Template:Failure modes configurations - Revision history

Kate Racaza: Redirected page to Competing Failure Modes Analysis

2012-06-29T07:38:04Z

Redirected page to Competing Failure Modes Analysis

← Older revision		Revision as of 07:38, 29 June 2012
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	~~===~~Failure Modes ~~Configurations===~~		#REDIRECT [[Competing Failure Modes Analysis]]


	~~'''Series Configuration'''~~

	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\|250px\| ]]~~

	~~The equation that describes series configuration is:~~

	~~::<math>R(t)={{R}_{1}}(t)\cdot {{R}_{2}}(t)\cdot ...\cdot {{R}_{n}}(t)</math>~~

	~~where <math>n</math> is the total number of failure modes considered.~~


	~~'''Parallel'''~~

	~~In a simple parallel configuration, at least one of the failure modes must not occur for the product to continue operation.~~

	~~<math></math>~~
	~~[[Image:WB.18 parallel.png\|center\|200px\| ]]~~

	~~The equation that describes parallel configuration is:~~

	~~::<math>R(t)=1-\underset{i=1}{\overset{n}{\mathop \prod }}\,(1-{{R}_{i}}(t))</math>~~

	~~where <math>n</math> is the total number of failure modes considered.~~


	~~'''Combination of Series and Parallel'''~~

	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\| ]~~]
	~~<math></math>~~


	~~'''k-out-of-n Parallel Configuration='''~~

	The k-out-of-n configuration is a special case of parallel redundancy. This type of configuration requires that at least <math>k</math> failure modes do not happen out of the total <math>n</math> parallel failure modes for the product to succeed.
	The simplest case of a k-out-of-n configuration is when the failure modes are independent and identical and have the same failure distribution and uncertainties about the parameters (in other words they are derived from the same test data). In this case, the reliability of the product with such a configuration can be evaluated using the binomial distribution, or:


	::<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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].


	~~'''Complex Systems'''~~

	~~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\| ]]~~

	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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].

	~~'''Example 2:'''~~
	~~{{Example: Competing Failures with Complex Configuration Example}}~~

Nicolette Young: /* Failure Modes Configurations */

2012-04-25T22:03:36Z

Failure Modes Configurations

← Older revision		Revision as of 22:03, 25 April 2012
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	<math></math>		<math></math>
	[[Image:WB.18 parallel.png\|center\|~~250px~~\| ]]		[[Image:WB.18 parallel.png\|center\|200px\| ]]

	The equation that describes parallel configuration is:		The equation that describes parallel 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\|~~250px~~\| ]]		[[Image:WB.18 series parallel.png\|center\|200px\| ]]
	<math></math>		<math></math>

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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\|~~250px~~\| ]]		[[Image:WB.18 complex systems.png\|center\|200px\| ]]

	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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].		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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].

Nicolette Young at 22:03, 25 April 2012

2012-04-25T22:03:02Z

← Older revision		Revision as of 22:03, 25 April 2012
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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\|~~500px~~\| ]]		[[Image:WB.18 series configuration.png\|center\|250px\| ]]

	The equation that describes series configuration is:		The equation that describes series configuration is:
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	<math></math>		<math></math>
	[[Image:WB.18 parallel.png\|center\|~~300px~~\| ]]		[[Image:WB.18 parallel.png\|center\|250px\| ]]

	The equation that describes parallel configuration is:		The equation that describes parallel 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\|~~400px~~\| ]]		[[Image:WB.18 series parallel.png\|center\|250px\| ]]
	<math></math>		<math></math>

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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\|~~400px~~\| ]]		[[Image:WB.18 complex systems.png\|center\|250px\| ]]

	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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].		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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].

Nicolette Young: /* Failure Modes Configurations */

2012-04-02T23:01:49Z

Failure Modes Configurations

← Older revision		Revision as of 23:01, 2 April 2012
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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\|~~400px~~\| ]]		[[Image:WB.18 series configuration.png\|center\|500px\| ]]

	The equation that describes series configuration is:		The equation that describes series configuration is:

Nicolette Young: /* Failure Modes Configurations */

2012-03-15T16:29:53Z

Failure Modes Configurations

← Older revision		Revision as of 16:29, 15 March 2012
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	<math></math>		<math></math>
	[[Image:WB.18 parallel.png\|center\|~~400px~~\| ]]		[[Image:WB.18 parallel.png\|center\|300px\| ]]

	The equation that describes parallel configuration is:		The equation that describes parallel 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:~~lda23~~.7.~~gif\|thumb~~\|center\|400px\| ]]		[[Image:WB.18 series parallel.png\|center\|400px\| ]]
	<math></math>		<math></math>

Line 53:		Line 53:
	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:4.15.~~gif\|thumb~~\|center\|~~500px~~\| ]]		[[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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].		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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].

Nicolette Young: /* Failure Modes Configurations */

2012-03-15T16:27:15Z

Failure Modes Configurations

← Older revision		Revision as of 16:27, 15 March 2012
Line 6:		Line 6:
	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:~~lda23~~.5.~~gif\|thumb~~\|center\|400px\| ]]		[[Image:WB.18 series configuration.png\|center\|400px\| ]]

	The equation that describes series configuration is:		The equation that describes series configuration is:
Line 20:		Line 20:

	<math></math>		<math></math>
	[[Image:~~lda23~~.6.~~gif\|thumb~~\|center\|400px\| ]]		[[Image:WB.18 parallel.png\|center\|400px\| ]]

	The equation that describes parallel configuration is:		The equation that describes parallel configuration is:

Harry Guo at 17:58, 21 February 2012

2012-02-21T17:58:32Z

← Older revision		Revision as of 17:58, 21 February 2012
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	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 ReliaSoft's System Reliability Reference.		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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].


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	[[Image:4.15.gif\|thumb\|center\|500px\| ]]		[[Image:4.15.gif\|thumb\|center\|500px\| ]]

	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 ReliaSoft's System Reliability Reference.		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 [http://reliawiki.com/index.php/Life_Data_Analysis_Reference ReliaSoft's System Reliability Reference].

	'''Example 2:'''		'''Example 2:'''
	{{Example: Competing Failures with Complex Configuration Example}}		{{Example: Competing Failures with Complex Configuration Example}}

Harry Guo: /* Failure Modes Configurations */

2012-02-21T17:57:24Z

Failure Modes Configurations

← Older revision		Revision as of 17:57, 21 February 2012
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	::<math>R(t)={{R}_{1}}(t)\cdot {{R}_{2}}(t)\cdot ...\cdot {{R}_{n}}(t)</math>		::<math>R(t)={{R}_{1}}(t)\cdot {{R}_{2}}(t)\cdot ...\cdot {{R}_{n}}(t)</math>


	where <math>n</math> is the total number of failure modes considered.		where <math>n</math> is the total number of failure modes considered.
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	::<math>R(t)=1-\underset{i=1}{\overset{n}{\mathop \prod }}\,(1-{{R}_{i}}(t))</math>		::<math>R(t)=1-\underset{i=1}{\overset{n}{\mathop \prod }}\,(1-{{R}_{i}}(t))</math>


	where <math>n</math> is the total number of failure modes considered.		where <math>n</math> is the total number of failure modes considered.

Harry Guo: /* Failure Modes Configurations */

2012-02-21T17:57:03Z

Failure Modes Configurations

← Older revision		Revision as of 17:57, 21 February 2012
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	===Failure Modes Configurations===		===Failure Modes Configurations===


	'''Series Configuration'''		'''Series Configuration'''
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	where <math>n</math> is the total number of failure modes considered.		where <math>n</math> is the total number of failure modes considered.


	'''Parallel'''		'''Parallel'''
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	where <math>n</math> is the total number of failure modes considered.		where <math>n</math> is the total number of failure modes considered.


	'''Combination of Series and Parallel'''		'''Combination of Series and Parallel'''
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	[[Image:lda23.7.gif\|thumb\|center\|400px\| ]]		[[Image:lda23.7.gif\|thumb\|center\|400px\| ]]
	<math></math>		<math></math>


	'''k-out-of-n Parallel Configuration='''		'''k-out-of-n Parallel Configuration='''
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	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 ReliaSoft's System Reliability Reference.		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 ReliaSoft's System Reliability Reference.


	'''Complex Systems'''		'''Complex Systems'''

Harry Guo: /* Failure Modes Configurations */

2012-02-21T17:56:40Z

Failure Modes Configurations

← Older revision		Revision as of 17:56, 21 February 2012
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	'''Series Configuration'''		'''Series Configuration'''

	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.