Quantitative Network Engineering with Fault Tree Analysis

This is a simple paper outlining how to use some Risk Analysis Techniques with Network Engineering to obtain quantitative results. An attempt to turn network engineering from an artful guessing game into a science.

Cutsets

The next step is to calculate all of the cutsets for the fault tree. A cutset is a unique set of events that can cause the top event to occur. This can be a single event, or a sequence of several events that all occur simultaneously.

Cutsets provide a lot of insight into the failure mechanisms of the system that has been modelled. They provide a list of all of the failure mechanisms of the system, and make it easy to identify weak points, critical points, and single points of failure in the system. Cutsets are qualitative in nature, but they provide the starting point for the application of statistical and probabilistic mathematics to quantify the failure mechanisms. Each cutset has a separate calculation run and provides a number that can be evaluated for acceptable risk, and compared against the other failure mechanisms (cutsets).

When looking at a system, it is possible that every single fault that leads to system failure could happen at the same time -- basically every basic event in the entire tree occurs. Indeed, the initiation of every fault simultaneously is a cutset, however there are smaller sequences of events known as minimal cutsets that are far more interesting. A minimal cutset is a minimum set group of events which will still cause the top event to occur. Looking at the minimum cutsets really trims down on the amount of analysis that needs to be done, and sifts out a lot of the less likely failure methods out where the failure method is already initiated by a smaller set of shared events.

As an example, consider the fault tree below:

The cutsets are basically all of the failure modes:

These are a lot of combinations out of the five events in the FTA. Closer inspection reveals that a lot of the cutsets don't add alot of value to a combination of events. For instance, if A can cause the top event by itself -- event A occuring simulatenously with event B is not of of too much interest. That is where the minimal cutsets show their worth:

There are quite a few methods to finding cutsets and the minimums: boolean reduction, top down and bottom up reductions, etc. A measured and interative approach that is consistent will usually provide the most reliable and complete set of cutsets that aren't missing or repeating anything.




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