Template:Grouped data rga - Revision history

Lisa Hacker: Redirected page to Crow Extended

2012-08-23T11:31:00Z

← Older revision		Revision as of 11:31, 23 August 2012
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	~~==Grouped Data== <!-- THIS SECTION HEADER IS LINKED FROM: Operational Mission Profile Testing. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK(S). -->~~		#REDIRECT [[Crow Extended]]

	~~Parameter estimation for grouped data is the same as described previously in the~~ [[Crow~~-AMSAA - NHPP\| Crow-AMSAA (NHPP) chapter]~~]. The equations used to estimate the parameters of the Crow Extended model are presented next. For test-find-test data, the maximum likelihood estimates of <math>{{\lambda }_{BD}}</math> and <math>{{\beta }_{BD}}</math> are calculated using the first occurrences of the BD modes such that:


	::<math>\underset{i=1}{\overset{k}{\mathop \sum }}\,{{n}_{i}}\left[ \frac{T_{i}^{\widehat{\beta }}\ln {{T}_{i}}-T_{i-1}^{\widehat{\beta }}\ln {{T}_{i-1}}}{T_{i}^{\widehat{\beta }}-T_{i-1}^{\widehat{\beta }}}-\ln {{T}_{k}} \right]~~=0</math>~~


	~~::<math>\widehat{\lambda }=\frac{n}{T_{k}^{\widehat{\beta }}}</math>~~


	where <math>{{n}_{i}}</math> is the number of distinct BD modes within the <math>{{i}^{th}}</math> interval. For test-fix-find-test data, the maximum likelihood estimates of <math>{{\lambda }_{BC}}</math> and <math>{{\beta }_{BC}}</math> are estimated in the same manner using the first occurrences of the BC modes.


	~~===Confidence Bounds===~~

	The confidence bounds on the parameters for the Crow Extended model for grouped data are calculated using the same as the procedure presented in Chapter 5. If there are no BC modes, the confidence bounds on the demonstrated failure intensity and MTBF, projected failure intensity and MTBF and growth potential failure intensity and MTBF are the same as the procedure presented in Section 9.5. If there are BC modes, then the confidence bounds on the demonstrated failure intensity and MTBF are the same as the procedure presented in Chapter 5 and the confidence bounds on the projected failure intensity and MTBF and growth potential failure intensity and MTBF are the same as in Section 9.5. The confidence bounds on time are the same as the procedure presented in Chapter 5.

Lisa Hacker: /* Grouped Data */

2012-08-23T00:56:58Z

Grouped Data

← Older revision		Revision as of 00:56, 23 August 2012
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	==Grouped Data== <!-- THIS SECTION HEADER IS LINKED FROM: Operational Mission Profile Testing. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK(S). -->		==Grouped Data== <!-- THIS SECTION HEADER IS LINKED FROM: Operational Mission Profile Testing. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK(S). -->

	Parameter estimation for grouped data ~~using the Crow-AMSAA model~~ is the same as described in ~~Chapter 5~~. The equations used to estimate the parameters of the Crow Extended model are presented next. For test-find-test data, the maximum likelihood estimates of <math>{{\lambda }_{BD}}</math> and <math>{{\beta }_{BD}}</math> are calculated using the first occurrences of the BD modes such that:		Parameter estimation for grouped data is the same as described previously in the [[Crow-AMSAA - NHPP\| Crow-AMSAA (NHPP) chapter]]. The equations used to estimate the parameters of the Crow Extended model are presented next. For test-find-test data, the maximum likelihood estimates of <math>{{\lambda }_{BD}}</math> and <math>{{\beta }_{BD}}</math> are calculated using the first occurrences of the BD modes such that:

Lisa Hacker: /* Grouped Data */

2012-08-23T00:55:28Z

Grouped Data

← Older revision		Revision as of 00:55, 23 August 2012
Line 1:		Line 1:
	==Grouped Data==		==Grouped Data== <!-- THIS SECTION HEADER IS LINKED FROM: Operational Mission Profile Testing. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK(S). -->

	Parameter estimation for grouped data using the Crow-AMSAA model is the same as described in Chapter 5. The equations used to estimate the parameters of the Crow Extended model are presented next. For test-find-test data, the maximum likelihood estimates of <math>{{\lambda }_{BD}}</math> and <math>{{\beta }_{BD}}</math> are calculated using the first occurrences of the BD modes such that:		Parameter estimation for grouped data using the Crow-AMSAA model is the same as described in Chapter 5. The equations used to estimate the parameters of the Crow Extended model are presented next. For test-find-test data, the maximum likelihood estimates of <math>{{\lambda }_{BD}}</math> and <math>{{\beta }_{BD}}</math> are calculated using the first occurrences of the BD modes such that:

Nicolette Young: Created page with '==Grouped Data== Parameter estimation for grouped data using the Crow-AMSAA model is the same as described in Chapter 5. The equations used to estimate the parameters of the Cro…'

2012-01-10T21:04:43Z

Created page with '==Grouped Data== Parameter estimation for grouped data using the Crow-AMSAA model is the same as described in Chapter 5. The equations used to estimate the parameters of the Cro…'

New page

==Grouped Data==

Parameter estimation for grouped data using the Crow-AMSAA model is the same as described in Chapter 5. The equations used to estimate the parameters of the Crow Extended model are presented next. For test-find-test data, the maximum likelihood estimates of <math>{{\lambda }_{BD}}</math> and <math>{{\beta }_{BD}}</math> are calculated using the first occurrences of the BD modes such that:

::<math>\underset{i=1}{\overset{k}{\mathop \sum }}\,{{n}_{i}}\left[ \frac{T_{i}^{\widehat{\beta }}\ln {{T}_{i}}-T_{i-1}^{\widehat{\beta }}\ln {{T}_{i-1}}}{T_{i}^{\widehat{\beta }}-T_{i-1}^{\widehat{\beta }}}-\ln {{T}_{k}} \right]=0</math>

::<math>\widehat{\lambda }=\frac{n}{T_{k}^{\widehat{\beta }}}</math>

where <math>{{n}_{i}}</math> is the number of distinct BD modes within the <math>{{i}^{th}}</math> interval. For test-fix-find-test data, the maximum likelihood estimates of <math>{{\lambda }_{BC}}</math> and <math>{{\beta }_{BC}}</math> are estimated in the same manner using the first occurrences of the BC modes.

===Confidence Bounds===

The confidence bounds on the parameters for the Crow Extended model for grouped data are calculated using the same as the procedure presented in Chapter 5. If there are no BC modes, the confidence bounds on the demonstrated failure intensity and MTBF, projected failure intensity and MTBF and growth potential failure intensity and MTBF are the same as the procedure presented in Section 9.5. If there are BC modes, then the confidence bounds on the demonstrated failure intensity and MTBF are the same as the procedure presented in Chapter 5 and the confidence bounds on the projected failure intensity and MTBF and growth potential failure intensity and MTBF are the same as in Section 9.5. The confidence bounds on time are the same as the procedure presented in Chapter 5.