Reliability block diagrams are created in order to illustrate the way that components are reliability-wise arranged in a system. So far, we have described possible "structural properties" of a system of components, such as series, parallel, etc. These structural properties, however, refer to the system's state of success or failure based on the states of its components. The physical structural arrangement, even though it is clearly related to the reliability-wise arrangement, it is not necessarily identical.
Consider the following circuit:
The equivalent resistance must always be less than 1.2
.
Draw the reliability block diagram for this circuit.
First, let's consider the case where all three resistors operate:
Thus, when all components operate, the equivalent resistance is 1, which is less than the maximum resistance of 1.2.
Next, consider the case where one of the resistors fails open. In this case, the resistance for the resistor is infinite and the equivalent resistance is:
Thus:
If two resistors fail open (e.g. #1 and #2), the equivalent resistance is:
Thus:
If all three resistors fail open:
Thus, if r1, r2, r3, or any combination of the three fails, the system fails. Put another way, r1 and r2 and r3 must succeed in order for the system to succeed.
The RBD is:
In this example, it can be seen that even though the three components were physically arranged in parallel, their reliability-wise arrangement is in series.
See Also:
RBDs and Analytical System Reliability
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