# Homework Help: Simple structure function - interpreting answer [Probability & Reliability Theory]

1. Oct 6, 2012

### slakedlime

1. The problem statement, all variables and given/known data
This isn't a homework question. I'm working through my book's exercises and am having difficulty interpreting an answer. Any guidance will be very much appreciated.

The problem is to come up with a structure function for a graph (image attached with this post). The answer is $\phi(x) = x_1 max (x_2, x_3, x_4) x_5$

2. The attempt at a solution
Two types of unbroken circuit are possible:

i) There is a connection from $x_1$ to $x_4$ (e.g. $x_1 → x_2 → x_4$ OR $x_1 → x_3 → x_2 → x_4$)
ii) The triangle $x_1,x_2, x_3$ is connected even if $x_4$ is broken. Hence, current can loop from $x_1 → x_2 → x_3$ or from $x_1 → x_3 → x2.$

In the diagram, I can see four nodes $x_1,x_2, x_3, x_4$. Where does $x_5$ come from?

The following part of the answer also confuses me:
$max (x_2, x_3, x_4)$

Why is this the case? I can't see how the circuit would function if $x_2$ and $x_3$ were both broken. Current simply could not flow from $x_1$ to $x_4$ unless component 2 or 3 were also working.

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