Flash Fire
Jet Fire
Pool Fire
PFDavg
Without common causes With common causes (Beta factor)
1oo1
DU
TI
λ×2
-
1oo2
1oo2D
12
2
DU DU
TI
λ×λ×3
()
()
()
⎡⎤
⎣⎦
2
DU DU
1-β×λ×TI β×λ×TI
+
32
1oo3
123
3
DU DU DU
TI
λ×λ×λ×4
()
()
()
⎡⎤
⎣⎦
3
DU DU
1-β×λ×TI β×λ×TI
+
42
2oo2
()
12
DU DU
TI
λ+λ×2
()
()
()
⎡⎤
⎣⎦
DU
DU
β×λ×TI
1-β×λ×TI + 2
2oo3
()
()
()
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
12 13
23
2
DU DU DU DU
DU DU
λ×λ+λ×λTI
×3
+λ×λ
()
()
()
⎡⎤
⎣⎦
2DU
DU
β×λ×TI
1-β×λ×TI + 2
Simplified equations
1oo1
(Et ≠ 100%)
()
⎡⎤
⎛⎞
⎢⎥
⎜⎟
⎝⎠
⎣⎦
DU
TI SL
λEt × + 1-Et
22
TI: Proof Test time interval
Et: Test Effectiveness
λDU: dangerous undetected failures
AVERAGE PROBABILITY OF FAILURE ON DEMAND (PFDAVG)
SIL
Safety
Integrity
Level
PFDavg
Average probability of
failure on
demand per year
(low demand)
RRF
Risk
Reduction
Factor
PFDavg
Average probability of
failure on
demand per hour
(high demand)
SIL 4 ≥ 10-5 and < 10-4 100000 to 10000 ≥ 10-9 and < 10-8
SIL 3 ≥ 10-4 and < 10-3 10000 to 1000 ≥ 10-8 and < 10-7
SIL 2 ≥ 10-3 and < 10-2 1000 to 100 ≥ 10-7 and < 10-6
SIL 1 ≥ 10-2 and < 10-1 100 to 10 ≥ 10-6 and < 10-5
SIL LEVELS ACCORDING IEC 61508 / IEC 61511
RISK IS
NEGLIGIBLE
Tolerable only if further
risk reduction
is impracticable or if its cost are
grossly disproportional to the gained
improvement.
As the risk is reduced, the less
proportionately, it is necessary to
spend to reduce it further,
to satisfy ALARP.
The concept of diminishing
proportion is shown by the triangle.
The ALARP or
tolerability Region
Risk is undertaken only if
a benefit is desired
Intolerable Region
Risk cannot be justified except
in extraordinary circumstances
Broadly Acceptable
Region
No need for detailed working
to demonstrate ALARP
It is necessary to maintain
assurance that risk remains
at this level
TOLERABLE RISKS AND ALARP (ANNEX ‘B’)
SAFETY INTEGRITY LEVEL CALCULATION
INCREASING RISK
Residual
Risk
Tolerable
Risk
EUC Risk
Necessary risk reduction
Actual risk reduction
Partial risk covered by
other technology
safety-related systems
Partial risk covered by
E/E/PE
safety-related system
Partial risk covered by
external risk
reduction facilities
Risk reduction obtained by all safety-related systems and external risk reduction systems
SFF
Hardware fault
tolerance
0
Hardware fault
tolerance
1
Hardware fault
tolerance
2
TYPE A Components
< 60% SIL 1 SIL 2 SIL3
60% - < 90% SIL 2 SIL 3 SIL 4
90% - < 99% SIL 3 SIL 4 SIL 4
> 99% SIL 3 SIL 4 SIL 4
TYPE B Components
< 60% Not allowed SIL 1 SIL2
60% - < 90% SIL 1 SIL 2 SIL 3
90% - < 99% SIL 2 SIL 3 SIL 4
> 99% SIL 3 SIL 4 SIL 4
Failure rates categories: λDD: dangerous detected; λDU: dangerous undetected
λSD: safe detected; λSU: safe undetected
SAFE FAILURE FRACTION (SFF) AND SIL LEVELS
∑∑∑ ∑
∑∑∑∑ ∑
DD SD SU DU
DD DU SD SU TOT
λ+λ+λλ
=1-
λ+λ+λ+λλ
AVAILABILITY AND RELIABILITY
RISK REDUCTION
Vapor cloud explosion (BLEVE)
S
SAFETY
AFETY:
:
FREEDOM
FREEDOM
FROM
FROM
UNACCEPTABLE
UNACCEPTABLE
RISK
RISK
MTTFs
1oo1
S
1
λ
1oo2
S
1
2λ
2oo2
2
S
1
2λ×MTTR
2oo3
2
S
1
6λ×MTTR
MEAN TIME TO FAILURE SPURIOUS
Fireball
Tolerable accident frequency 1
=
Frequency of accidents without protections RRF
A
1oo1
A
1oo2
B
A
2oo2
B
A
2oo3
B
C
V
o
t
i
n
g
SYSTEM ARCHITECTURES
Basic Concepts:
Acronyms:
MTBF: Mean Time Between Failures
MTTF: Mean Time To Failure
MTTR: Mean Time To Repair
MTBM: Mean Time Between Maintenance
MSD: Expected Mean System Downtime
Failure Rate :
Failures per unit time
λ=Components exposed to functional failure
-9
1 F I T = 1 × 1 0 F a i l u r e s p e r ho u r
MTBF = MTTF + MTTR
MTTF = MTBF- MTTR = 1
λ
Operating Time
Availability
Operating Time + Repair Time
MTTF MTTF μ
=
MTTF + MTTR MTBF μ+λ
MTBM
MTBM + MSD
==
===
=
λ
Unavailability = 1- Availability = μ
Failure time
Time
TTF
t
1
0
Operating time
Reliability
Success
MTBF
MTTF MTTR
Repair
time
(failure)
Success Failure
UNRELIABILITY
UNAVAILABILITY
RELIABILITY
AVAILABILITY
MTTR
MTTF
Quantitative Method for SIL level determination
As found in IEC 61508 Annex ‘C’
Process and
process
control system
Consequence
of Hazardous
Event
Frequency
of Hazardous
Event
Process
Risk
Tolerable
Risk Target
Non-SIS
prevention /
mitigation
protection
layers
SIS
Other
protection
layers
Necessary Risk Reduction
Safety integrity of non-SIS prevention/
mitigation protection layers, other pro-
tection layers, and SIS matched to the
necessary risk reduction
IEC
IEC
61508
61508
IEC
IEC
61511
61511
UNDERSTANDING
UNDERSTANDING
S
SAFETY
AFETY
I
INTEGRITY
NTEGRITY
L
LEVELS
EVELS
ITALY
G.M. INTERNATIONAL S.R.L
Via San Fiorano, 70
20058 Villasanta (MI)
Tel: +39 039 2325038
Fax: +39 039 2325107
info@gmintsrl.com
www.gmintsrl.com
RUSSIA
Serpukhovsky Val 8, Office 10
115191 Moscow
Tel: +7 495 950 5779
Fax: +7 495 952 1006
info@gminternational.ru
www.gminternational.ru
UNITED STATES OF AMERICA
GM International Safety Inc.
17453 Village Green Drive
Houston, TX 77040
Tel: +1 713 896 0777
Fax: +1 713 896 0782
info@gmisafety.com
www.gmisafety.com
