## F Fault Tree Analysis F Fault Tree Basics [

Any accident starts with an initiating event, often the failure of an operational component. In order to counter-act this, a technical system usually disposes of a protective & safety systems made up of stand-by components. These are normally capable of coping with the major part of initiating events and may be considered as barriers between those and the undesired events. The undesired events only occur if these barriers fail. If components from several barriers have to fail for the undesired event to occur, these are combined with the initiating event by an "AND" gate. If several of these combination exist, they are input into an "OR" gate, just as contributions from different initiating events to the undesired events. Any system represented by a fault tree has basic events which act in series (OR gates) or in parallel (AND gates), with a combination of the two being most frequent. The basic event may be described by a binary variable.

Where y is the structure function of a system. A group of basic events which, in case they are true, are just sufficient to cause the undesired event is called a minimal cut set. A fault tree may have several minimal cut sets, each of which represents one way of bringing about the undesired event. Representation of the fault tree in terms of its minimal cut sets gives insight into the structure of the system under investigation. The structure function of the system as function of the minimal cut sets described as:

1, if basic event i is true, e.g. component i has failed. 0, if basic event iis not true, e.g. component i is working.

Analogous description may be used for the state of the system:

1, if the undesired event has occured. 0, if the undesired event has not occured.

1, if the undesired event has occured. 0, if the undesired event has not occured.

The K; represent the L minimal cut sets of the system, which the value of L depending on its complexity, and ki are the binary functions associated with them.

Fault trees for complex systems normally must be evaluated with the aid of a computer program. There are mainly three methods available for this purpose: (1) direct simulation of the fault tree, (2) minimal cut set calculation using a simulation procedure, and (3) minimal cut set calculation by analytical methods. The last procedure was used to calculate undesired events of the study objects, and to be discussed in more details in the following section.

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