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Risk analysis of oil and gas pipelines is a difficult task as a result of the complexity of the factors leading to the failure. The uncertainty of the behavior of these products in case of failure of the pipeline adds to the complexity of risk models of such infrastructures. Bow- tie analysis is a new technique for the risk assessment of industrial systems especially the safety analysis of the industrial processes. This technique combines the Fault Tree (FT) with Event Tree (ET) models, which allows the analysis of different scenarios and the estimation of the probability and consequence of failures. Top event of the FT becomes the starting event of an ET.

Figure 2-6 presents a schematic view of the Bow-tie diagrams. The technique has been proved to be advantageous as it simplifies the complicated mechanism of industrial process failures. Combination of Bow-tie with the other techniques such as fuzzy set theory or statistical analysis (Parvizsedghy and Zayed 2015a; and Shahriar et al. 2012) can lead to the estimation of the probability of failure and may provide an image of the possible scenarios of failure.

Figure 2- 6: Generic Bow-tie Model (adapted from Dianous & Fievez 2006)

The FT explores the potential causes of the top event or the risk factor of a system. Causes of the top event are expanded at different levels based on the existence of data. Basic events are the lowest level of the causes that can lead to the failure of the system and their estimation is possible according to the existing data. Detailed causes are connected with logical relationships (i.e. AND/OR) (Mokhtari et al. 2011). ET models the major hazards, which are controlled by the safety barriers. The barriers are demonstrated on the bow-ties, and their performance indicates the probability of happening of each major hazard (Dianous and Fievez 2006). As a result, different scenarios of a failure are identified and analyzed. Different scenarios indicate the success or failure of each safety barrier. The probability of the success or failure is multiplied by the probability of the occurrence of the top event to compute the occurrence frequency of each scenario of failure. Bow-ties are graphical diagrams of presenting the logical relationships between various factors responsible for the failure and the major

consequences of a failure. Figure 2-7 depicts the key symbols of a fault tree each of which indicates a logical relationship.

Figure 2- 7: Elements of a Bow-tie model (adapted from Ferdous et al. 2012)

BE-Basic Event; IE-Intermediate Events; CE- Critical Event; OE-Outcome Events ARAMIS project developed structure of risk assessment through Bow-tie analysis; however, in the implementation phase they encountered several problems. One of the problems was mentioned as defining the frequency of occurrence of dangerous events, as well as the leading causes. In the previous works, a generic form of probability distributions was used, and the safety systems were not identified very clearly (Dianous and Fi´evez 2006). The shapes of various components of the Bow-tie diagrams follow a standard set of rules. A summary description of the components of fault tree and the defined shapes are depicted in Table 2-17. Traditional Fault-tree models analyzed the probability of failure of the top event of the fault tree by assigning crisp values to the

basic events. Then, in the analysis phase, the logical relation of the basic events with the top event was considered, and the computation of the failure probability was performed.

Table 2- 16: Description and shapes of Graphical symbols used in Fault tree models (adapted from Ferdous 2006)

Graphical symbol Shape name Representing Event

Fau lt t re e e vent s ym bo ls

Rectangle Applied for representing Intermediate event or

top-event.

Circle Represents the basic event

Diamond Undeveloped Event

Oval Conditional event use for representing any

conditions

House External Events

Fau lt t re e ga te sy m bo ls AND Gate

AND gates combine the input events, all of which has to occur simultaneously for the output event to occur.

OR Gate OR gates combine the output event that occurs

if at least one of the input events occurs.

INHABIT Gate Input event produces output event when a

conditional event occurs.

TRANSFER Gate Transferring gate information or event

information under a sub-tree.

Yuhua and Datao (2005) described the process of quantitative analysis as follows:

1) Probability of occurrence of each basic event should be obtained from experts or the historical data;

3) Finally, the probabilities are calculated multiplying probabilities of occurrence of all included basic events in each minimal cut-set.

The computation would be performed in a reasonable time if the fault tree were not huge; however, the problems would arise if the tree is enormous, and the number of cut sets is too much. In that case, Equation 2-2 might be used to calculate the probability of occurrence of the top event.

P(T)=P (⋃ Kjn

j=1 )= ∑ P(Ki)ni=1 - ∑ni<j=2P(KiKj)+ ∑ni<j<k=3P(KiKjKk)

+ …+(-1)n-1P(K1K2…Kn)P(Kj)= ∏_i∈KjFi(t) (2-1)

Where:

K1, K2,..Kn: the minimum cut-sets, N: the total number of cut-sets

Fi(t): the probability of the basic event Xi.