Fault Tree Analysis (FTA)
FTA provides an easy process for tracking and memorializing business interruption probabilities. This analysis process was initially introduced to study the probability of system failure where failure was not an option, e.g. space flight or nuclear reactors. The system we are concerned with here is the entire organization and the combination of all twelve business processes.
FTA, for use in BIA/BCP, is a failure analysis in which an undesired state of the system’s processes and subprocesses are analyzed, for the most part using and/or logic to combine a series of lowerlevel events. This analysis of these undesired events, minidisasters and disasters, is mapped using symbols in a manner similar to process mapping. However, an undesired state is taken as the root ('top event') of a faulttree.
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These faulttrees may be as complex or as simple as is culturally acceptable. Once the mapping is completed, the probability of the occurrence of the topevent is calculated by assigning probabilities of the occurrence of each of the basicevents and then either summing or multiplying these probabilities using the basic rules of probability.
Generally if it is an “Or” gate the probabilities are summed, if it is an “And” gate the
probabilities are multiplied.
This can become somewhat more complex if one’s model includes situations where mutual exclusivity has to be considered. Mutually exclusive simply means two events cannot possibly occur simultaneously within the same time frame.
If one is dealing with an “Or” gate the math formula for mutually exclusive basicevents A and B is
P(A or B) = P(A) + P(B). P stands for probability. If events A and B are not mutually exclusive the formula becomes P(A or B) = P(A) + P(B) – P(A & B).
This simply requires one to calculate (or estimate) one more probability, the probability of both events occurring at the same time; e.g. an earthquake and a fire.
When an “And” gate is used one must then compute the probability of a basic event occurring given that another basic event has occurred. This is called conditional probability.
Example: the probabilities for the fault tree case above (picture) are estimated as:
.08 for Road Access Interrupted,
.001 for Terrorist Attacks and
.07 for Fire at Vendor’s Facility.
These are assumed to be mutually exclusive events and there for the probability of the subprocess of “Receive Inventory from Vendor” being interrupted is .05+.001+.07 = .151 or about 15 %.
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