Same Example Modeled with RBDs or Fault Trees - Revision history

Lisa Hacker at 21:00, 18 September 2023

2023-09-18T21:00:48Z

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	<noinclude>{{Banner BlockSim Examples}}{{Navigation box}}		<noinclude>{{Banner BlockSim Examples}}{{Navigation box}}
	''This example also appears in the [~~[Fault_Tree_Diagrams_and_System_Analysis\|~~System ~~Analysis Reference book]~~]''.		''This example also appears in the [https://help.reliasoft.com/reference/system_analysis System analysis reference]''.
	<br>		<br>
	</noinclude>		</noinclude>

Richard House: /* Mode C */

2016-01-05T23:15:17Z

Mode C

← Older revision		Revision as of 23:15, 5 January 2016
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	The failure distribution settings for event CA are shown in the figure below.		The failure distribution settings for event CA are shown in the figure below.

	[[Image:10.34.gif\|center\|~~550px~~\|Failure distribution settings for event ''C'' ''A''.\|link=]]		[[Image:10.34.gif\|center\|600px\|Failure distribution settings for event ''C'' ''A''.\|link=]]

	The failure distribution properties for event CB are set in the same manner.		The failure distribution properties for event CB are set in the same manner.

Richard House: /* Analysis and Discussion */

2015-12-22T21:09:58Z

Analysis and Discussion

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	::1. The reliability of the component at 1 year (8,760 hours) can be calculated using the Analytical Quick Calculation Pad (QCP) or by viewing the reliability vs. time plot, as displayed in the following figure. <math>R(t=8760)=86.4975%\,\!</math>.		::1. The reliability of the component at 1 year (8,760 hours) can be calculated using the Analytical Quick Calculation Pad (QCP) or by viewing the reliability vs. time plot, as displayed in the following figure. <math>R(t=8760)=86.4975%\,\!</math>.
	[[Image:10_37.png\|center\|400px\|Reliability vs. time plot for the component.]]		[[Image:10_37.png\|center\|400px\|Reliability vs. time plot for the component.\|link=]]
	::2. Using the Analytical QCP, the B10 life of the component is estimated to be 7,373.94 hours.		::2. Using the Analytical QCP, the B10 life of the component is estimated to be 7,373.94 hours.
	::3. Using the Analytical QCP, the mean life of the component is estimated to be 21,659.68 hours.		::3. Using the Analytical QCP, the mean life of the component is estimated to be 21,659.68 hours.
	::4. The ranking of the modes after 1 year can be shown via the Static Reliability Importance plot, as shown in the figure below.		::4. The ranking of the modes after 1 year can be shown via the Static Reliability Importance plot, as shown in the figure below.
	[[Image:10.38.png\|center\|400px\|Static reliability importance for each of the modes at ''t''=8,760 hours.]]		[[Image:10.38.png\|center\|400px\|Static reliability importance for each of the modes at ''t''=8,760 hours.\|link=]]
	::5. Re-computing the results for 1, 2 and 3 assuming mode B is removed:		::5. Re-computing the results for 1, 2 and 3 assuming mode B is removed:
	:::a) R(t=8760) =98.72%.		:::a) R(t=8760) =98.72%.

Richard House: /* The Entire Component */

2015-12-22T21:08:44Z

The Entire Component

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	[[Image:10.35.png\|center\|400px\|RBD of the component.\|link=]]		[[Image:10.35.png\|center\|400px\|RBD of the component.\|link=]]


	[[Image:10.36.png\|center\|400px\|Fault tree of the component.\|link=]]		[[Image:10.36.png\|center\|400px\|Fault tree of the component.\|link=]]

Richard House: /* The Entire Component */

2015-12-22T21:08:26Z

The Entire Component

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	The last step is to set up the model for the component based on the primary modes (A, B, C, D, E and F). Modes A, B and C can each be represented by single blocks that encapsulate the subdiagrams already created. The RBD in the first figure below represents the primary failure modes for the component while the fault tree in second figure below illustrates the same. The node represented by 2/3 in the RBD indicates a 2-out-of-3 configuration. The Voting OR gate in the fault tree accomplishes the same. Subdiagrams are used in both configurations for the sub-modes.		The last step is to set up the model for the component based on the primary modes (A, B, C, D, E and F). Modes A, B and C can each be represented by single blocks that encapsulate the subdiagrams already created. The RBD in the first figure below represents the primary failure modes for the component while the fault tree in second figure below illustrates the same. The node represented by 2/3 in the RBD indicates a 2-out-of-3 configuration. The Voting OR gate in the fault tree accomplishes the same. Subdiagrams are used in both configurations for the sub-modes.

	[[Image:10.35.png\|center\|400px\|RBD of the component.]]		[[Image:10.35.png\|center\|400px\|RBD of the component.\|link=]]

	[[Image:10.36.png\|center\|400px\|Fault tree of the component.]]		[[Image:10.36.png\|center\|400px\|Fault tree of the component.\|link=]]

	Once the diagrams have been created, the reliability equation for the system can be obtained, as follows:		Once the diagrams have been created, the reliability equation for the system can be obtained, as follows:

Richard House: /* Mode C */

2015-12-22T21:07:47Z

Mode C

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	To model this, you can think of a scenario similar to standby redundancy. Basically, if CA occurs then CB gets initiated. A Standby container can be used to model this, as shown in the figure below.		To model this, you can think of a scenario similar to standby redundancy. Basically, if CA occurs then CB gets initiated. A Standby container can be used to model this, as shown in the figure below.

	[[Image:10.32.png\|center\|150px\|Standby container for mode C.]]		[[Image:10.32.png\|center\|150px\|Standby container for mode C.\|link=]]

	In this case, event CA is set as the active component and CB as the standby. If event CA occurs, CB will be initiated. For this analysis, a perfect switch is assumed. The properties are set in BlockSim as follows:		In this case, event CA is set as the active component and CB as the standby. If event CA occurs, CB will be initiated. For this analysis, a perfect switch is assumed. The properties are set in BlockSim as follows:
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	The fault tree for mode C is shown in the figure below. Note that the sequence is enforced by the Standby gate (used as a Sequence Enforcing gate).		The fault tree for mode C is shown in the figure below. Note that the sequence is enforced by the Standby gate (used as a Sequence Enforcing gate).

	[[Image:10.31.png\|center\|150px\|Standby (Sequence Enforcing) gate for model ''C'']]		[[Image:10.31.png\|center\|150px\|Standby (Sequence Enforcing) gate for model ''C''\|link=]]

	'''Mode C Discussion'''		'''Mode C Discussion'''
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	The failure distribution settings for event CA are shown in the figure below.		The failure distribution settings for event CA are shown in the figure below.

	[[Image:10.34.gif\|center\|550px\|Failure distribution settings for event ''C'' ''A''.]]		[[Image:10.34.gif\|center\|550px\|Failure distribution settings for event ''C'' ''A''.\|link=]]

	The failure distribution properties for event CB are set in the same manner.		The failure distribution properties for event CB are set in the same manner.

Richard House: /* Mode B */

2015-12-22T21:06:14Z

Mode B

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	The reliability block diagram for mode B is shown in the figure below.		The reliability block diagram for mode B is shown in the figure below.
	[[Image:10.29.png\|center\|150px\|Reliability block diagram for mode ''B''.]]		[[Image:10.29.png\|center\|150px\|Reliability block diagram for mode ''B''.\|link=]]

	'''Fault Tree Solution for Mode B'''		'''Fault Tree Solution for Mode B'''
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	The fault tree for mode B is shown in the figure below. A Load Sharing gate is used.		The fault tree for mode B is shown in the figure below. A Load Sharing gate is used.

	[[Image:10.30.png\|center\|200px\|Fault tree diagram for mode ''B''(using a Load Sharing gate unique to BlockSim).]]		[[Image:10.30.png\|center\|200px\|Fault tree diagram for mode ''B''(using a Load Sharing gate unique to BlockSim).\|link=]]

	'''Mode B Discussion'''		'''Mode B Discussion'''

Richard House: /* Mode A */

2015-12-22T21:05:36Z

Mode A

Richard House at 15:30, 21 September 2012

2012-09-21T15:30:12Z

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	& +{{R}_{T2}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{S1}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{T1}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{Y}} \\		& +{{R}_{T2}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{S1}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{T1}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{Y}} \\
	& +{{R}_{T2}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{S2}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{T1}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{Y}}		& +{{R}_{T2}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{S2}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{T1}}\text{ }\!\!\cdot\!\!\text{ }{{R}_{Y}}
	\end{align}</math>		\end{align}\,\!</math>

	Based on the given probabilities, distribution parameters are computed for each block (either RBD block or the fault tree event block). One way is to compute them using the Parameter Experimenter, as shown in the figure below. In this figure and for S1, the probability is 1 in 10,000 in one year (8,760 hours), thus the exponential failure rate is 1.1416e-8. This can be repeated for S2 and Y.		Based on the given probabilities, distribution parameters are computed for each block (either RBD block or the fault tree event block). One way is to compute them using the Parameter Experimenter, as shown in the figure below. In this figure and for S1, the probability is 1 in 10,000 in one year (8,760 hours), thus the exponential failure rate is 1.1416e-8. This can be repeated for S2 and Y.
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	:*If event CA has not occurred, then event CB will not occur.		:*If event CA has not occurred, then event CB will not occur.
	:*Events CA and CB both occur based on a Weibull distribution.		:*Events CA and CB both occur based on a Weibull distribution.
	:*For event CA, <math>\beta \,\!</math> = 2 and <math>\eta \,\!</math> = 30,000 hours.		:*For event CA, <math>\beta \,\!</math> = 2 and <math>\eta \,\!</math> = 30,000 hours.
	:*For event CB, <math>\beta \,\!</math> = 2 and <math>\eta \,\!</math> = 10,000 hours.		:*For event CB, <math>\beta \,\!</math> = 2 and <math>\eta \,\!</math> = 10,000 hours.

	'''RBD Solution for Mode C'''		'''RBD Solution for Mode C'''
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	Contained Items		Contained Items

	:*CA : Active failure distribution, Weibull distribution (<math>\beta \,\!</math> = 2, <math>\eta \,\!</math> = 30,000).		:*CA : Active failure distribution, Weibull distribution (<math>\beta \,\!</math> = 2, <math>\eta \,\!</math> = 30,000).
	:*CA : Quiescent failure distribution: None, cannot fail or age in this mode.		:*CA : Quiescent failure distribution: None, cannot fail or age in this mode.
	:*CB : Active failure distribution, Weibull distribution (<math>\beta \,\!</math> = 2, <math>\eta \,\!</math> = 10,000).		:*CB : Active failure distribution, Weibull distribution (<math>\beta \,\!</math> = 2, <math>\eta \,\!</math> = 10,000).
	:*CB : Quiescent failure distribution: None, cannot fail or age in this mode.		:*CB : Quiescent failure distribution: None, cannot fail or age in this mode.

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	& +R{{(t)}_{A}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{B}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{D}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{C}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{E}} \\		& +R{{(t)}_{A}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{B}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{D}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{C}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{E}} \\
	& -2(R{{(t)}_{A}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{B}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{F}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{D}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{C}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{E}})		& -2(R{{(t)}_{A}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{B}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{F}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{D}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{C}}\text{ }\!\!\cdot\!\!\text{ }R{{(t)}_{E}})
	\end{align}</math>		\end{align}\,\!</math>

	where <math>R{{(t)}_{A}}\,\!</math>, <math>R{{(t)}_{B}}\,\!</math> and <math>R{{(t)}_{C}}\,\!</math> are the reliability equations corresponding to the sub-modes.		where <math>R{{(t)}_{A}}\,\!</math>, <math>R{{(t)}_{B}}\,\!</math> and <math>R{{(t)}_{C}}\,\!</math> are the reliability equations corresponding to the sub-modes.

	===Analysis and Discussion===		===Analysis and Discussion===

Richard House: /* Mode B */

2012-08-10T07:06:11Z

Mode B

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	There are three dependent events associated with mode B : events BA, BB and BC.		There are three dependent events associated with mode B : events BA, BB and BC.

	:• Two out of the three events must occur for mode B to occur.		:*Two out of the three events must occur for mode B to occur.
	::o Events BA, BB and BC all have an exponential distribution with a mean of 50,000 hours.		::o Events BA, BB and BC all have an exponential distribution with a mean of 50,000 hours.
	::o The events are dependent (i.e., if BA, BB or BC occurs, then the remaining events are more likely to occur). Specifically, when one event occurs, the MTTF of the remaining events is halved.		::o The events are dependent (i.e., if BA, BB or BC occurs, then the remaining events are more likely to occur). Specifically, when one event occurs, the MTTF of the remaining events is halved.

← Older revision		Revision as of 21:05, 22 December 2015
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	The RBD that satisfies the conditions for mode A is shown in the figure below.		The RBD that satisfies the conditions for mode A is shown in the figure below.

	[[Image:6.png\|center\|400px\|Reliability block diagram for mode A.]]		[[Image:6.png\|center\|400px\|Reliability block diagram for mode A.\|link=]]

	Each mode is identified in the RBD. Furthermore, two additional items are included: a starting block (NF) and an end node (2/2). The starting block and the end node are set so they cannot fail and, therefore, will not affect the results. The end node is used to define a 2-out-of-2 configuration (i.e., both paths leading into the node must work).		Each mode is identified in the RBD. Furthermore, two additional items are included: a starting block (NF) and an end node (2/2). The starting block and the end node are set so they cannot fail and, therefore, will not affect the results. The end node is used to define a 2-out-of-2 configuration (i.e., both paths leading into the node must work).
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	The fault tree for mode A is shown in the figure below.		The fault tree for mode A is shown in the figure below.

	[[Image:7.png\|center\|400px\|Fault tree for mode ''A''.]]		[[Image:7.png\|center\|400px\|Fault tree for mode ''A''.\|link=]]

	Each mode is identified as an event in the fault tree. The following figure shows an alternative representation for mode A using [[Fault_Tree_Diagrams_and_System_Analysis#Using_Mirrored_Blocks_to_Represent_Complex_RBDs_as_FTDs\|mirrored events]] for S1 and S2.		Each mode is identified as an event in the fault tree. The following figure shows an alternative representation for mode A using [[Fault_Tree_Diagrams_and_System_Analysis#Using_Mirrored_Blocks_to_Represent_Complex_RBDs_as_FTDs\|mirrored events]] for S1 and S2.

	[[Image:8.png\|center\|400px\|An alternative representation of the fault tree for mode ''A'' using mirrored events.]]		[[Image:8.png\|center\|400px\|An alternative representation of the fault tree for mode ''A'' using mirrored events.\|link=]]

	'''Mode A Discussion'''		'''Mode A Discussion'''
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	Based on the given probabilities, distribution parameters are computed for each block (either RBD block or the fault tree event block). One way is to compute them using the Parameter Experimenter, as shown in the figure below. In this figure and for S1, the probability is 1 in 10,000 in one year (8,760 hours), thus the exponential failure rate is 1.1416e-8. This can be repeated for S2 and Y.		Based on the given probabilities, distribution parameters are computed for each block (either RBD block or the fault tree event block). One way is to compute them using the Parameter Experimenter, as shown in the figure below. In this figure and for S1, the probability is 1 in 10,000 in one year (8,760 hours), thus the exponential failure rate is 1.1416e-8. This can be repeated for S2 and Y.

	[[Image:10.26.gif\|center\|550px\|BlockSim's Parameter Experimenter.]]		[[Image:10.26.gif\|center\|550px\|BlockSim's Parameter Experimenter.\|link=]]

	Events T1 and T2 need to be modeled using a life distribution that does not have a constant failure rate. Using BlockSim's Parameter Experimenter and selecting the Weibull distribution, the parameter values for events T1 and T2 are shown in the figures below.		Events T1 and T2 need to be modeled using a life distribution that does not have a constant failure rate. Using BlockSim's Parameter Experimenter and selecting the Weibull distribution, the parameter values for events T1 and T2 are shown in the figures below.

	[[Image:10.27.gif\|center\|550px\|Parameter values for event ''T''1.]]		[[Image:10.27.gif\|center\|550px\|Parameter values for event ''T''1.\|link=]]

	===Mode B===		===Mode B===