Pfd Calculations With 24-Hour Mttr - Rockwell Automation Allen-Bradley 1715-AENTR User Manual

Appendix D PFD and PFH Calculations for a SIL 2 System
Table 60 - PFD Calculations for 1715 I/O Components
Firmware
Cat No.
Version
1715-AENTR A 3.003
1715-IB16D A 3.001
274
• 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
Common Terms
λ = failure rate = 1/MTBF
λ
= rate of safe failures
s
λ = rate of dangerous failures = (λ
d
λ = dangerous, detected failure rate = λ
dd
λ = dangerous, undetected failure rate = λ
du
SFF = safe failure fraction =(λ
= channel equivalent down time = λ
T
CE1oo1
DC = diagnostic coverage
1oo2 Configuration (For energize to action: Dual 1715-OB8DE or 1715-OF8I)
STR = Spurious Trip Rate = 2 x (λ
1oo2
T = system equivalent down time = λ
GE1oo2
PFD = 2 x [(1-ß
1oo2
PFH = 2 x [(1-ß
1oo2
2oo2 Configuration (For de-energize to trip: Dual 1715-OB8DE or 1715-OF8I)
STR = Spurious Trip Rate = 2 x (λ
2oo2
PFD = 2 x PFD
2oo2
PFH = 2 x PFH
2oo2
1oo2D Configuration (Dual configuration of 1715-AENTR, 1715-IB16D, or 1715-IF16)
STR = Spurious Trip Rate = 2 x (λ
1oo2D
T ' = (λ x (T
1
CE du
T ' = T1/3 + MRT
GE
= 2 x (1-ß) x λ
PFD
1oo2D
PFH = 2 x (1-ß) x λ
1oo2D
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 specific to1715 I/O components in ControlLogix® systems.
Description
(1)
Ethernet adapter redundant module
16-channel digital input module
Rockwell Automation Publication 1715-UM001J-EN-P - December 2020
+ λ )
du dd
x DC
d
x (1-DC)
d
+ λ )/(λ + λ +λ )
s dd s du dd
/λ x (T /2 + MRT) + (λ
du d 1
λ
) + ß x (λ
s + dd
λ x (T
du/ d
2
) x λ + (1-ß) x λ
] x T x T + (ß
D dd du CE GE
) x λ + (1-ß) x λ ] x (1-ß) x λ
D dd du du
λ ) x (λ λ
s + dd s +
1oo1
1oo1
λ
) x (λ
s + dd s +
/2 + MRT) + ((λ λ x MTTR)) / (λ
+ )
s du
dd d
x ((1-ß) x λ ) x λ λ
+ (1-ß
+
D
du du dd
((1-ß) x λ + (1-ß ) x λ λ
x +
D
du du dd
Table 60 are calculated for a 20-year mission time and
Simplex Configuration
PFDde
—
6.44E-05
/λ x MTTR)
dd d
λ
)
s + dd
/3 + MRT) + (λ λ x MTTR)
1 dd/ d
x λ x MTTR) + ß x λ
x (T /2 + MRT)
D dd du 1
+ ß x λ
x T
CE du
) x MTTR + ß x (λ λ )
dd s + dd
λ λ
) x MTTR + ß x (λ )
dd s + dd
+ λ + λ )
dd s
d
' + 2 x (1 - K) x λ x ' + (ß x λ
) x T ' x T T
s
d CE GE dd CE
'
) x T + 2 x (1 - k) x λ + ß x λ
s
d CE dd du
Duplex Configuration
PFDe PFDde
— 1.26E-05
8.67E-05 8.37E-06
x (T /2 + MRT))
1
du
PFDe
1.96E-05
1.27E-05