trip Rate = 2 x (
λ
s +
λ
dd
) + ß x (
λ
s +
λ
dd
)
T
GE1oo2
= system equivalent down time =
λ
du/
λ
d
x (T
1
/3 + MRT) + (
λ
dd/
λ
d
x MTTR)
PFD
1oo2
= 2 x [(1-ß
D
) x
λ
dd
+ (1-ß) x
λ
du
]
2
x T
CE
x T
GE
+ (ß
D
x
λ
dd
x MTTR) + ß x
λ
du
x (T
1
/2 + MRT)
PFH
1oo2
= 2 x [(1-ß
D
) x
λ
dd
+ (1-ß) x
λ
du
] x (1-ß) x
λ
du
x T
CE
+ ß x
λ
du
2oo2 Configuration (For de-energize to trip: Dual 1715-OB8DE or 1715-OF8I)
STR
2oo2
= Spurious Trip Rate = 2 x (
λ
s +
λ
dd
) x (
λ
s +
λ
dd
) x MTTR + ß x (
λ
s +
λ
dd
)
PFD
2oo2
= 2 x PFD
1oo1
PFH
2oo2
= 2 x PFH
1oo1
1oo2D Configuration (Dual configuration of 1715-AENTR, 1715-IB16D, or 1715-IF16)
STR
1oo2D
= Spurious Trip Rate = 2 x (
λ
s +
λ
dd
) x (
λ
s +
λ
dd
) x MTTR + ß x (
λ
s +
λ
dd
)
T
CE
' = (
λ
du
x (T
1
/2 + MRT) + ((
λ
dd
+
λ
s
d
)
x MTTR)) / (
λ
du
+
λ
dd
+
λ
s
d
)
T
GE
' = T1/3 + MRT
PFD
1oo2D
= 2 x (1-ß) x
λ
du
x
((1-ß) x
λ
du
+ (1-ß
D
) x
λ
dd
+
λ
s
d
)
x T
CE
'
x T
GE
'
+ 2 x (1 - K) x
λ
dd
x
T
CE
'
+ (ß x
λ
du
x (T
1
/2 + MRT))
PFH
1oo2D
= 2 x (1-ß) x
λ
du
x
((1-ß) x
λ
du
+ (1-ß
D
) x
λ
dd
+
λ
s
d
) x T
CE
'
+ 2 x (1 - k) x
λ
dd
+ ß x
λ
du
Table 60 - PFD Calculations for 1715 I/O Components
Cat No.
Ser
ies
Firmware
Version
(1)
Description
Simplex Configuration
Duplex Configuration
PFDde
PFDe
PFDde
PFDe
1715-AENTR
A
3.003
Ethernet adapter redundant module
—
—
1.26E-05
1.96E-05
1715-IB16D
A
3.001
16-channel digital input module
6.44E-05
8.67E-05
8.37E-06
1.27E-05