7.9.1 Discussions of FTA
Methods
There are basically three methods for solving fault trees: (1)
direct simulation (Reference [81]),
(2) Monte Carlo (Reference [82]),
and (3) direct analysis (Reference
[83]).
Direct simulation basically uses Boolean logic hardware (similar
to that in digital computers) in a onetoone correspondence with the fault
tree Boolean logic to form an analog circuit. This method usually is
prohibitively expensive. A hybrid method obtains parts of the solution using
the analog technique and parts from a digital calculation, in an effort to be
cost competitive. Because of the expense involved, this method rarely is
used.
Monte Carlo methods are perhaps the most simplest in principle
but in practice can be expensive. Since Monte Carlo is not practical without
the use of a digital computer, it is discussed in that framework. The most
easily understood Monte Carlo technique is called "direct simulation." The
term "simulation" frequently is used in conjunction with Monte Carlo methods,
because Monte Carlo is a form of mathematical simulation. (This simulation
should not be confused with direct analog simulation.) Probability data are
provided as input, and the simulation program represents the fault tree on a
computer to provide quantitative results. In this manner, thousands or
millions of trials can be simulated. A typical simulation program involves the
following steps.
(1) 

Assign failure data to input fault events within the
tree and, if desired, repair data.

(2) 

Represent the fault tree on a computer to
provide quantitative results for the overall system performance,
subsystem performance, and the basic input event
performance.

(3) 

List the failure that leads to the
undesired event and identify minimal cut sets contributing to the
failure.

(4) 

Compute and rank basic input failure and
availability performance results. 
In performing these steps, the computer program simulates the
fault tree and, using the input data, randomly selects the various parameter
data from assigned statistical distributions; and then tests whether or not
the TOP event occurred within the specified time period. Each test is a trial,
and a sufficient number of trials is run to obtain the desired quantitative
resolution. Each time the TOP event occurs, the contributing effects of input
events and the logical gates causing the specified TOP event are stored and
listed as computer output. The output provides a detailed perspective of the
system under simulated operating conditions and provides a quantitative basis
to support objective decisions.
A number of computer programs have been developed for fault tree
analysis. References
[83]  [85] provide additional information on fault tree analysis. In
practice, the methods used for fault tree analysis will depend on which ones
are available for the computer being used. It will rarely, if ever, be
worthwhile generating a computer program especially for a particular
problem.