FTA - Fault Tree Analysis

In complex systems such as chemical processes, the analysis of all possible error mechanisms and accident scenarios is now a necessity as well as a requirement from the legislation. There are many methods in the literature for this need. Fault Tree Analysis (FTA) is one of the methods developed to determine the root cause and probability of occurrence of top event.

FTA is a methodology that allows the modeling of factors and combinations that may lead undesired events to occur. Various combinations of events leading to the top event can be represented logically and graphically via this method.

Fault tree analysis is a deductive failure analysis that focuses on a specific undesired event and aims to identify these causes. The undesired event is the top event in the fault tree diagram. For the success of the analysis, the selection of the top event is crucial. If too general is selected, the analysis may become unmanageable. If selected very specifically, there is not enough insight into the sequence of events leading top event. Although fault tree analysis appears to be a laborious and not suitable for analyzing large systems, it can provide clear information about the root causes and probability of occurrence of the event of interest when applied correctly.

It is recommended that the FTA be carried out during the design phase in order to avoid the cost of alteration after the design. Reviewing the analysis just before and during the operation phase will help in identifying and resolving potential problems.

Multiple Occurring Events and Gate Calculations in FTA

Fault tree analysis is constructs by determining the intermediate and primary events leading top event. All basic events are considered to be statistically independent, unless they are caused by a common cause failure. If fault tree has no multiple occurring events, the tree is considered independent. If fault tree has multiple occurring events, the simplification should be performed by determining the minimal cut sets translating tree into an equivalent set of Boolean equations given below.

a x a = a

a + a = a

a + ab = a

a (a + b) = a

A minimal cut set is a combination of components or events whose simultaneous failure is just sufficient to make the system fail. If the multiple occurring events are not mathematically counted correctly on gate calculation and minimum cut sets not determined, probability of occurrence of top event may be inaccurate and generally produces very erroneous results.

Steps in FTA-

1. Define the undesired event to study.
2. Obtain an understanding of the system.
3. Construct the fault tree.
4. Evaluate the fault tree.
5. Control the hazards identified.

Example-

TP top event is predicted to be caused by different combinations of intermediate events G1, G2 and G3 and basic events A, B and C in the above fictional fault tree. When fault tree is examined, it is understood that tree has multiple occurring events therefore tree is not independent. In this case, a fault tree can be translated into an equivalent set of Boolean equations shown below, the minimum cut sets must be determined for correct tree probability calculation.

TP = AAB + AC + ABB + ABC + CC,

TP = AB + AC + AB + ABC + C,

AA=A

BB=B

TP = AB + AC + ABC + C

C + AC + ABC = C

TP = AB + C (minimal cut sets)

If A=0.1 B=0.05 C=0.01 in probability

TP = 0.1x0.05 + 0.01

TP=1.5xE-2

When TP is not translated into an equivalent set of Boolean equations,

TP = AAB + AC + ABB + ABC + CC

TP = 0.1x0.1x0.05 + 0.1x0.05x0.05 + 0.1x0.05x0.01 + 0.01x0.01

TP = 0.0005 + 0.00025 + 0.00005 + 0.0001

TP = 9xE-4

As can be seen from the example, when the multiple occurring events are not taken into account correctly, the probability of top event (TP) is underestimated 16.67 times and causes an erroneous result. If the above example is carried out by means of computer software, it must be ensured that the same ID number is assigned to multiple occurring events in order to avoid the error described above.

Conclusions

Fault tree analysis is an advanced technique that can be applied qualitatively or quantitatively based on graphical representation of various parallel and sequential fault combinations. Faults may be component hardware errors, human errors.