Template:Reliability block diagrams for failure modes - Revision history

Lisa Hacker: Replaced content with 'Category: For Deletion'

2012-07-25T09:36:55Z

Replaced content with 'Category: For Deletion'

← Older revision		Revision as of 09:36, 25 July 2012
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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?
	~~<br>~~

	~~Figure "Reliability block diagram for Example 17" shows the diagram for this configuration.~~
	~~<br>~~

	~~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\|center\|300px\|<div align="center"> Electrical network diagram. </div>]]~~
	~~<br>~~
	~~[[Image:chp4image34.png\|center\|300px\|<div align="center"> RBD of Electircal network diagram</div>]]~~
	~~<br>~~
	~~[[Image:chp4image35.png\|center\|300px\|<div align="center"> Reliability block diagram for Example 17. </div>]]~~
	~~<br>~~
	~~[[Image:chp4image36.png\|center\|300px\|<div align="center"> Reliability block diagram for Example 18.</div>~~]]
	~~<br>~~

	~~===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:~~
	~~<br>~~
	~~:• Mode B, C or F occurs.<br>~~
	~~:• Modes A and E, A and D or E and D occur.<br>~~
	~~<br>~~
	~~Draw the block diagram and obtain the reliability equation.~~
	~~====Solution to Example 18====~~
	~~The diagram is shown in Figure "Reliability block diagram for Example 18"~~
	~~<br>~~
	~~The reliability equation, as obtained from BlockSim is:~~
	~~<br>~~

	~~::<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>~~
	~~<br>~~

	~~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:~~

	~~<br>~~
	~~::<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>~~

	~~<br>~~

Melinda Caroline: /* Example 17 */

2012-05-08T23:25:48Z

Example 17

← Older revision		Revision as of 23:25, 8 May 2012
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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.		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\|center\|~~200px~~\|<div align="center"> Electrical network diagram. </div>]]		[[Image:chp4image33.png\|center\|300px\|<div align="center"> Electrical network diagram. </div>]]
	<br>		<br>
	[[Image:chp4image34.png\|center\|~~200px~~\|<div align="center"> RBD of Electircal network diagram</div>]]		[[Image:chp4image34.png\|center\|300px\|<div align="center"> RBD of Electircal network diagram</div>]]
	<br>		<br>
	[[Image:chp4image35.png\|center\|~~200px~~\|<div align="center"> Reliability block diagram for Example 17. </div>]]		[[Image:chp4image35.png\|center\|300px\|<div align="center"> Reliability block diagram for Example 17. </div>]]
	<br>		<br>
	[[Image:chp4image36.png\|center\|~~200px~~\|<div align="center"> Reliability block diagram for Example 18.</div>]]		[[Image:chp4image36.png\|center\|300px\|<div align="center"> Reliability block diagram for Example 18.</div>]]
	<br>		<br>

Chuck Smith: /* Example 17 */

2012-04-25T17:49:08Z

Example 17

← Older revision		Revision as of 17:49, 25 April 2012
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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.		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\|center\|~~500px~~\|<div align="center"> Electrical network diagram. </div>]]		[[Image:chp4image33.png\|center\|200px\|<div align="center"> Electrical network diagram. </div>]]
	<br>		<br>
	[[Image:chp4image34.png\|center\|~~500px~~\|<div align="center"> RBD of Electircal network diagram</div>]]		[[Image:chp4image34.png\|center\|200px\|<div align="center"> RBD of Electircal network diagram</div>]]
	<br>		<br>
	[[Image:chp4image35.png\|center\|~~500px~~\|<div align="center"> Reliability block diagram for Example 17. </div>]]		[[Image:chp4image35.png\|center\|200px\|<div align="center"> Reliability block diagram for Example 17. </div>]]
	<br>		<br>
	[[Image:chp4image36.png\|center\|~~500px~~\|<div align="center"> Reliability block diagram for Example 18.</div>]]		[[Image:chp4image36.png\|center\|200px\|<div align="center"> Reliability block diagram for Example 18.</div>]]
	<br>		<br>

Nicolette Young: /* Example 17 */

2012-03-19T22:19:04Z

Example 17

← Older revision		Revision as of 22:19, 19 March 2012
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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.		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"> Electrical network diagram. </div>]]		[[Image:chp4image33.png\|center\|500px\|<div align="center"> Electrical network diagram. </div>]]
	<br>		<br>
	[[Image:chp4image34.png~~\|thumb~~\|center\|~~400px~~\|<div align="center"> RBD of Electircal network diagram</div>]]		[[Image:chp4image34.png\|center\|500px\|<div align="center"> RBD of Electircal network diagram</div>]]
	<br>		<br>
	[[Image:chp4image35.png~~\|thumb~~\|center\|~~400px~~\|<div align="center"> Reliability block diagram for Example 17. </div>]]		[[Image:chp4image35.png\|center\|500px\|<div align="center"> Reliability block diagram for Example 17. </div>]]
	<br>		<br>
	[[Image:chp4image36.png~~\|thumb~~\|center\|~~400px~~\|<div align="center"> Reliability block diagram for Example 18.</div>]]		[[Image:chp4image36.png\|center\|500px\|<div align="center"> Reliability block diagram for Example 18.</div>]]
	<br>		<br>

Dingzhou Cao: /* Example 17 */

2012-03-06T21:27:47Z

Example 17

← Older revision		Revision as of 21:27, 6 March 2012
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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.		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>]]		[[Image:chp4image33.png\|thumb\|center\|400px\|<div align="center"> Electrical network diagram. </div>]]
	<br>		<br>
	[[Image:chp4image34.png\|thumb\|center\|400px\|<div align="center"> ~~Fig 4.26~~ RBD of Electircal network diagram</div>]]		[[Image:chp4image34.png\|thumb\|center\|400px\|<div align="center"> RBD of Electircal network diagram</div>]]
	<br>		<br>
	[[Image:chp4image35.png\|thumb\|center\|400px\|<div align="center"> ~~Fig 4.27~~ Reliability block diagram for Example 17. </div>]]		[[Image:chp4image35.png\|thumb\|center\|400px\|<div align="center"> Reliability block diagram for Example 17. </div>]]
	<br>		<br>
	[[Image:chp4image36.png\|thumb\|center\|400px\|<div align="center"> ~~Fig 4.28~~ Reliability block diagram for Example 18.</div>]]		[[Image:chp4image36.png\|thumb\|center\|400px\|<div align="center"> Reliability block diagram for Example 18.</div>]]
	<br>		<br>

Dingzhou Cao: /* Solution to Example 18 */

2012-03-06T00:07:27Z

Solution to Example 18

← Older revision		Revision as of 00:07, 6 March 2012
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	Draw the block diagram and obtain the reliability equation.		Draw the block diagram and obtain the reliability equation.
	====Solution to Example 18====		====Solution to Example 18====
	The diagram is shown in Figure ~~4.28~~		The diagram is shown in Figure "Reliability block diagram for Example 18"
	<br>		<br>
	The reliability equation, as obtained from BlockSim is:		The reliability equation, as obtained from BlockSim is:

Dingzhou Cao: /* Example 17 */

2012-03-06T00:07:02Z

Example 17

← Older revision		Revision as of 00:07, 6 March 2012
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	<br>		<br>

	Figure ~~4.27~~ shows the diagram for this configuration.		Figure "Reliability block diagram for Example 17" shows the diagram for this configuration.
	<br>		<br>

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	[[Image:chp4image33.png\|thumb\|center\|400px\|<div align="center"> Fig 4.25 Electircal network diagram. </div>]]		[[Image:chp4image33.png\|thumb\|center\|400px\|<div align="center"> Fig 4.25 Electircal network diagram. </div>]]
	<br>		<br>
	[[Image:chp4image34.png\|thumb\|center\|400px\|<div align="center"> Fig 4.26 RBD of ~~the~~ network ~~in Figure 4.25.~~</div>]]		[[Image:chp4image34.png\|thumb\|center\|400px\|<div align="center"> Fig 4.26 RBD of Electircal network diagram</div>]]
	<br>		<br>
	[[Image:chp4image35.png\|thumb\|center\|400px\|<div align="center"> Fig 4.27 Reliability block diagram for Example 17. </div>]]		[[Image:chp4image35.png\|thumb\|center\|400px\|<div align="center"> Fig 4.27 Reliability block diagram for Example 17. </div>]]

Pengying niu: /* Example 17 */

2012-02-09T17:05:48Z

Example 17

← Older revision		Revision as of 17:05, 9 February 2012
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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.		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\|Fig 4.25 Electircal network diagram.]]		[[Image:chp4image33.png\|thumb\|center\|400px\|<div align="center"> Fig 4.25 Electircal network diagram. </div>]]
	<br>		<br>
	[[Image:chp4image34.png\|thumb\|center\|400px\|Fig 4.26 RBD of the network in Figure 4.25.]]		[[Image:chp4image34.png\|thumb\|center\|400px\|<div align="center"> Fig 4.26 RBD of the network in Figure 4.25.</div>]]
	<br>		<br>
	[[Image:chp4image35.png\|thumb\|center\|400px\|Fig 4.27 Reliability block diagram for Example 17.]]		[[Image:chp4image35.png\|thumb\|center\|400px\|<div align="center"> Fig 4.27 Reliability block diagram for Example 17. </div>]]
	<br>		<br>
	[[Image:chp4image36.png\|thumb\|center\|400px\|Fig 4.28 Reliability block diagram for Example 18.]]		[[Image:chp4image36.png\|thumb\|center\|400px\|<div align="center"> Fig 4.28 Reliability block diagram for Example 18.</div>]]
	<br>		<br>

Pengying niu: /* Solution to Example 18 */

2012-02-07T19:08:41Z

Solution to Example 18

← Older revision		Revision as of 19:08, 7 February 2012
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	Draw the block diagram and obtain the reliability equation.		Draw the block diagram and obtain the reliability equation.
	====Solution to Example 18====		====Solution to Example 18====
	The diagram is shown in Figure ~~fig35~~		The diagram is shown in Figure 4.28
	<br>		<br>

	The reliability equation, as obtained from BlockSim is:		The reliability equation, as obtained from BlockSim is:
	<br>		<br>

Pengying niu: /* Example 17 */

2012-02-07T19:06:55Z

Example 17

← Older revision		Revision as of 19:06, 7 February 2012
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	[[Image:chp4image35.png\|thumb\|center\|400px\|Fig 4.27 Reliability block diagram for Example 17.]]		[[Image:chp4image35.png\|thumb\|center\|400px\|Fig 4.27 Reliability block diagram for Example 17.]]
	<br>		<br>
	[[Image:chp4image36.png\|thumb\|center\|400px\|Fig 4/28 Reliability block diagram for Example 18.]]		[[Image:chp4image36.png\|thumb\|center\|400px\|Fig 4.28 Reliability block diagram for Example 18.]]
	<br>		<br>