Complex Failure Modes Example - Revision history

Lisa Hacker at 18:52, 18 September 2023

2023-09-18T18:52:17Z

← Older revision		Revision as of 18:52, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[Competing_Failure_Modes_Analysis#Complex_Failure_Modes_Analysis\|~~Life ~~Data Analysis Reference book]~~]''. </noinclude>		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''. </noinclude>

	Assume that a product has five independent failure modes: A, B, C, D and E. Furthermore, assume that failure of the product will occur if mode A occurs, modes B and C occur simultaneously or if modes D and E occur simultaneously. The objective is to estimate the reliability of the product at 100 hours, with 90% two-sided confidence bounds.		Assume that a product has five independent failure modes: A, B, C, D and E. Furthermore, assume that failure of the product will occur if mode A occurs, modes B and C occur simultaneously or if modes D and E occur simultaneously. The objective is to estimate the reliability of the product at 100 hours, with 90% two-sided confidence bounds.

Lisa Hacker at 00:29, 10 March 2023

2023-03-10T00:29:58Z

@@ Line 5: / Line 5: @@
 The product is tested to failure, and the failure times due to each mode are recorded in the following table.
-<center><math>\begin{matrix}
+|}
 '''Solution'''

Richard House at 18:12, 26 September 2012

2012-09-26T18:12:07Z

← Older revision		Revision as of 18:12, 26 September 2012
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	\text{829} & \text{154} & \text{1165} & \text{1093} & \text{127} \\		\text{829} & \text{154} & \text{1165} & \text{1093} & \text{127} \\
	\text{878} & \text{200} & \text{1337} & \text{1283} & \text{148} \\		\text{878} & \text{200} & \text{1337} & \text{1283} & \text{148} \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>

	'''Solution'''		'''Solution'''
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	[[Image:Competing Failure Mode Example 2 Diagram.png\|center\|450px\| ]]		[[Image:Competing Failure Mode Example 2 Diagram.png\|center\|450px\| ]]

	Click '''Analyze''' to analyze the diagram, and then use the Quick Calculation Pad (QCP) to estimate the reliability. The estimated R( ~~<math>~~100~~</math>~~ hours ~~<math>~~)~~</math>~~ and the 90% two-sided confidence bounds are:		Click '''Analyze''' to analyze the diagram, and then use the Quick Calculation Pad (QCP) to estimate the reliability. The estimated R(100 hours) and the 90% two-sided confidence bounds are:

	::<math>\begin{matrix}		::<math>\begin{matrix}
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	\hat{R}(100)=0.824397 \\		\hat{R}(100)=0.824397 \\
	{{{\hat{R}}}_{L}}(100)=0.719090 \\		{{{\hat{R}}}_{L}}(100)=0.719090 \\
	\end{matrix}</math>		\end{matrix}\,\!</math>

Kate Racaza at 02:52, 9 August 2012

2012-08-09T02:52:25Z

← Older revision		Revision as of 02:52, 9 August 2012
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	'''Solution'''		'''Solution'''

	The reliability block diagram (RBD) approach can be used to analyze the ~~failure modes~~. But before creating a diagram, the data sets of the failure modes need to be segregated so that each mode can be represented by a single block in the diagram. Recall that when you analyze a particular mode, the failure times for all other ~~unrelated~~ modes are considered to be suspensions. This captures the fact that those units operated for a period of time without experiencing the failure mode of interest before they were removed from observation when they failed due to another mode. We can easily perform this step via Weibull++'s Batch Auto Run utility. To do this, enter the data from the table into a single data sheet. Choose the '''2P-Weibull''' distribution and the '''MLE''' analysis method, and then click the '''Batch Auto Run''' icon on the control panel. When prompted to select the subset IDs, select them all. Click the '''Processing Preferences''' tab. In the '''Extraction Options''' area, select the second option, as shown next.		The reliability block diagram (RBD) approach can be used to analyze the reliability of the product. But before creating a diagram, the data sets of the failure modes need to be segregated so that each mode can be represented by a single block in the diagram. Recall that when you analyze a particular mode, the failure times for all other competing modes are considered to be suspensions. This captures the fact that those units operated for a period of time without experiencing the failure mode of interest before they were removed from observation when they failed due to another mode. We can easily perform this step via Weibull++'s Batch Auto Run utility. To do this, enter the data from the table into a single data sheet. Choose the '''2P-Weibull''' distribution and the '''MLE''' analysis method, and then click the '''Batch Auto Run''' icon on the control panel. When prompted to select the subset IDs, select them all. Click the '''Processing Preferences''' tab. In the '''Extraction Options''' area, select the second option, as shown next.

	[[Image:Batch Auto Run.png\|center\|450 px\| ]]		[[Image:Batch Auto Run.png\|center\|450 px\| ]]

Kate Racaza: updated problem statement

2012-08-09T02:40:20Z

updated problem statement

← Older revision		Revision as of 02:40, 9 August 2012
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	''This example appears in the [[Competing_Failure_Modes_Analysis#Complex_Failure_Modes_Analysis\|Life Data Analysis Reference book]]''. </noinclude>		''This example appears in the [[Competing_Failure_Modes_Analysis#Complex_Failure_Modes_Analysis\|Life Data Analysis Reference book]]''. </noinclude>

	Assume that a product has five independent failure modes: A, B, C, D and E. Furthermore, assume that failure of the product will occur if mode A occurs, modes B and C occur simultaneously or if modes D and E occur simultaneously. The objective is to estimate the reliability of the product at 100 hours, with 90% two-sided confidence bounds. The times-to~~-failure data for~~ each mode are ~~given~~ in the following table.		Assume that a product has five independent failure modes: A, B, C, D and E. Furthermore, assume that failure of the product will occur if mode A occurs, modes B and C occur simultaneously or if modes D and E occur simultaneously. The objective is to estimate the reliability of the product at 100 hours, with 90% two-sided confidence bounds.

			The product is tested to failure, and the failure times due to each mode are recorded in the following table.

	<center><math>\begin{matrix}		<center><math>\begin{matrix}

Richard House at 07:48, 7 August 2012

2012-08-07T07:48:14Z

← Older revision		Revision as of 07:48, 7 August 2012
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	Assume that a product has five independent failure modes: A, B, C, D and E. Furthermore, assume that failure of the product will occur if mode A occurs, modes B and C occur simultaneously or if modes D and E occur simultaneously. The objective is to estimate the reliability of the product at 100 hours, with 90% two-sided confidence bounds. The times-to-failure data for each mode are given in the following table.		Assume that a product has five independent failure modes: A, B, C, D and E. Furthermore, assume that failure of the product will occur if mode A occurs, modes B and C occur simultaneously or if modes D and E occur simultaneously. The objective is to estimate the reliability of the product at 100 hours, with 90% two-sided confidence bounds. The times-to-failure data for each mode are given in the following table.


	<center><math>\begin{matrix}		<center><math>\begin{matrix}
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	\text{878} & \text{200} & \text{1337} & \text{1283} & \text{148} \\		\text{878} & \text{200} & \text{1337} & \text{1283} & \text{148} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	'''Solution'''		'''Solution'''

	The reliability block diagram (RBD) approach can be used to analyze the failure modes. But before creating a diagram, the data sets of the failure modes need to be segregated so that each mode can be represented by a single block in the diagram. Recall that when you analyze a particular mode, the failure times for all other unrelated modes are considered to be suspensions. This captures the fact that those units operated for a period of time without experiencing the failure mode of interest before they were removed from observation when they failed due to another mode. We can easily perform this step via Weibull++'s Batch Auto Run utility. To do this, enter the data from the table into a single data sheet. Choose the '''2P-Weibull''' distribution and the '''MLE''' analysis method, and then click the '''Batch Auto Run''' icon on the control panel. When prompted to select the subset IDs, select them all. Click the '''Processing Preferences''' tab. In the '''Extraction Options''' area, select the second option, as shown next.		The reliability block diagram (RBD) approach can be used to analyze the failure modes. But before creating a diagram, the data sets of the failure modes need to be segregated so that each mode can be represented by a single block in the diagram. Recall that when you analyze a particular mode, the failure times for all other unrelated modes are considered to be suspensions. This captures the fact that those units operated for a period of time without experiencing the failure mode of interest before they were removed from observation when they failed due to another mode. We can easily perform this step via Weibull++'s Batch Auto Run utility. To do this, enter the data from the table into a single data sheet. Choose the '''2P-Weibull''' distribution and the '''MLE''' analysis method, and then click the '''Batch Auto Run''' icon on the control panel. When prompted to select the subset IDs, select them all. Click the '''Processing Preferences''' tab. In the '''Extraction Options''' area, select the second option, as shown next.


	[[Image:Batch Auto Run.png\|center\|450 px\| ]]		[[Image:Batch Auto Run.png\|center\|450 px\| ]]


	This will extract the data sets that are required for the analysis. Select the check box in the '''Calculation Options''' area and click '''OK'''. The data sets are extracted into separate data sheets in the folio and automatically calculated.		This will extract the data sets that are required for the analysis. Select the check box in the '''Calculation Options''' area and click '''OK'''. The data sets are extracted into separate data sheets in the folio and automatically calculated.
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	The following figure shows the completed diagram.		The following figure shows the completed diagram.


	[[Image:Competing Failure Mode Example 2 Diagram.png\|center\|450px\| ]]		[[Image:Competing Failure Mode Example 2 Diagram.png\|center\|450px\| ]]


	Click '''Analyze''' to analyze the diagram, and then use the Quick Calculation Pad (QCP) to estimate the reliability. The estimated R( <math>100</math> hours <math>)</math> and the 90% two-sided confidence bounds are:		Click '''Analyze''' to analyze the diagram, and then use the Quick Calculation Pad (QCP) to estimate the reliability. The estimated R( <math>100</math> hours <math>)</math> and the 90% two-sided confidence bounds are:

Kate Racaza: updated example

2012-07-24T06:06:12Z

updated example

← Older revision		Revision as of 06:06, 24 July 2012
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	''~~'Competing Failures with Complex Configuration Example'~~''		<noinclude>{{Banner Weibull Examples}}
			''This example appears in the [[Competing_Failure_Modes_Analysis#Complex_Failure_Modes_Analysis\|Life Data Analysis Reference book]]''. </noinclude>

	Assume that a product has five failure modes: A, B, C, D and F. Furthermore, assume that failure of the product 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. ~~Times~~-to-failure for each mode is given in the ~~next~~ table.		Assume that a product has five independent failure modes: A, B, C, D and E. Furthermore, assume that failure of the product will occur if mode A occurs, modes B and C occur simultaneously or if modes D and E occur simultaneously. The objective is to estimate the reliability of the product at 100 hours, with 90% two-sided confidence bounds. The times-to-failure data for each mode are given in the following table.


	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	\text{TTF for A} & \text{TTF for B} & \text{TTF for C} & \text{TTF for D} & \text{TTF for F} \\		\text{TTF for A} & \text{TTF for B} & \text{TTF for C} & \text{TTF for D} & \text{TTF for E} \\
	\text{276} & \text{23} & \text{499} & \text{467} & \text{67} \\		\text{276} & \text{23} & \text{499} & \text{467} & \text{67} \\
	\text{320} & \text{36} & \text{545} & \text{540} & \text{72} \\		\text{320} & \text{36} & \text{545} & \text{540} & \text{72} \\
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	~~The RBD that describes this configuration is shown next.~~		'''Solution'''

			The reliability block diagram (RBD) approach can be used to analyze the failure modes. But before creating a diagram, the data sets of the failure modes need to be segregated so that each mode can be represented by a single block in the diagram. Recall that when you analyze a particular mode, the failure times for all other unrelated modes are considered to be suspensions. This captures the fact that those units operated for a period of time without experiencing the failure mode of interest before they were removed from observation when they failed due to another mode. We can easily perform this step via Weibull++'s Batch Auto Run utility. To do this, enter the data from the table into a single data sheet. Choose the '''2P-Weibull''' distribution and the '''MLE''' analysis method, and then click the '''Batch Auto Run''' icon on the control panel. When prompted to select the subset IDs, select them all. Click the '''Processing Preferences''' tab. In the '''Extraction Options''' area, select the second option, as shown next.

	~~<math></math>~~
	~~[[Image:WB.18 RBD.png\|center\|250px\| ]]~~

	One folio with multiple data sheets was created in Weibull++ for each of the data sets and each file was analyzed using the two-parameter Weibull distribution, MLE as the analysis method and Fisher Matrix as the confidence bounds method. A diagram is created by choosing '''Diagram''' from the Insert menu. The failure modes can be inserted into the diagram by selecting them from the '''Adding Block''' window.		[[Image:Batch Auto Run.png\|center\|450 px\| ]]

	[[Image:~~Competing Failure Mode Example 2 Adding Block~~.png~~\|thumb~~\|center\|~~250px~~\| ]]


	~~The nodes~~ are ~~inserted by clicking choosing Add Node from~~ the ~~Diagram menu~~. ~~The number of required paths can be specified by double clicking~~ the ~~node and entering the appropriate number (1~~ in the ~~first node~~ and 2 in the ~~second node)~~.		This will extract the data sets that are required for the analysis. Select the check box in the '''Calculation Options''' area and click '''OK'''. The data sets are extracted into separate data sheets in the folio and automatically calculated.

	~~<math~~>~~</math~~>		Next, create a diagram by choosing '''Insert > Tools > Diagram'''. Add blocks by right-clicking the diagram and choosing '''Add Block''' on the shortcut menu. When prompted to select the data sheet of the failure mode that the block will represent, select the data sheet for mode A. Use the same approach to add the blocks that will represent failure modes B, C , D and E. Add a connector by right-clicking the diagram sheet and choosing '''Connect Blocks''', and then connect the blocks in an appropriate configuration to describe the relationships between the failure modes. To insert a node, which acts as a switch that the diagram paths move through, right-click the diagram and choose '''Add Node'''. Specify the number of required paths in the node by double-clicking the node and entering the appropriate number (use 2 in both nodes).
	~~[[Image:Competing Failure Mode Example~~ 2 ~~Node Path~~.~~png\|thumb\|center\|250px\| ]]~~

	The ~~diagam is:~~		The following figure shows the completed diagram.

	~~<math></math>~~
	~~[[Image:Competing Failure Mode Example 2 Diagram.png\|thumb\|center\|250px\| ]]~~

			[[Image:Competing Failure Mode Example 2 Diagram.png\|center\|450px\| ]]

	~~Using~~ the Quick Calculation Pad (QCP), the estimated R( <math>100</math> hours <math>)</math> and the 90% two-sided confidence bounds are:
			Click '''Analyze''' to analyze the diagram, and then use the Quick Calculation Pad (QCP) to estimate the reliability. The estimated R( <math>100</math> hours <math>)</math> and the 90% two-sided confidence bounds are:

	::<math>\begin{matrix}		::<math>\begin{matrix}
	{{{\hat{R}}}_{U}}(100)=0.~~991~~ \\		{{{\hat{R}}}_{U}}(100)=0.895940 \\
	\hat{R}(100)=0.~~9905~~ \\		\hat{R}(100)=0.824397 \\
	{{{\hat{R}}}_{L}}(100)=0.~~9080~~ \\		{{{\hat{R}}}_{L}}(100)=0.719090 \\
	\end{matrix}</math>		\end{matrix}</math>

Kate Racaza: moved Template:Example: Competing Failures with Complex Configuration Example to Complex Failure Modes Example: incorrect title and namespace

2012-07-24T04:04:47Z

moved Template:Example: Competing Failures with Complex Configuration Example to Complex Failure Modes Example: incorrect title and namespace

← Older revision	Revision as of 04:04, 24 July 2012
(No difference)

Nicolette Young at 22:04, 25 April 2012

2012-04-25T22:04:08Z

← Older revision		Revision as of 22:04, 25 April 2012
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	<math></math>		<math></math>
	[[Image:WB.18 RBD.png\|center\|~~400px~~\| ]]		[[Image:WB.18 RBD.png\|center\|250px\| ]]

	One folio with multiple data sheets was created in Weibull++ for each of the data sets and each file was analyzed using the two-parameter Weibull distribution, MLE as the analysis method and Fisher Matrix as the confidence bounds method. A diagram is created by choosing '''Diagram''' from the Insert menu. The failure modes can be inserted into the diagram by selecting them from the '''Adding Block''' window.		One folio with multiple data sheets was created in Weibull++ for each of the data sets and each file was analyzed using the two-parameter Weibull distribution, MLE as the analysis method and Fisher Matrix as the confidence bounds method. A diagram is created by choosing '''Diagram''' from the Insert menu. The failure modes can be inserted into the diagram by selecting them from the '''Adding Block''' window.

	[[Image:Competing Failure Mode Example 2 Adding Block.png\|thumb\|center\|~~400px~~\| ]]		[[Image:Competing Failure Mode Example 2 Adding Block.png\|thumb\|center\|250px\| ]]


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	<math></math>		<math></math>
	[[Image:Competing Failure Mode Example 2 Node Path.png\|thumb\|center\|~~400px~~\| ]]		[[Image:Competing Failure Mode Example 2 Node Path.png\|thumb\|center\|250px\| ]]

	The diagam is:		The diagam is:

	<math></math>		<math></math>
	[[Image:Competing Failure Mode Example 2 Diagram.png\|thumb\|center\|~~500px~~\| ]]		[[Image:Competing Failure Mode Example 2 Diagram.png\|thumb\|center\|250px\| ]]

Nicolette Young at 16:31, 15 March 2012

2012-03-15T16:31:09Z

← Older revision		Revision as of 16:31, 15 March 2012
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	<math></math>		<math></math>
	[[Image:~~lda23~~.9.~~gif\|thumb~~\|center\|400px\| ]]		[[Image:WB.18 RBD.png\|center\|400px\| ]]

	One folio with multiple data sheets was created in Weibull++ for each of the data sets and each file was analyzed using the two-parameter Weibull distribution, MLE as the analysis method and Fisher Matrix as the confidence bounds method. A diagram is created by choosing '''Diagram''' from the Insert menu. The failure modes can be inserted into the diagram by selecting them from the '''Adding Block''' window.		One folio with multiple data sheets was created in Weibull++ for each of the data sets and each file was analyzed using the two-parameter Weibull distribution, MLE as the analysis method and Fisher Matrix as the confidence bounds method. A diagram is created by choosing '''Diagram''' from the Insert menu. The failure modes can be inserted into the diagram by selecting them from the '''Adding Block''' window.