10.3 LED System Reliability
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Fig. 10.6 The relationship between components of LED system and the system reliability
Fig. 10.7 An example of a
system failure tree
A 1
A 2
A 1
A 3
AND
AND
OR
A 4
will fail as long as A1 fails. Therefore, the failure tree can be simplified. The simplified failure tree is shown in Fig. 10.8. The bottom event of the failure tree can often be
represented by a Boolean variable, whose purpose is to build the system failure tree
more effectively. Thus, FT can be seen as a graphical Boolean variable. Boolean variables are usually 0 or 1. If A1 and A2 are Boolean variables, the Boolean operations
A1 ⊗ A2 and A1 ⊕ A2 are also Boolean variables.
In the logical formulas, ⊗ and ⊕ represent AND gates and OR gates, respectively.
Therefore, A1 ⊗ A2 means that only if A1 and A2 fail at the same time, the system
will fail. A1 ⊕ A2 means that if A1 or A2 fails, the system will fail. System failure
can be described by logical formulas, and the system failure tree can be simplified
by using Boolean operations.
In Bayesian networks, cause and effect variables are represented by nodes. Each
node has its own probability distribution. Nodes can be an abstraction of any problem,