Template:Crow-amsaa(nhpp) - Revision history

Lisa Hacker: Redirected page to Crow-AMSAA - NHPP

2012-08-23T23:36:35Z

Lisa Hacker at 00:29, 23 August 2012

2012-08-23T00:29:05Z

← Older revision		Revision as of 00:29, 23 August 2012
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	*Reliability of the configuration currently on test		*Reliability of the configuration currently on test
	~~<br>~~
	*Reliability of the configuration on test at the end of the test phase		*Reliability of the configuration on test at the end of the test phase
	~~<br>~~
	*Expected reliability if the test time for the phase is extended		*Expected reliability if the test time for the phase is extended
	~~<br>~~
	*Growth rate		*Growth rate
	~~<br>~~
	*Confidence intervals		*Confidence intervals
	~~<br>~~
	*Applicable goodness-of-fit tests		*Applicable goodness-of-fit tests
	~~<br>~~

	The reliability growth pattern for the Crow-AMSAA model is exactly the same pattern as for the Duane postulate (Chapter 4). That is, the cumulative number of failures is linear when plotted on ln-ln scale. Unlike the Duane postulate, the Crow-AMSAA model is statistically based. Under the Duane postulate, the failure rate is linear on ln-ln scale. However for the Crow-AMSAA model statistical structure, the failure intensity of the underlying non-homogeneous Poisson process (NHPP) is linear when plotted on ln-ln scale.		The reliability growth pattern for the Crow-AMSAA model is exactly the same pattern as for the Duane postulate (Chapter 4). That is, the cumulative number of failures is linear when plotted on ln-ln scale. Unlike the Duane postulate, the Crow-AMSAA model is statistically based. Under the Duane postulate, the failure rate is linear on ln-ln scale. However for the Crow-AMSAA model statistical structure, the failure intensity of the underlying non-homogeneous Poisson process (NHPP) is linear when plotted on ln-ln scale.

	Let <math>N(t)</math> be the cumulative number of failures observed in cumulative test time <math>t</math> and let <math>\rho (t)</math> be the failure intensity for the Crow-AMSAA model. Under the NHPP model, <math>\rho (t)\Delta t</math> is approximately the probably of a failure occurring over the interval <math>[t,t+\Delta t]</math> for small <math>\Delta t</math> . In addition, the expected number of failures experienced over the test interval <math>[0,T]</math> under the Crow-AMSAA model is given by:		Let <math>N(t)</math> be the cumulative number of failures observed in cumulative test time <math>t</math> and let <math>\rho (t)</math> be the failure intensity for the Crow-AMSAA model. Under the NHPP model, <math>\rho (t)\Delta t</math> is approximately the probably of a failure occurring over the interval <math>[t,t+\Delta t]</math> for small <math>\Delta t</math> . In addition, the expected number of failures experienced over the test interval <math>[0,T]</math> under the Crow-AMSAA model is given by:

Lisa Hacker at 00:28, 23 August 2012

2012-08-23T00:28:40Z

← Older revision		Revision as of 00:28, 23 August 2012
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	~~=Crow-AMSAA (NHPP)=~~		In "Reliability Analysis for Complex, Repairable Systems" (1974), Dr. Larry H. Crow noted that the Duane model could be stochastically represented as a Weibull process, allowing for statistical procedures to be used in the application of this model in reliability growth. This statistical extension became what is known as the Crow-AMSAA (NHPP) model. This method was first developed at the U.S. Army Materiel Systems Analysis Activity (AMSAA). It is frequently used on systems when usage is measured on a continuous scale. It can also be applied for the analysis of one shot items when there is high reliability and large number of trials.
	In Reliability Analysis for Complex, Repairable Systems (1974), Dr. Larry H. Crow noted that the Duane model could be stochastically represented as a Weibull process, allowing for statistical procedures to be used in the application of this model in reliability growth. This statistical extension became what is known as the Crow-AMSAA (NHPP) model. This method was first developed at the U.S. Army Materiel Systems Analysis Activity (AMSAA). It is frequently used on systems when usage is measured on a continuous scale. It can also be applied for the analysis of one shot items when there is high reliability and large number of trials.
	Test programs are generally conducted on a phase by phase basis. The Crow-AMSAA model is designed for tracking the reliability within a test phase and not across test phases. A development testing program may consist of several separate test phases. If corrective actions are introduced during a particular test phase then this type of testing and the associated data are appropriate for analysis by the Crow-AMSAA model. The model analyzes the reliability growth progress within each test phase and can aid in determining the following:		Test programs are generally conducted on a phase by phase basis. The Crow-AMSAA model is designed for tracking the reliability within a test phase and not across test phases. A development testing program may consist of several separate test phases. If corrective actions are introduced during a particular test phase then this type of testing and the associated data are appropriate for analysis by the Crow-AMSAA model. The model analyzes the reliability growth progress within each test phase and can aid in determining the following:
	<br>		<br>

	• Reliability of the configuration currently on test		*Reliability of the configuration currently on test
	<br>		<br>
	• Reliability of the configuration on test at the end of the test phase		*Reliability of the configuration on test at the end of the test phase
	<br>		<br>
	• Expected reliability if the test time for the phase is extended		*Expected reliability if the test time for the phase is extended
	<br>		<br>
	• Growth rate		*Growth rate
	<br>		<br>
	• Confidence intervals		*Confidence intervals
	<br>		<br>
	• Applicable goodness-of-fit tests		*Applicable goodness-of-fit tests
	<br>		<br>

Nicolette Young: /* Change of Slope */

2012-01-09T17:13:54Z

Change of Slope

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Nicolette Young: /* Applicability */

2012-01-09T17:13:21Z

Applicability

← Older revision		Revision as of 17:13, 9 January 2012
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	{{crow discrete reliability growth model camsaa}}		{{crow discrete reliability growth model camsaa}}

	~~==Applicability==~~		{{applicability camsaa}}
	The Duane and Crow-AMSAA models are the most frequently used reliability growth models. Their relationship comes from the fact that both make use of the underlying observed linear relationship between the logarithm of cumulative MTBF and cumulative test time. However, the Duane model does not provide a capability to test whether the change in MTBF observed over time is significantly different from what might be seen due to random error between phases. The Crow-AMSAA model allows for such assessments. Also, the Crow-AMSAA allows for development of hypothesis testing procedures to determine growth presence in the data where ( <math>\beta <1</math> indicates that there is growth in MTBF, <math>\beta =1</math> indicates a constant MTBF and <math>\beta >1</math> indicates a decreasing MTBF). Additionally, the Crow-AMSAA model views the process of reliability growth as probabilistic, while the Duane model views the process as deterministic.

	==Change of Slope==		==Change of Slope==

Nicolette Young: /* Crow Discrete Reliability Growth Model */

2012-01-09T17:07:33Z

Crow Discrete Reliability Growth Model

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Nicolette Young: /* Estimation and Analysis with Missing Data */

2012-01-09T17:06:34Z

Estimation and Analysis with Missing Data

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 {{goodness-of-fit test camsaa}}
-==Estimation and Analysis with Missing Data==
+{{estimation and analysis with missing data camsaa}}
 ==Crow Discrete Reliability Growth Model==

Nicolette Young: /* Goodness-of-Fit Tests */

2012-01-06T16:58:37Z

Goodness-of-Fit Tests

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 {{grouped data confidence bounds camsaa}}
-==Goodness-of-Fit Tests==
+{{goodness-of-fit test camsaa}}
 ==Estimation and Analysis with Missing Data==

Nicolette Young: /* Grouped Data Confidence Bounds */

2012-01-05T23:06:01Z

Grouped Data Confidence Bounds

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Nicolette Young: /* Grouped Data */

2012-01-05T23:05:12Z

Grouped Data

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 {{confidence bounds camsaa}}
-==Grouped Data==
+{{grouped data camsaa}}
 ==Grouped Data Confidence Bounds==