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| = Reliability Block Diagrams for Failure Modes and Other Applications =
| | [[Category: For Deletion]] |
| In this reference, most of the examples and derivations assume that each block represents a component/subassembly in a larger system. The same methodology and principles can also be used for other applications. For example, all derivations assume that the event under consideration is the event of failure of a component. One can easily take this principle and apply it to failure modes for a component/subsystem or system. To illustrate this, consider the following example.
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| ===Example 17===
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| Assume that a system has five failure modes: A, B, C, D and F. Furthermore, assume that failure of the entire system will occur if mode A occurs, modes B and C occur simultaneously or if either modes C and D, C and F or D and F occur simultaneously. Given the probability of occurrence of each mode, what is the probability of failure of the system?
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| <br>
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| Figure "Reliability block diagram for Example 17" shows the diagram for this configuration.
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| <br>
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| Analysis of this diagram follows the same principles as the ones presented in this chapter and can be performed in BlockSim, if desired.
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| [[Image:chp4image33.png|thumb|center|400px|<div align="center"> Electrical network diagram. </div>]] | |
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| [[Image:chp4image34.png|thumb|center|400px|<div align="center"> RBD of Electircal network diagram</div>]]
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| [[Image:chp4image35.png|thumb|center|400px|<div align="center"> Reliability block diagram for Example 17. </div>]]
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| [[Image:chp4image36.png|thumb|center|400px|<div align="center"> Reliability block diagram for Example 18.</div>]]
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| ===Example 18===
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| Assume that a system has six failure modes: A, B, C, D, E and F. Furthermore, assume that failure of the entire system will occur if:
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| <br>
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| :• Mode B, C or F occurs.<br>
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| :• Modes A and E, A and D or E and D occur.<br>
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| Draw the block diagram and obtain the reliability equation.
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| ====Solution to Example 18====
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| The diagram is shown in Figure "Reliability block diagram for Example 18"
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| The reliability equation, as obtained from BlockSim is:
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| ::<math>\begin{align}
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| {{R}_{System}}= & (-2{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
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| & +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{F}} \\
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| & +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
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| & +{{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}})
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| \end{align}</math>
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| <br>
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| The BlockSim equation includes the node reliability term <math>{{R}_{2/3}},</math> which cannot fail, or <math>{{R}_{2/3}}=1</math> . This can be removed, yielding:
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| <br>
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| ::<math>\begin{align}
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| {{R}_{System}}= & (-2{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
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| & +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{F}} \\
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| & +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
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| & +{{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{E}}\cdot {{R}_{F}})
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| \end{align}</math>
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| <br>
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