Reliability HotWire: eMagazine for the Reliability Professional
Reliability HotWire

Issue 20, October 2002

Reliability Basics
Difference Between Physical and Reliability-Wise Arrangement

Reliability block diagrams are created in order to illustrate the way that components are reliability-wise arranged in a system. There are different "structural properties" of a system, such as series, parallel, etc. These structural properties refer to the system's state of success or failure based on the states of its components. However, although the physical structural arrangement is clearly related to the reliability-wise arrangement, the two are not necessarily identical.

Example

Consider the following circuit. The equivalent resistance must always be less than 1.2Ω

Resistor circuit with three components physically in parallel

Figure 1: Resistor circuit

To draw the reliability block diagram (RBD) for this circuit, let's first consider the case where all three resistors are operational. To calculate the equivalent resistance:

Equation - 1/req = 1/r1 + 1/r2 + 1/r3

Therefore, the total equivalent resistance is 1Ω, which is less than the maximum resistance of 1.2Ω.

Next, consider the case where one of the resistors fails open. In this case, the resistance for the resistor that fails is infinite and the equivalent resistance for the system is shown next.

Equation - req = 1/infinity + 1/3 + 1/3 + 1/3 = 2/3

Thus:

req = 1.5, which is greater than 1.2 so the system failed

If two resistors fail open, the equivalent resistance is:

Equation - req = 1/req = 1/infinity + 1/infinity + 1/3 = 1/3

Thus,

req = 3, which is greater than 1.2 and the system failed.

If all of the resistors fail open then:

req = infinity, which is greater than 1.2 and the system failed

Therefore, if any of the resistors fail, or any combination of the three fail, the system fails. Or, each of the resistors must succeed in order for the system to succeed. The RBD for the system is shown in Figure 2.

RBD of resistors in series

Figure 2: RBD of resistors in series

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.

 

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