Rockwell Automation 1715-OF8I Redundant I/O System User Manual - Manual (Page 290)

290 Rockwell Automation Publication 1715-UM001C-EN-P - March 2014
Appendix E PFD and PFH Calculations for a SIL 2 System
Calculations for 1715 I/O
Modules
For the calculations presented in this chapter, these values were used as the two
application-dependent variables:
• Proof test interval (T
1
) is listed for each table
• Mean time to repair (MTTR) is listed for each section
• 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. Refer to IEC 61508, Part 6, for more information
about calculating PFD values for your system.
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
1oo1 Configuration
STR
1oo1
= Spurious Trip Rate = λ
s +
λ
dd
PFD
1oo1
= (λ
dd
+ λ
du
) x T
ce
PFH
1oo1
= λ
du
1oo2 Configuration
STR
1oo2
= Spurious Trip Rate = 2 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
PFD
2oo2
= 2 x (λ
du
+ λ
dd
) x T
CE
PFH
2oo2
= 2 x λ
du
x T
CE
1oo2D Configuration
T
CE
' = (λ
du
x (T 1 /2 + MRT) + ((λ
dd
+ λ
s d
) x MTTR)) / (λ
du
+ λ
dd
+ λ
s d
)
TGE' = (λ
du
x (T1/3 + MRT) + ((λ
dd
+ λ
s d
) x MTTR)) / (λ
du
+ λ
dd
+ λ
s d
)
PFD 1oo2D = 2 x ((1-ß) x λ
du
) x ((1-ß
D
) x λ
dd
+ (1-ß) x λ
du
+ λ
s d
) x T
CE
x T
GE
+ (ß
D
x λ
dd
x MTTR) + (ß x λ
du
x (T 1 /2 + MRT))
PFH 1oo2D = 2 x (1-ß) x λ
du
x ((1-ß
D
) x λ
dd
+ (1-ß) x λ
du
+ λ
s d
) x T
CE
' + ß x λ
du