6.9 Bow Tie Analysis

6.
9 BOW TIE ANALYSIS 611
The software (BQR) considers also an inspection each 8760 h, which achieves the PDF of 4.46E-4.
This PDF represents SIL level 3 over 10 years.
6.9 BOW TIE ANALYSIS

Bow tie analysis is the newest quantitative risk analysis and has been in use since the 1970s. It was
incorporated by the Shell Oil Company into hazards management at the beginning of the 1990s.
Bow tie analysis includes FTA, ETA, and LOPA concepts and allows reliability engineers to assess
all combinations of events from incident causes to incident consequences for the layers of protection
that prevent accidents and mitigate consequences. Such methodology can be used to assess different
types of problems, but in safety terms this type of analysis is used to assess and support accident
analysis, process hazards, and perform risk management.
An example of bow tie analysis is an incident of gas release from a pipeline, as shown in Fig. 6.48.
On the left side of the bow tie are all the causes of the incident and on the right side are all the
consequences. In bow tie analysis, events are as follows:
• Potential causes (material quality, corrosive product, corrosion, vehicle accident, material drop,
seismic effect, and pipeline disruption);
• Control measures (inspection, safety procedures, behavior audit, and geology analysis);
• Loss of control (pipeline gas leakage);
• Recovery measures (alarm, SIF, and emergency teams);
• Consequences (toxic gas release, jet fire, explosion, and fire ball).
Material
Quality
Co rrosion Inspection
Toxic
Corrosive Emergency Gas
Product Team Release
Vehicle Safety
Accident Procedures
Emergency Jet
Team Fire
Pipeline Valve
Pipeline
OR Gas Alarm Closed
Disruption
Leakage (SIF)
Material Behavior
Emergency
Drop Audit Explosion
Team
Seismic Geology Analysis Emergency Fire Ball

Effect on Pipeline Project Team
FIGURE 6.48
Pipeline gas leak (bow tie).
612 CHAPTER 6 RELIABILITY AND SAFETY PROCESSES
As shown in Fig. 6.49, bow tie analysis can be a combination of FTA and ETA for layers of
protection. In a pipeline gas leak, the potential causes are corrosion, pipeline disruption, and seismic
effect.
Corrosion can be caused by inappropriate material quality in the pipeline or corrosive products in
the pipeline, which do not meet pipeline specifications.
As a control measure to avoid corrosion, it is necessary to perform inspections periodically.
Pipeline disruption can be caused by vehicle accidents or material drops on the pipeline. As a
control measure to avoid vehicle accidents it is necessary to follow traffic safety procedures. The
control measure to avoid material drop on a pipeline when equipment or material are being moved
around the pipeline area is to perform a behavior audit to verify that safety procedures are being
conducted.
Seismic effect is another potential cause of accidents and the control measure is to perform
geology analysis in the project phase to verify that the pipeline is in an area that is not subject to
seismic effects.
If one of the main potential causes happens, that is, corrosion, pipeline disruption, or seismic effect
of the pipeline, the incident of a pipeline gas leak may occur. If the incident occurs, there are four
Material
Quality
OR
Corrosive Corrosion
Product
Inspection Toxic
Emergency Gas
Team Release
Vehicle
Traffic
AND Emergency Jet

Team Fire
Safety Pipeline Valve
Procedure Pipeline Gas Alarm Closed
OR
Disruption Leakage (SIF)
Material Emergency
Movement Team Explosion
AND
Behavior
Audit Emergency Fire Ball
Team
Seismic
Effect
AND
Geology Analysis
on Pipeline Project
FIGURE 6.49
Pipeline gas leak (bow tie). Bow tie, FTA þ ETA: Pipeline gas leakage.
6.9 BOW TIE ANALYSIS 613
probable consequences: toxic gas release, jet fire, explosion, or fire balls. Thus some recovery mea-
sures exist to avoid the accident, which are an alarm and SIF. With an alarm an operation emergency
response is required, but if an SIF is used the valve will block the pipeline feed and reduce the amount
of gas release.
To mitigate toxic gas release, jet fire, explosion, and fire ball consequences, emergency teams try to
evacuate the vulnerable areas before some of the consequences occur. In addition, whenever possible
the emergency team tries to eliminate ignition sources.
In most cases, bow tie analysis is performed qualitatively to assess an accident or incident, but
when performing quantitatively it is a good tool because it includes most quantitative risk analysis
methodology concepts and calculates the final event consequence probabilities.
In this case, depending on bow tie configuration, control measures can be taken into account in the
fault tree logic when performing bow tie configuration, as shown in Fig. 6.49.
No matter what the bow tie configuration is in Fig. 6.48, the control measure probability of failure
will be multiplied for fault tree logic gate results. For example, in the corrosion case in Fig. 6.48, the
probability of corrosion will be:
PðcorrosionÞ ¼ PðMaterial QualityÞ W PðCorrosive productÞ
¼ PðMaterial QualityÞ þ PðCorrosive productÞ PðMaterial QualityÞ
PðCorrosive productÞ
Actually, in this case the value of P(corrosion) will be multiplied per P(inspection) before calcu-
lating the logic gate “OR,” which gives the value of the pipeline gas leak.
In Fig. 6.49 the probability of corrosion is calculated by:
PðcorrosionÞ ¼ PðMaterial QualityÞ W PðCorrosive productÞ X PðInspectionÞ
¼ ðPðMaterial QualityÞ þ PðCorrosive productÞ PðMaterial QualityÞ
PðCorrosive productÞÞ PðInspectionÞ
6.9.1 TIME-INDEPENDENT BOW TIE ANALYSIS

If the final probability consequence results of the bow tie diagram are needed, it is necessary to
consider the values of probability of potential causes, control measures, and recovery measures. To
make this process easier it is best first to calculate the left side of the bow tie diagram and define the
incident probability and then calculate the right side and define the consequence probability. For the
bow tie diagram in Fig. 6.49 the values of probability for potential causes and control measures are:
Pðmaterial qualityÞ ¼ 0:1
Pðcorrosive productÞ ¼ 0:2
PðinspectionÞ ¼ 0:01
Pðvehicle trafficÞ ¼ 0:3
Pðsafety proceduresÞ ¼ 0:01
Pðmaterial movementÞ ¼ 0:1

Pðbehavior auditÞ ¼ 0:005
Pðseismic effectÞ ¼ 0:005
Pðgeology analysis on pipelineÞ ¼ 0:001
Thus the pipeline gas leak probability will be:
PðPipeline Gas LeakageÞ ¼ ðPðCorrosionÞ W PðPipeline DisruptionÞ W PðSeismic effectÞÞ
¼ PðCorrosionÞ þ PðPipeline DisruptionÞ þ PðSeismic effectÞ
ðPðCorrosionÞ PðPipeline DisruptionÞÞ ðPðCorrosionÞ PðSeismic effectÞÞ
ðPðPipeline DisruptionÞ PðSeismic effectÞÞ.
To make the probability calculations easier, calculate each partial probability first and then sub-
stitute the probability values in the previous equation. Thus we have:
¼ PðCorrosionÞ þ PðPipeline DisruptionÞ þ PðSeismic effectÞ ðPðCorrosionÞ
PðPipeline DisruptionÞÞ ðPðCorrosionÞ PðSeismic effectÞÞ ðPðPipeline DisruptionÞ
PðSeismic effectÞÞ.
To make the probability calculation easier it is necessary to calculate each partial probability first
and after substitute probabilities values in the previous equation. Thus we have:
PðCorrosionÞ ¼ ½PðMaterial QualityÞ W PðCorrosive productÞ X PðInspectionÞ
¼ ½PðMaterial QualityÞ þ PðCorrosive productÞ PðMaterial QualityÞ
PðCorrosive productÞ PðInspectionÞ.
¼ ½ð0:1 þ 0:2Þ ð0:1 0:2Þ 0:01 ¼ ½ð0:3Þ ð0:02Þ 0:01 ¼ 0:0028
PðCorrosionÞ ¼ 0:0028
PðPipeline DisruptionÞ ¼ ½PðVehicle TrafficÞ X PðSafety proceduresÞ W ½PðMaterial MovementÞ X
PðBehavior AuditÞ
¼ ½PðVehicle TrafficÞ PðSafety proceduresÞ þ ½PðMaterial MovementÞ PðBehavior AuditÞ

½PðVehicle TrafficÞ PðSafety proceduresÞ ½PðMaterial MovementÞ PðBehavior AuditÞ.
¼ ½ð0:3 0:01Þ þ ð0:01 0:005Þ ½ð0:3 0:01Þ ð0:01 0:005Þ

¼ ½0:003 þ 0:00005 ½ð0:003Þ ð0:00005Þ
¼ 0:00305 0:00000015 ¼ 0:00305
PðPipeline DisruptionÞ ¼ 0:00305
PðSeismic effectÞ ¼ PðSeismic EffectÞ X PðGeology Analysis on pipelineÞ

¼ PðSeismic EffectÞ PðGeology Analysis on pipelineÞ ¼ 0:005 0:01 ¼ 0:00005
PðSeismic effectÞ ¼ 0:00005
Finally, the pipeline gas leak probability is:
PðSeismic effectÞÞ
¼ 0:0028 þ 0:00305 þ 0:00005 ð0:0028 0:00305Þ ð0:0028 0:00005Þ
ð0:00305 0:00005Þ
¼ 0:0059 ð0:00000854Þ ð0:00000014Þ ð0:0000001525Þ ¼ 0:0058:
PðPipeline Gas LeakageÞ ¼ 0:0058
The next step in the bow tie analysis is to calculate the consequences on the right side of the bow tie
diagram. In this case, we consider the following probabilities:
• The probability of alarm failure is 10%.
• The probability of SIF failure is 0.1%.
• The probability the emergency team eliminates all ignition sources is an 80% chance of an
accident being toxic gas release.
• If the emergency team is not able to eliminate the early ignition source the probability is a 10%
chance of an accident scenario being a jet fire.
• When the emergency team is not able to eliminate the ignition source and a toxic cloud enters a
confined place the probability is 1% of an accident scenario being an explosion.
• When the emergency team is not able to eliminate the late ignition source but avoids a toxic cloud
entering a confined place, the probability is a 9% chance of an accident scenario being a fire ball.
In doing so, for the probability of a gas leak, the probabilities of toxic gas release, jet fire, ex-
plosion, and fire balls are:
PðToxic Gas ReleaseÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ
¼ PðPipeline Gas leakageÞ PðAlarmÞ PðSIFÞ Pðemergency teamÞ
¼ 0:0058 0:1 0:001 0:8 ¼ 0:000000464
PðToxic Gas ReleaseÞ ¼ 0:000000464
PðJet FireÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ PðSIFÞ X Pðemergency teamÞ
¼ 0:0058 0:1 0:001 0:1 ¼ 0:000000058
PðJet FireÞ ¼ 0:000000058

PðExplosionÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ
¼ 0:0058 0:1 0:001 0:01 ¼ 0:0000000058
PðExplosionÞ ¼ 0:0000000058
PðFire BallÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ
¼ 0:0058 0:1 0:001 0:09 ¼ 0:0000000522
PðFire BallÞ ¼ 0:0000000522
Such consequence probabilities can be used in the qualitative risk analysis, but as we discussed
before, the probability of accidents occurring varies over time, which is the subject of the next section.
6.9.2 TIME-DEPENDENT BOW TIE ANALYSIS

As performed in other risk analysis methodologies, time-dependent bow tie analysis uses CDFs for
events and consequently the probability of failure increases over time based on the CDF. In bow tie
analysis, not all events are described by CDFs because the probability is really constant over time. A
good example of a probability that is constant over time is an event such as emergency team inter-
vention where there is one probability of success or failure based on the number of observations. Some
potential causes, such as poor material quality and poor geology analysis, have similar concepts, that
is, constant probability over time. However, other events or equipment are better represented by CDFs
because of an increased chance of failure over time. Table 6.10 shows the failure rate for each potential
cause, and the control measures and recovery measures related to the bow tie diagram are given in
Fig. 6.49.
The probability of a poor quality of material is constant over time as well as the probability of
failure in geology analysis and the probability of failure in emergency team actions. Thus such events
have a similar probability in 1.5 years (13,140 h) and 5 years (43,800 h). However, the other events
have different failure rates and consequently different probabilities over time based on the CDFs,
which are described by an exponential function, having different values in 1.5 years and 5 years. The
values of the probabilities in 1.5 years are similar to the values found in the static bow tie analysis
example in Section 6.5.1. Thus dynamic bow tie analysis was conducted with probability values for
5 years and compared with values for 1.5 years.
The probability in 5 years (43,800 h) described in the sixth column is defined by:
PðInspectionÞðtÞ ¼ 1 elt ¼ 1 e0:00000001t ¼ 1 e0:00000001ð43800Þ ¼ 0:04

PðVehicle$TrafficÞðtÞ ¼ 1 elt ¼ 1 e0:00000027t ¼ 1 e0:00000027ð43800Þ ¼ 0:7
PðSafety$ProcedureÞðtÞ ¼ 1 elt ¼ 1 e0:00000001t ¼ 1 e0:00000001ð43800Þ ¼ 0:04
PðMateral$MovementÞðtÞ ¼ 1 elt ¼ 1 e0:00000008t ¼ 1 e0:00000008ð43800Þ ¼ 0:30
Table 6.10 Probability Variation Over Time

l(oc/h) t(h) P(1.5 years) t(h) P(5 years)
P(material quality) x 13,140 0.1 43,800 0.1

P(corrosive product) 1.7E-05 13,140 0.2 43,800 0.5
P(inspection) 1E-06 13,140 0.01 43,800 0.04
P(vehicle traffic) 2.7E-05 13,140 0.3 43,800 0.7
P(safety procedures) 1E-06 13,140 0.01 43,800 0.04
P(material movement) 8E-06 13,140 0.1 43,800 0.3
P(behavior audit) 3.8E-07 13,140 0.005 43,800 0.02
P(seismic effect) 3.8E-07 13,140 0.005 43,800 0.02
P(geology analysis on pipeline) x 13,140 0.01 43,800 0.01
P(alarm) 8E-06 13,140 0.1 43,800 0.3
P(SIF) 1E-07 13,140 0.001 43,800 0.004
Emergency team(toxic gas x 13,140 0.8 43,800 0.8
leakage)
Emergency team(jet fire) x 13,140 0.1 43,800 0.01
Emergency team(explosion) x 13,140 0.01 43,800 0
Emergency team(fire ball) x 13,140 0.9 43,800 0.9
PðBehavior$AuditÞðtÞ ¼ 1 elt ¼ 1 e0:0000000038t ¼ 1 e0:0000000038ð43800Þ ¼ 0:02

PðSeismic$EffectÞðtÞ ¼ 1 elt ¼ 1 e0:0000000038t ¼ 1 e0:0000000038ð43800Þ ¼ 0:02
PðAlarmÞðtÞ ¼ 1 elt ¼ 1 e0:00000008t ¼ 1 e0:00000008ð43800Þ ¼ 0:3
PðSIFÞðtÞ ¼ 1 elt ¼ 1 e0:000000001t ¼ 1 e0:000000001ð43800Þ ¼ 0:004
The next step is to substitute the probabilities values from Table 6.10 in the following equations to
find the probability of a pipeline gas leak in 5 years:
PðPipeline DisruptionÞÞ ðPðCorrosionÞ PðSeismic effectÞÞ
ðPðPipeline DisruptionÞ PðSeismic effectÞÞ.
As discussed it is necessary to calculate each partial probability first and then substitute the
probability values in the previous equation. Thus we have:
PðCorrosionÞ ¼ ½PðMaterial QualityÞ W PðCorrosive productÞ X PðInspectionÞ
¼ ½PðMaterial QualityÞ þ PðCorrosive productÞ PðMaterial QualityÞ
PðCorrosive productÞ PðInspectionÞ.
¼ ½ð0:1 þ 0:5Þ ð0:1 0:5Þ 0:04 ¼ ½ð0:6Þ ð0:05Þ 0:04 ¼ 0:022
PðCorrosionÞ ¼ 0:022
PðPipeline DisruptionÞ ¼ ½PðVehicle TrafficÞ X PðSafety proceduresÞ W ½PðMaterial MovementÞ X

PðBehavior AuditÞ
¼ ½PðVehicle TrafficÞ PðSafety proceduresÞ þ ½PðMaterial MovementÞ PðBehavior AuditÞ

½PðVehicle TrafficÞ PðSafety proceduresÞ ½PðMaterial MovementÞ PðBehavior AuditÞ.
¼ ½ð0:7 0:04Þ þ ð0:3 0:02Þ ½ð0:7 0:04Þ ð0:3 0:02Þ

¼ ½0:028 þ 0:006 ½ð0:028Þ ð0:006Þ
¼ 0:034 0:000168 ¼ 0:0338
PðPipeline DisruptionÞ ¼ 0:0338
PðSeismic effectÞ ¼ PðSeismic EffectÞ X PðGeology Analysis on pipelineÞ
¼ PðSeismic EffectÞ PðGeology Analysis on pipelineÞ ¼ 0:02 0:01
¼ 0:0002
PðSeismic effectÞ ¼ 0:0002
Finally, the pipeline gas leakage probability is:
PðSeismic effectÞÞ.
¼ 0:022 þ 0:0338 þ 0:0002 ð0:022 0:0338Þ ð0:022 0:0002Þ ð0:0338 0:0002Þ.
¼ 0:056 ð0:0007436Þ ð0:0000044Þ ð0:00000676Þ ¼ 0:00633:
PðPipeline Gas LeakageÞ ¼ 0:00633
The next step in bow tie analysis is calculating the consequences that are the right side of bow tie
diagram. In doing so, regarding the probability of gas leakage and other events over 5 years, the
probability of toxic gas release, jet fire, explosion, and fire ball are:
PðToxic Gas ReleaseÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ
¼ 0:055 0:3 0:004 0:8 ¼ 0:000528
PðToxic Gas ReleaseÞ ¼ 0:000528
PðJet FireÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ
¼ 0:055 0:3 0:004 0:1 ¼ 0:0000066
PðJet FireÞ ¼ 0:0000066
PðExplosionÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ

¼ 0:055 0:3 0:004 0:01 ¼ 0:00000066
PðExplosionÞ ¼ 0:00000066
PðFire BallÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ
¼ 0:055 0:3 0:004 0:09 ¼ 0:00000594
PðFire BallÞ ¼ 0:00000594
The probability of failure in 5 years is higher for all consequences and it is important to compare
such values in the risk matrix to know if a new value of risk for each consequence is tolerable. To
compare the risk matrix it is necessary to have probability values.
Remember that potential causes, control measures, and recovery measures can be represented in
any kind of CDF (normal, Weibull, lognormal, loglogistic, logistic, Gumbel, gamma, and generalized
gamma) depending on historical data. In this bow tie example, the exponential CDF was used to make
it easier to understand.
Also note that such dynamic reliability analysis can be performed using software. One alternative
to performing bow tie analysis is to use partial analysis starting from the left side of the bow tie to
calculate the incident event by ETA and then go to the right side of the bow tie and calculate the
consequences frequency.
In Table 6.4, if we consider l ¼ 8 106 for material quality and l ¼ 1 106 for geology
analysis of the pipeline, performing Monte Carlo simulation to define the pipeline gas leak we have
l ¼ 4.8 1010 and R(43,800) ¼ 100%. Thus performing the calculation of the left side of the bow tie
the frequency of consequences will be:
FðToxic Gas ReleaseÞ ¼ FðPipeline Gas leakageÞ PðAlarmÞ PðSIFÞ Pðemergency teamÞ
¼ 4:8 1010 0:3 0:004 0:8 ¼ 4:6 1013
FðToxic Gas ReleaseÞ ¼ 4:6 1013
FðJet FireÞ ¼ FðPipeline Gas leakageÞ PðAlarmÞ PðSIFÞ Pðemergency teamÞ
¼ 4:8 1010 0:3 0:004 0:1 ¼ 5:76 1014
FðJet FireÞ ¼ 5:76 1014
FðExplosionÞ ¼ FðPipeline Gas leakageÞ PðAlarmÞ PðSIFÞ Pðemergency teamÞ
¼ 4:8 1010 0:3 0:004 0:01 ¼ 5:76 1015
FðExplosionÞ ¼ 5:76 1015
FðFire BallÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ
¼ 4:8 1010 0:3 0:004 0:09 ¼ 5:2 1015

FðFire BallÞ ¼ 5:2 1015
Fig. 6.50 shows the failure rate function of the pipeline gas leak as a result of simulation.
Each consequence has an individual risk. In the worst case (toxic gas leak) the risk is lower than
1 104. Unless such consequence causes are higher number of deaths (more than 10,000,000) into
operational ground, the individual risk will be intolerable.
Bow tie analysis is a good quantitative risk analysis tool to have a complete idea about potential
incident causes, consequences, and control measures as a whole.
This methodology can qualitatively assess and identify the potential causes, control measures,
recovery measures, and consequences to better understand accidents or even as a risk analysis tool to
find out if a risk is tolerable. In addition, this method can also be used for risk management. In this
case, potential causes, control measures, and recovery measures have to be updated constantly. In
doing so the cut sets for incidents would be highlighted as well as control measures and recovery
measures. As dynamic bow tie analysis gives different values for most events over time, if the bow tie
is updated automatically by software, as shown in Fig. 6.51, it is possible to see the CDF of the incident
and the consequences as well as the risk of each consequence over time to support decisions and better
manage risk.
1E-8 Failure Rate

Fault Tree1
Failure Rate Line
8E-9
Failure Rate, f(t)/R(t)
6E-9
4E-9
2E-9
(43800) = 4.8E-10
0
175,200 350,400 525,600 700,800 876,000
Time, (t)
FIGURE 6.50
Pipeline gas leak failure rate.

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6.

9 BOW TIE ANALYSIS 611

Seismic Geology Analysis Emergency Fire Ball

AND Emergency Jet

6.9.1 TIME-INDEPENDENT BOW TIE ANALYSIS

Pðmaterial movementÞ ¼ 0:1

¼ ½PðVehicle TrafficÞ PðSafety proceduresÞ þ ½PðMaterial MovementÞ PðBehavior AuditÞ

¼ ½ð0:3 0:01Þ þ ð0:01 0:005Þ ½ð0:3 0:01Þ ð0:01 0:005Þ

PðSeismic effectÞ ¼ PðSeismic EffectÞ X PðGeology Analysis on pipelineÞ

PðJet FireÞ ¼ 0:000000058

6.9.2 TIME-DEPENDENT BOW TIE ANALYSIS

PðInspectionÞðtÞ ¼ 1 elt ¼ 1 e0:00000001t ¼ 1 e0:00000001ð43800Þ ¼ 0:04

Table 6.10 Probability Variation Over Time

P(material quality) x 13,140 0.1 43,800 0.1

PðBehavior$AuditÞðtÞ ¼ 1 elt ¼ 1 e0:0000000038t ¼ 1 e0:0000000038ð43800Þ ¼ 0:02

PðPipeline DisruptionÞ ¼ ½PðVehicle TrafficÞ X PðSafety proceduresÞ W ½PðMaterial MovementÞ X

¼ ½PðVehicle TrafficÞ PðSafety proceduresÞ þ ½PðMaterial MovementÞ PðBehavior AuditÞ

¼ ½ð0:7 0:04Þ þ ð0:3 0:02Þ ½ð0:7 0:04Þ ð0:3 0:02Þ

PðExplosionÞ ¼ PðPipeline Gas leakageÞ X PðAlarmÞ X PðSIFÞ X Pðemergency teamÞ

¼ 4:8 1010 0:3 0:004 0:09 ¼ 5:2 1015

1E-8 Failure Rate

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