Competing Failure Modes Analysis - Revision history

Lisa Hacker at 21:33, 18 September 2023

2023-09-18T21:33:14Z

← Older revision		Revision as of 21:33, 18 September 2023
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	==Complex Failure Modes Analysis==<!-- THIS SECTION HEADER IS LINKED TO EXTERNAL SEARCH IN THE W++/A HELP FILE. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->		==Complex Failure Modes Analysis==<!-- THIS SECTION HEADER IS LINKED TO EXTERNAL SEARCH IN THE W++/A HELP FILE. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->
	In addition to being viewed as a series system, the relationship between the different competing failures modes can be more complex. After performing separate analysis for each failure mode, a diagram that describes how each failure mode can result in a product failure can be used to perform analysis for the item in question. Such diagrams are usually referred to as Reliability Block Diagrams (RBD) (for more on RBDs see ~~ReliaSoft's~~ System ~~Analysis Reference~~ and [https://www.hbkworld.com/en/products/software/analysis-simulation/reliability/blocksim-system-reliability-availability-maintainability-ram-analysis-software ~~ReliaSoft's~~ BlockSim software]).		In addition to being viewed as a series system, the relationship between the different competing failures modes can be more complex. After performing separate analysis for each failure mode, a diagram that describes how each failure mode can result in a product failure can be used to perform analysis for the item in question. Such diagrams are usually referred to as Reliability Block Diagrams (RBD) (for more on RBDs see [https://help.reliasoft.com/reference/system_analysis System analysis reference] and [https://www.hbkworld.com/en/products/software/analysis-simulation/reliability/blocksim-system-reliability-availability-maintainability-ram-analysis-software BlockSim software]).

	A reliability block diagram is made of blocks that represent the failure modes and arrows and connects the blocks in different configurations. Note that the blocks can also be used to represent different components or subsystems that make up the product. Weibull++ provides the capability to use a diagram to model, series, parallel, k-out-of-n configurations in addition to any complex combinations of these configurations.		A reliability block diagram is made of blocks that represent the failure modes and arrows and connects the blocks in different configurations. Note that the blocks can also be used to represent different components or subsystems that make up the product. Weibull++ provides the capability to use a diagram to model, series, parallel, k-out-of-n configurations in addition to any complex combinations of these configurations.
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	::<math>R(t)=\overset{n}{\mathop{\underset{r=k}{\mathop{\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,\left( \underset{k}{\mathop{\overset{n}{\mathop{{}}}\,}}\, \right){{R}^{r}}(t){{(1-R(t))}^{n-r}}\,\!</math>		::<math>R(t)=\overset{n}{\mathop{\underset{r=k}{\mathop{\underset{}{\overset{}{\mathop \sum }}\,}}\,}}\,\left( \underset{k}{\mathop{\overset{n}{\mathop{{}}}\,}}\, \right){{R}^{r}}(t){{(1-R(t))}^{n-r}}\,\!</math>

	In the case where the k-out-of-n failure modes are not identical, other approaches for calculating the reliability must be used (e.g. the event space method). Discussion of these is beyond the scope of this reference. Interested readers can consult the [~~[RBDs_and_Analytical_System_Reliability#k-out-of-n_Parallel_Configuration\|~~ System ~~Analysis Reference book]~~].		In the case where the k-out-of-n failure modes are not identical, other approaches for calculating the reliability must be used (e.g. the event space method). Discussion of these is beyond the scope of this reference. Interested readers can consult the [https://help.reliasoft.com/reference/system_analysis System analysis reference].

	'''Complex Systems'''		'''Complex Systems'''
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	[[Image:WB.18 complex systems.png\|center\|400px\| ]]		[[Image:WB.18 complex systems.png\|center\|400px\| ]]

	The previous configuration cannot be broken down into a group of series and parallel configurations. This is primarily due to the fact that failure mode C has two paths leading away from it, whereas B and D have only one. Several methods exist for obtaining the reliability of a complex configuration including the decomposition method, the event space method and the path-tracing method. Discussion of these is beyond the scope of this reference. Interested readers can consult the [~~[RBDs_and_Analytical_System_Reliability#Complex_Systems\|~~System ~~Analysis Reference book]~~].		The previous configuration cannot be broken down into a group of series and parallel configurations. This is primarily due to the fact that failure mode C has two paths leading away from it, whereas B and D have only one. Several methods exist for obtaining the reliability of a complex configuration including the decomposition method, the event space method and the path-tracing method. Discussion of these is beyond the scope of this reference. Interested readers can consult the [https://help.reliasoft.com/reference/system_analysis System analysis reference].

	===Complex Failure Modes Example===		===Complex Failure Modes Example===
	{{:Complex Failure Modes Example}}		{{:Complex Failure Modes Example}}

Lisa Hacker at 19:30, 15 September 2023

2023-09-15T19:30:11Z

← Older revision		Revision as of 19:30, 15 September 2023
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	==Complex Failure Modes Analysis==<!-- THIS SECTION HEADER IS LINKED TO EXTERNAL SEARCH IN THE W++/A HELP FILE. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->		==Complex Failure Modes Analysis==<!-- THIS SECTION HEADER IS LINKED TO EXTERNAL SEARCH IN THE W++/A HELP FILE. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->
	In addition to being viewed as a series system, the relationship between the different competing failures modes can be more complex. After performing separate analysis for each failure mode, a diagram that describes how each failure mode can result in a product failure can be used to perform analysis for the item in question. Such diagrams are usually referred to as Reliability Block Diagrams (RBD) (for more on RBDs see ~~[[System_Analysis_Reference\|~~ReliaSoft's System Analysis Reference]] and [~~http~~://www.~~reliasoft~~.com/~~BlockSim~~/ ReliaSoft's BlockSim software]).		In addition to being viewed as a series system, the relationship between the different competing failures modes can be more complex. After performing separate analysis for each failure mode, a diagram that describes how each failure mode can result in a product failure can be used to perform analysis for the item in question. Such diagrams are usually referred to as Reliability Block Diagrams (RBD) (for more on RBDs see ReliaSoft's System Analysis Reference and [https://www.hbkworld.com/en/products/software/analysis-simulation/reliability/blocksim-system-reliability-availability-maintainability-ram-analysis-software ReliaSoft's BlockSim software]).

	A reliability block diagram is made of blocks that represent the failure modes and arrows and connects the blocks in different configurations. Note that the blocks can also be used to represent different components or subsystems that make up the product. Weibull++ provides the capability to use a diagram to model, series, parallel, k-out-of-n configurations in addition to any complex combinations of these configurations.		A reliability block diagram is made of blocks that represent the failure modes and arrows and connects the blocks in different configurations. Note that the blocks can also be used to represent different components or subsystems that make up the product. Weibull++ provides the capability to use a diagram to model, series, parallel, k-out-of-n configurations in addition to any complex combinations of these configurations.

Lisa Hacker: /* CFM Example */

2023-05-23T17:35:13Z

CFM Example

← Older revision		Revision as of 17:35, 23 May 2023
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	Or the reliability of the unit (or system) under both modes is <math>{{R}_{sys}}(100)=69.094%\,\!</math>.		Or the reliability of the unit (or system) under both modes is <math>{{R}_{sys}}(100)=69.094%\,\!</math>.

	You can also perform this analysis using Weibull++'s built-in CFM analysis options, which allow you to generate a probability plot that contains the combined mode line as well as the individual mode lines.		You can also perform this analysis using Weibull++'s built-in CFM analysis options, which allow you to generate a probability plot that contains the combined mode line as well as the individual mode lines.

	~~<div class="noprint">~~
	~~{{Examples Box\|Weibull++ Examples\|<p>More CFM examples are available! See also:</p>~~
	{{Examples Both\|http://www.reliasoft.com/Weibull/examples/rc10/index.htm\|Competing Failure Modes Analysis\|http://www.reliasoft.tv/weibull/appexamples/weibull_app_ex_10.html\|Watch the video...}}<nowiki/>
	}}
	~~</div>~~

	==Confidence Bounds for CFM Analysis==		==Confidence Bounds for CFM Analysis==

Lisa Hacker: /* CFM Example */

2023-03-10T00:24:15Z

CFM Example

← Older revision		Revision as of 00:24, 10 March 2023
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	\|1 \|\|13 \|\| V\|\|1\|\|181\|\|W		\|1 \|\|13 \|\| V\|\|1\|\|181\|\|W
	\|- align="center"		\|- align="center"
	\|2 \|\|23 \|\| V\|\|212\|\|~~147~~\|\|W		\|2 \|\|23 \|\| V\|\|1\|\|212\|\|W
			\|- align="center"
			\|1 \|\|28 \|\| V\|\|1\|\|245\|\|W
	\|- align="center"		\|- align="center"
	\|1 \|\|30 \|\| V\|\|1\|\|247\|\|V		\|1 \|\|30 \|\| V\|\|1\|\|247\|\|V
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	\|1 \|\|80 \|\| V\|\|1\|\|266\|\|W		\|1 \|\|80 \|\| V\|\|1\|\|266\|\|W
	\|- align="center"		\|- align="center"
	\|1 \|\|88 \|\| V\|\|1\|\|275\|\|V		\|1 \|\|88 \|\| V\|\|1\|\|275\|\|W
	\|- align="center"		\|- align="center"
	\|1 \|\|106 \|\| V\|\|1\|\|293\|\|V		\|1 \|\|106 \|\| V\|\|1\|\|293\|\|W
	\|- align="center"		\|- align="center"
	\|1 \|\|143 \|\| V\|\|1\|\|300\|\|V		\|1 \|\|143 \|\| V\|\|1\|\|300\|\|suspended
	\|}		\|}

Lisa Hacker: /* CFM Example */

2023-03-10T00:19:38Z

CFM Example

← Older revision		Revision as of 00:19, 10 March 2023
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	30 units are tested, and the failure times are recorded in the following table. The failures that are due to the random voltage spikes are denoted by a V. The failures that are due to wearout failures are denoted by a W.		30 units are tested, and the failure times are recorded in the following table. The failures that are due to the random voltage spikes are denoted by a V. The failures that are due to wearout failures are denoted by a W.

			{\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
			\|- align="center"
			!Number in State
			!Failure Time*
			!Failure Mode
			!Number in State
			!Failure Time*
			!Failure Mode
			\|- align="center"
			\|1 \|\|2 \|\| V\|\|1\|\|147\|\|W
			\|- align="center"
			\|1 \|\|10 \|\| V\|\|1\|\|173\|\|V
			\|- align="center"
			\|1 \|\|13 \|\| V\|\|1\|\|181\|\|W
			\|- align="center"
			\|2 \|\|23 \|\| V\|\|212\|\|147\|\|W
			\|- align="center"
			\|1 \|\|30 \|\| V\|\|1\|\|247\|\|V
			\|- align="center"
			\|1 \|\|65 \|\| V\|\|1\|\|261\|\|V
			\|- align="center"
			\|1 \|\|80 \|\| V\|\|1\|\|266\|\|W
			\|- align="center"
			\|1 \|\|88 \|\| V\|\|1\|\|275\|\|V
			\|- align="center"
			\|1 \|\|106 \|\| V\|\|1\|\|293\|\|V
			\|- align="center"
			\|1 \|\|143 \|\| V\|\|1\|\|300\|\|V
			\|}


	~~<center><math>\begin{matrix}~~
	~~Number & Failure & Failure & Number & Failure & Failure \\~~
	~~in State & Time* & Mode & in State & Time* & Mode \\~~
	~~\text{1} & \text{2} & \text{V} & \text{1} & \text{147} & \text{W} \\~~
	~~\text{1} & \text{10} & \text{V} & \text{1} & \text{173} & \text{V} \\~~
	~~\text{1} & \text{13} & \text{V} & \text{1} & \text{181} & \text{W} \\~~
	~~\text{2} & \text{23} & \text{V} & \text{1} & \text{212} & \text{W} \\~~
	~~\text{1} & \text{28} & \text{V} & \text{1} & \text{245} & \text{W} \\~~
	~~\text{1} & \text{30} & \text{V} & \text{1} & \text{247} & \text{V} \\~~
	~~\text{1} & \text{65} & \text{V} & \text{1} & \text{261} & \text{V} \\~~
	~~\text{1} & \text{80} & \text{V} & \text{1} & \text{266} & \text{W} \\~~
	~~\text{1} & \text{88} & \text{V} & \text{1} & \text{275} & \text{W} \\~~
	~~\text{1} & \text{106} & \text{V} & \text{1} & \text{293} & \text{W} \\~~
	~~\text{1} & \text{143} & \text{V} & \text{8} & \text{300} & \text{suspended} \\~~
	~~\end{matrix}\,\!</math></center>~~

	''*Failure times given are in thousands of cycles.''		''*Failure times given are in thousands of cycles.''

Richard House: /* Complex Failure Modes Analysis */

2017-08-10T18:40:16Z

Complex Failure Modes Analysis

← Older revision		Revision as of 18:40, 10 August 2017
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	In addition to being viewed as a series system, the relationship between the different competing failures modes can be more complex. After performing separate analysis for each failure mode, a diagram that describes how each failure mode can result in a product failure can be used to perform analysis for the item in question. Such diagrams are usually referred to as Reliability Block Diagrams (RBD) (for more on RBDs see [[System_Analysis_Reference\|ReliaSoft's System Analysis Reference]] and [http://www.reliasoft.com/BlockSim/ ReliaSoft's BlockSim software]).		In addition to being viewed as a series system, the relationship between the different competing failures modes can be more complex. After performing separate analysis for each failure mode, a diagram that describes how each failure mode can result in a product failure can be used to perform analysis for the item in question. Such diagrams are usually referred to as Reliability Block Diagrams (RBD) (for more on RBDs see [[System_Analysis_Reference\|ReliaSoft's System Analysis Reference]] and [http://www.reliasoft.com/BlockSim/ ReliaSoft's BlockSim software]).

	A reliability block diagram is made of blocks that represent the failure modes and arrows and connects the blocks in different configurations. Note that the blocks can also be used to represent different components or subsystems that make up the product. Weibull ++ provides the capability to use a diagram to model, series, parallel, k-out-of-n configurations in addition to any complex combinations of these configurations.		A reliability block diagram is made of blocks that represent the failure modes and arrows and connects the blocks in different configurations. Note that the blocks can also be used to represent different components or subsystems that make up the product. Weibull++ provides the capability to use a diagram to model, series, parallel, k-out-of-n configurations in addition to any complex combinations of these configurations.

	In this analysis, the failure modes are assumed to be statistically independent. (Note: In the context of this reference, statistically independent implies that failure information for one failure mode provides no information about, i.e. does not affect, other failure mode). Analysis of dependent modes is more complex. Advanced RBD software such as ReliaSoft's BlockSim can handle and analyze such dependencies, as well as provide more advanced constructs and analyses (see http://www.ReliaSoft.com/BlockSim).		In this analysis, the failure modes are assumed to be statistically independent. (Note: In the context of this reference, statistically independent implies that failure information for one failure mode provides no information about, i.e. does not affect, other failure mode). Analysis of dependent modes is more complex. Advanced RBD software such as ReliaSoft's BlockSim can handle and analyze such dependencies, as well as provide more advanced constructs and analyses (see http://www.ReliaSoft.com/BlockSim).

Sharon Honecker: /* Variance/Covariance Matrix */ Added "-1" to Fisher Matrix since the Var-Cov matrix is the inverse of the Fisher Information Matrix.

2016-12-08T21:24:17Z

Variance/Covariance Matrix: Added "-1" to Fisher Matrix since the Var-Cov matrix is the inverse of the Fisher Information Matrix.

← Older revision		Revision as of 21:24, 8 December 2016
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	0 & 0 & 0 & 0 & 0 & Cov({{{\hat{a}}}_{n}},{{{\hat{b}}}_{n}}) & Var({{{\hat{b}}}_{n}}) \\		0 & 0 & 0 & 0 & 0 & Cov({{{\hat{a}}}_{n}},{{{\hat{b}}}_{n}}) & Var({{{\hat{b}}}_{n}}) \\
	\end{matrix} \right) \\		\end{matrix} \right) \\
	& =\left( \begin{matrix}		& ={\left( \begin{matrix}
	-\frac{{{\partial }^{2}}\Lambda }{\partial a_{1}^{2}} & -\frac{{{\partial }^{2}}\Lambda }{\partial a_{1}^{{}}\partial {{b}_{1}}} & 0 & 0 & 0 & 0 & 0 \\		-\frac{{{\partial }^{2}}\Lambda }{\partial a_{1}^{2}} & -\frac{{{\partial }^{2}}\Lambda }{\partial a_{1}^{{}}\partial {{b}_{1}}} & 0 & 0 & 0 & 0 & 0 \\
	-\frac{{{\partial }^{2}}\Lambda }{\partial a_{1}^{{}}\partial {{b}_{1}}} & -\frac{{{\partial }^{2}}\Lambda }{\partial b_{1}^{2}} & 0 & 0 & 0 & 0 & 0 \\		-\frac{{{\partial }^{2}}\Lambda }{\partial a_{1}^{{}}\partial {{b}_{1}}} & -\frac{{{\partial }^{2}}\Lambda }{\partial b_{1}^{2}} & 0 & 0 & 0 & 0 & 0 \\
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	0 & 0 & 0 & 0 & 0 & -\frac{{{\partial }^{2}}\Lambda }{\partial a_{n}^{2}} & -\frac{{{\partial }^{2}}\Lambda }{\partial a_{n}^{{}}\partial {{b}_{n}}} \\		0 & 0 & 0 & 0 & 0 & -\frac{{{\partial }^{2}}\Lambda }{\partial a_{n}^{2}} & -\frac{{{\partial }^{2}}\Lambda }{\partial a_{n}^{{}}\partial {{b}_{n}}} \\
	0 & 0 & 0 & 0 & 0 & -\frac{{{\partial }^{2}}\Lambda }{\partial a_{n}^{{}}\partial {{b}_{n}}} & -\frac{{{\partial }^{2}}\Lambda }{\partial b_{n}^{2}} \\		0 & 0 & 0 & 0 & 0 & -\frac{{{\partial }^{2}}\Lambda }{\partial a_{n}^{{}}\partial {{b}_{n}}} & -\frac{{{\partial }^{2}}\Lambda }{\partial b_{n}^{2}} \\
	\end{matrix} \right) \\		\end{matrix} \right)}^{-1} \\
	\end{align}\,\!</math>		\end{align}\,\!</math>

Nicolette Young: /* Failure Modes Configurations */

2015-12-23T17:16:54Z

Failure Modes Configurations

← Older revision		Revision as of 17:16, 23 December 2015
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	The basic competing failure modes configuration, which has already been discussed, is a series configuration. In a series configuration, the occurrence of any failure mode results in failure for the product.		The basic competing failure modes configuration, which has already been discussed, is a series configuration. In a series configuration, the occurrence of any failure mode results in failure for the product.

	[[Image:WB.18 series configuration.png\|center\|~~300px~~\| ]]		[[Image:WB.18 series configuration.png\|center\|400px\| ]]

	The equation that describes series configuration is:		The equation that describes series configuration is:
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	While many smaller products can be accurately represented by either a simple series or parallel configuration, there may be larger products that involve both series and parallel configurations in the overall model of the product. Such products can be analyzed by calculating the reliabilities for the individual series and parallel sections and then combining them in the appropriate manner.		While many smaller products can be accurately represented by either a simple series or parallel configuration, there may be larger products that involve both series and parallel configurations in the overall model of the product. Such products can be analyzed by calculating the reliabilities for the individual series and parallel sections and then combining them in the appropriate manner.

	[[Image:WB.18 series parallel.png\|center\|~~200px~~\| ]]		[[Image:WB.18 series parallel.png\|center\|250px\| ]]

	'''k-out-of-n Parallel Configuration='''		'''k-out-of-n Parallel Configuration='''
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	In many cases, it is not easy to recognize which components are in series and which are in parallel in a complex system.		In many cases, it is not easy to recognize which components are in series and which are in parallel in a complex system.

	[[Image:WB.18 complex systems.png\|center\|~~200px~~\| ]]		[[Image:WB.18 complex systems.png\|center\|400px\| ]]

	The previous configuration cannot be broken down into a group of series and parallel configurations. This is primarily due to the fact that failure mode C has two paths leading away from it, whereas B and D have only one. Several methods exist for obtaining the reliability of a complex configuration including the decomposition method, the event space method and the path-tracing method. Discussion of these is beyond the scope of this reference. Interested readers can consult the [[RBDs_and_Analytical_System_Reliability#Complex_Systems\|System Analysis Reference book]].		The previous configuration cannot be broken down into a group of series and parallel configurations. This is primarily due to the fact that failure mode C has two paths leading away from it, whereas B and D have only one. Several methods exist for obtaining the reliability of a complex configuration including the decomposition method, the event space method and the path-tracing method. Discussion of these is beyond the scope of this reference. Interested readers can consult the [[RBDs_and_Analytical_System_Reliability#Complex_Systems\|System Analysis Reference book]].

Kate Racaza at 22:05, 30 November 2015

2015-11-30T22:05:18Z

← Older revision		Revision as of 22:05, 30 November 2015
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	You can also perform this analysis using Weibull++'s built-in CFM analysis options, which allow you to generate a probability plot that contains the combined mode line as well as the individual mode lines.		You can also perform this analysis using Weibull++'s built-in CFM analysis options, which allow you to generate a probability plot that contains the combined mode line as well as the individual mode lines.

			<div class="noprint">
	{{Examples Box\|Weibull++ Examples\|<p>More CFM examples are available! See also:</p>		{{Examples Box\|Weibull++ Examples\|<p>More CFM examples are available! See also:</p>
	{{Examples Both\|http://www.reliasoft.com/Weibull/examples/rc10/index.htm\|Competing Failure Modes Analysis\|http://www.reliasoft.tv/weibull/appexamples/weibull_app_ex_10.html\|Watch the video...}}<nowiki/>		{{Examples Both\|http://www.reliasoft.com/Weibull/examples/rc10/index.htm\|Competing Failure Modes Analysis\|http://www.reliasoft.tv/weibull/appexamples/weibull_app_ex_10.html\|Watch the video...}}<nowiki/>
	}}		}}
			</div>

	==Confidence Bounds for CFM Analysis==		==Confidence Bounds for CFM Analysis==

Richard House at 18:15, 26 September 2012

2012-09-26T18:15:15Z

Show changes