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a substantial majority of OR gates. If fault trees have too many OR gates, every fault of event may lead
to the top event. This may not be the case, but a large majority of OR gates will certainly indicate this.
An evaluator needs to be sure that logic symbols are well defined and understood. If nonstandard
symbols are used, they must not get mixed with other symbols.
Check for proper control of transfers. Transfers are reference numbers permitting linking between pages
of FTA graphics. Fault trees can be extremely large, requiring the uses of many pages and clear interpage
references. Occasionally, a transfer number may be changed during fault tree construction. If the
corresponding sub-tree does not have the same transfer number, then improper logic will result.
Cut sets (minimum combinations of events that lead to the top event) need to be evaluated for
completeness and accuracy. Establishing the correct number of cuts and their depth is a matter of
engineering judgment. The fault tree in Figure 8-6 obscures some of the logic visible in Figure 8-5,
preventing identification of necessary corrective action. Figure 8-7 illustrates that event Figure 8-6 was
not complete.
FAA System Safety Handbook, Chapter 8: Safety Analysis/Hazard Analysis Tasks
December 30, 2000
8- 34
Airplane
Crashes
Propulsion
Flight
Controls
Electrical
Power
Pilot Error
Hydraulic
Power
Figure 8-7: More Comprehensive Fault Tree
Each fault tree should include a list of minimum cut sets. Without this list, it is difficult to identify
critical faults or combinations of events. For large or complicated fault trees, a computer is necessary to
catch all of the cut sets; it is nearly impossible for a single individual to find all of the cut sets.
For a large fault tree, it may be difficult to determine whether or not the failure paths were completely
developed. If the evaluator is not totally familiar with the system, the evaluator may need to rely upon
other means. A good indication is the shape of the symbols at the branch bottom. If the symbols are
primarily circles (primary failures), the tree is likely to be complete. On the other hand, if many symbols
are diamonds (secondary failures or areas needing development), then it is likely the fault tree needs
expansion.
Faulty logic is probably the most difficult area to evaluate, unless the faults lie within the gates, which are
relatively easy to spot. A gate-to-gate connection shows that the analyst might not completely understand
the workings of the system being evaluated. Each gate must lead to a clearly defined specific event, i.e.,
what is the event and when does it occur? If the event consists of any component failures that can directly
cause that event, an OR gate is needed to define the event. If the event does not consist of any component
failures, look for an AND gate.
When reviewing an FTA with quantitative hazard probabilities of occurrence, identify the events with
relatively large probability of occurrence. They should be discussed in the analysis summaries, probably
as primary cause factors.
A large fault tree performed manually is susceptible to errors and omissions. There are many advantages
of computer modeling relative to manual analysis (of complex systems):
· Logic errors and event (or branch) duplications can be quickly spotted.
· Cut sets (showing minimum combinations leading to the top event) can be listed.
· Numerical calculations (e.g., event probabilities) can be quickly done.
· A neat, readable, fault tree can be drawn.
FAA System Safety Handbook, Chapter 8: Safety Analysis/Hazard Analysis Tasks
December 30, 2000
8- 35
8.10.1 Success Trees
In some cases it is appropriate to use Success Trees in modeling systems. Success Trees depict
the system in its success state. The analyst considers what components or subsystems must work
for the system to successfully work. Success Trees are the “inverse” of Fault Trees. For example,
see figure 8-7 above. The Success Tree of the above fault tree which is represented as an “or”
gate with six inputs would look like an “and” gate with six inputs. The logic is inverted from
Failure State to Success State. Since a cut set is the minimum combination of events that lead to
the top event, a path set represents the minimum combination of successful events for a
successful top event.
8.11 Evaluating Quantitative Techniques
Quantitative analysis techniques are used for various purposes, including:
· Establishing overall risk levels (usually specified in terms of risk severity and risk
probability).
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