An electrical circuit is particularly simple to analyze by a fault tree because the connections are straightforward. Consider the protection circuit shown in Fig. 1.24 (14).

When the switch is closed, power is applied to the timer coil. This closes the timer contacts and applies power to the relay coil, which in turn closes the relay contacts. Power is then supplied through the fuse to the motor. When the switch is opened, the reverse procedure applies.

The fuse and the timer are safeguards; if the motor fails shorted while the relay contacts are closed, then the fuse opens and shuts off the power, and if the switch fails to open again after some time (which is preset) then the timer will open its contacts and remove power from the motor.

The overheating of the wire A-В is an undesirable event in this circuit and it can be prevented if the safeguards operate. As an example of fault tree technique, the following paragraphs analyze the causes which might allow the overheating of A-B.

Figure 1.25 shows the basic fault tree for the undesirable event: an over­heated wire. It could arise only as a result of excessive current and the power being applied for an extended time. The excessive current could come only if the motor fails shorted and the fuse fails to open, and the extended time during which this overpower is applied may result if either the relay contacts fail in a closed position, or the power is not removed from the relay coil.

The power is not removed from the relay coil only if both the timer fails and the switch fails to open. Thus the symbols demonstrate the logical connections between the events.

There are two analytical techniques for constructing fault trees. Each develops the tree to a different depth of detail. The first considers primary component failures that occur while the component is functioning within conditions for which it was designed. The second technique considers secondary component failures that occur when the component is subjected to abnormal conditions.

1.6.2.2.1 Primary failure technique. This method is used mainly in the communication field (control and instrumentation) and in data processing systems (control).

To illustrate the technique we may further analyze the causes of an over­heated wire (Figure 1.26) (14). The motor failed shorted and relay contacts failed closed are both primary failures. To cause the timer to be unable to open there are two other primary causes: the timer coil failed to open and the timer contacts failed closed. If the switch fails to open, a primary failure of the switch contacts failed closed may be responsible, although there are other possible external causes which are here undeveloped.

1.6.2.2.2 Secondary failure technique. This method requires a greater insight into the system and its component parts because it needs a knowl­edge of how systems might operate and interact in abnormal conditions. It is used mainly in accident analysis and therefore it is of most concern to this discussion.

To illustrate this technique we can again further develop the example (Figs. 1.27a and 1.27b) (14). The motor and relay are sensitive to the failure of one another. In Fig. 1.26, relay contacts failed closed was a primary fault, but there may be a secondary reason; they may fail to open because

they have been fused shut by an overcurrent. The overcurrent is a cause of failure only if the relay contacts fuse. Therefore an inhibit conditional gate is needed to describe this situation. The overcurrent might arise if failure of the fuse occurred and the motor failed shorted.

The motor failed shorted might also come from a secondary (abnormal conditions) failure, an extended period of power, but power applied for extended time is a cause for failure only if the motor actually does fail shorted, so another inhibit gate is required. This extended power might arise from a failure of the relay contacts or power not being removed from the relay coil.

Now we notice that the tree is no longer a simple structure but some faults occur in different parts of the tree; thus interconnections or transfers are required.