Using FMRA to Estimate Baseline Reliability - Revision history

Lisa Hacker at 05:20, 23 August 2012

2012-08-23T05:20:55Z

← Older revision		Revision as of 05:20, 23 August 2012
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	==Introduction==		==Introduction==
	As you may have seen when exploring the different standards and templates for FMEA, the analysis method can be modified to meet different objectives. Regardless of what the objective is, at the end of the day the FMEA process will produce a wealth of information from a cross-functional team that should be leveraged for subsequent Design for Reliability (DFR) activities.		As you may have seen when exploring the different standards and templates for FMEA, the analysis method can be modified to meet different objectives. Regardless of what the objective is, at the end of the day the FMEA process will produce a wealth of information from a cross-functional team that should be leveraged for subsequent Design for Reliability (DFR) activities.

Dingzhou Cao: /* Illustrating the FMRA Process */

2012-04-26T00:06:25Z

Illustrating the FMRA Process

← Older revision		Revision as of 00:06, 26 April 2012
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	</center>		</center>
	<br>		<br>
	<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math></center>		<center><math>\frac{-\text{ln}(1-Q(t))}{t}=\lambda </math></center>

	Note that the exponential distribution is the default choice because a single probability value/time is the only information available. When better information is obtained, other more appropriate models should be utilized to describe the reliability. (See later discussion in the “FMRA Vetting Process” section.)		Note that the exponential distribution is the default choice because a single probability value/time is the only information available. When better information is obtained, other more appropriate models should be utilized to describe the reliability. (See later discussion in the “FMRA Vetting Process” section.)

Chris Kahn: /* Illustrating the FMRA Process */

2012-04-03T22:42:44Z

Illustrating the FMRA Process

← Older revision		Revision as of 22:42, 3 April 2012
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	Note that more complex configurations may be appropriate to describe the reliability-wise relationships of the failure causes and/or components. These can be implemented in the analysis after the first draft is completed. (See later discussion in the “Next Steps” section.)		Note that more complex configurations may be appropriate to describe the reliability-wise relationships of the failure causes and/or components. These can be implemented in the analysis after the first draft is completed. (See later discussion in the “Next Steps” section.)

	<center>[[File:~~fmra_table_small~~.png]]</center>		<center>[[File:fmra_table_3.png]]</center>

	It is extremely important to note at this point that, even though we just computed a system reliability value, this first draft FMRA value may be nowhere close to the true reliability. What we need to do now is go back through the first draft and review each entry and result. We will call this subsequent step the “FMRA Vetting” process.		It is extremely important to note at this point that, even though we just computed a system reliability value, this first draft FMRA value may be nowhere close to the true reliability. What we need to do now is go back through the first draft and review each entry and result. We will call this subsequent step the “FMRA Vetting” process.

Chris Kahn: /* Illustrating the FMRA Process */

2012-04-03T22:33:35Z

Illustrating the FMRA Process

← Older revision		Revision as of 22:33, 3 April 2012
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	Note that more complex configurations may be appropriate to describe the reliability-wise relationships of the failure causes and/or components. These can be implemented in the analysis after the first draft is completed. (See later discussion in the “Next Steps” section.)		Note that more complex configurations may be appropriate to describe the reliability-wise relationships of the failure causes and/or components. These can be implemented in the analysis after the first draft is completed. (See later discussion in the “Next Steps” section.)

	<center>[[File:~~fmra_table~~.png]]</center>		<center>[[File:fmra_table_small.png]]</center>

	It is extremely important to note at this point that, even though we just computed a system reliability value, this first draft FMRA value may be nowhere close to the true reliability. What we need to do now is go back through the first draft and review each entry and result. We will call this subsequent step the “FMRA Vetting” process.		It is extremely important to note at this point that, even though we just computed a system reliability value, this first draft FMRA value may be nowhere close to the true reliability. What we need to do now is go back through the first draft and review each entry and result. We will call this subsequent step the “FMRA Vetting” process.

Chris Kahn: /* Illustrating the FMRA Process */

2012-04-03T22:26:19Z

Illustrating the FMRA Process

← Older revision		Revision as of 22:26, 3 April 2012
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	To illustrate the FMRA process, consider a simple example based on the assembly/component DFMEAs for a single light pendant chandelier. The following picture shows the rating scale that was used by the team when they assigned an occurrence rating to each failure cause identified in the FMEA. In addition to the qualitative ratings and criteria (e.g., 1 = 1 in 1 Million), the scale also has a quantitative value associated with each rating (e.g., 1 in 1 Million = 0.000001).		To illustrate the FMRA process, consider a simple example based on the assembly/component DFMEAs for a single light pendant chandelier. The following picture shows the rating scale that was used by the team when they assigned an occurrence rating to each failure cause identified in the FMEA. In addition to the qualitative ratings and criteria (e.g., 1 = 1 in 1 Million), the scale also has a quantitative value associated with each rating (e.g., 1 in 1 Million = 0.000001).

	<center>[[File:~~fmra_occurrence_scale~~.png]]</center>		<center>[[File:fmra_occurrence_scale_large.png]]</center>

	Based on this probability of occurrence and its corresponding probabilistic definition, one can easily build a one-parameter exponential reliability model for each failure cause as follows:		Based on this probability of occurrence and its corresponding probabilistic definition, one can easily build a one-parameter exponential reliability model for each failure cause as follows:

Lisa Hacker: /* Illustrating the FMRA Process */

2012-04-03T17:30:04Z

Illustrating the FMRA Process

← Older revision		Revision as of 17:30, 3 April 2012
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	</center>		</center>
	<br>		<br>
	<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math>		<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math></center>

	Note that the exponential distribution is the default choice because a single probability value/time is the only information available. When better information is obtained, other more appropriate models should be utilized to describe the reliability. (See later discussion in the “FMRA Vetting Process” section.)		Note that the exponential distribution is the default choice because a single probability value/time is the only information available. When better information is obtained, other more appropriate models should be utilized to describe the reliability. (See later discussion in the “FMRA Vetting Process” section.)

Lisa Hacker: /* Illustrating the FMRA Process */

2012-04-03T17:29:52Z

Illustrating the FMRA Process

← Older revision		Revision as of 17:29, 3 April 2012
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	Based on this probability of occurrence and its corresponding probabilistic definition, one can easily build a one-parameter exponential reliability model for each failure cause as follows:		Based on this probability of occurrence and its corresponding probabilistic definition, one can easily build a one-parameter exponential reliability model for each failure cause as follows:
	<br>		<br>
	<center><math>\text{Probability }\!\!~\!\!\text{ of }\!\!~\!\!\text{ Failure }\!\!~\!\!\text{ at }\!\!~\!\!\text{ Time}~t=Q\left( t \right).</math>		<center><math>\text{Probability }\!\!~\!\!\text{ of }\!\!~\!\!\text{ Failure }\!\!~\!\!\text{ at }\!\!~\!\!\text{ Time}~t=Q\left( t \right)</math>

	</center>		</center>

Lisa Hacker: /* Illustrating the FMRA Process */

2012-04-03T17:29:39Z

Illustrating the FMRA Process

← Older revision		Revision as of 17:29, 3 April 2012
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	</center>		</center>
	~~<br>~~
	Assuming an exponential distribution, its single parameter λ can be estimated as follows:		Assuming an exponential distribution, its single parameter λ can be estimated as follows:
	<br>		<br>
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	<br>		<br>
	<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math>		<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math>
	~~</center>~~
	~~<br>~~
	Note that the exponential distribution is the default choice because a single probability value/time is the only information available. When better information is obtained, other more appropriate models should be utilized to describe the reliability. (See later discussion in the “FMRA Vetting Process” section.)		Note that the exponential distribution is the default choice because a single probability value/time is the only information available. When better information is obtained, other more appropriate models should be utilized to describe the reliability. (See later discussion in the “FMRA Vetting Process” section.)

Lisa Hacker: /* Illustrating the FMRA Process */

2012-04-03T17:29:21Z

Illustrating the FMRA Process

← Older revision		Revision as of 17:29, 3 April 2012
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	Based on this probability of occurrence and its corresponding probabilistic definition, one can easily build a one-parameter exponential reliability model for each failure cause as follows:		Based on this probability of occurrence and its corresponding probabilistic definition, one can easily build a one-parameter exponential reliability model for each failure cause as follows:
			<br>
	<center><math>\text{Probability }\!\!~\!\!\text{ of }\!\!~\!\!\text{ Failure }\!\!~\!\!\text{ at }\!\!~\!\!\text{ Time}~t=Q\left( t \right).</math>		<center><math>\text{Probability }\!\!~\!\!\text{ of }\!\!~\!\!\text{ Failure }\!\!~\!\!\text{ at }\!\!~\!\!\text{ Time}~t=Q\left( t \right).</math>

	</center>		</center>
			<br>
	Assuming an exponential distribution, its single parameter λ can be estimated as follows:		Assuming an exponential distribution, its single parameter λ can be estimated as follows:
			<br>
	<center><math>1-Q\left( T \right)=R\left( t \right)={{e}^{-\lambda t}}</math>		<center><math>1-Q\left( T \right)=R\left( t \right)={{e}^{-\lambda t}}</math>
	</center>		</center>
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	<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math>		<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math>
	</center>		</center>
			<br>
	Note that the exponential distribution is the default choice because a single probability value/time is the only information available. When better information is obtained, other more appropriate models should be utilized to describe the reliability. (See later discussion in the “FMRA Vetting Process” section.)		Note that the exponential distribution is the default choice because a single probability value/time is the only information available. When better information is obtained, other more appropriate models should be utilized to describe the reliability. (See later discussion in the “FMRA Vetting Process” section.)

Lisa Hacker: /* Illustrating the FMRA Process */

2012-04-03T17:28:56Z

Illustrating the FMRA Process

← Older revision		Revision as of 17:28, 3 April 2012
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	<center><math>1-Q\left( T \right)=R\left( t \right)={{e}^{-\lambda t}}</math>		<center><math>1-Q\left( T \right)=R\left( t \right)={{e}^{-\lambda t}}</math>
	</center>		</center>
			<br>
	<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math>		<center><math>\frac{-\text{ln}(1=Q(t))}{t}=\lambda </math>
	</center>		</center>