Template:Reliability block diagrams for failure modes: Difference between revisions

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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.
===Example 17===
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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Figure 4.27 shows the diagram for this configuration.
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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.
 
[[Image:chp4image33.png|thumb|center|400px|<div align="center"> Fig 4.25 Electircal network diagram. </div>]]
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[[Image:chp4image34.png|thumb|center|400px|<div align="center"> Fig 4.26 RBD of the network in Figure 4.25.</div>]]
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[[Image:chp4image35.png|thumb|center|400px|<div align="center"> Fig 4.27 Reliability block diagram for Example 17. </div>]]
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[[Image:chp4image36.png|thumb|center|400px|<div align="center"> Fig 4.28 Reliability block diagram for Example 18.</div>]]
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===Example 18===
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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:• Mode B, C or F occurs.<br>
:• 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.
====Solution to Example 18====
The diagram is shown in Figure 4.28
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The reliability equation, as obtained from BlockSim is:
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::<math>\begin{align}
{{R}_{System}}= & (-2{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
& +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{F}} \\
& +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
& +{{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{2/3}}\cdot {{R}_{E}}\cdot {{R}_{F}}) 
\end{align}</math>
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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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::<math>\begin{align}
{{R}_{System}}= & (-2{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
& +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{F}} \\
& +{{R}_{A}}\cdot {{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{E}}\cdot {{R}_{F}} \\
& +{{R}_{B}}\cdot {{R}_{C}}\cdot {{R}_{D}}\cdot {{R}_{E}}\cdot {{R}_{F}}) 
\end{align}</math>
 
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Latest revision as of 09:36, 25 July 2012

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