Crow-AMSAA Model - Grouped Data Example - Revision history

Lisa Hacker at 21:20, 18 September 2023

2023-09-18T21:20:22Z

← Older revision		Revision as of 21:20, 18 September 2023
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [~~[Crow-AMSAA (NHPP)\|~~Reliability ~~Growth and Repairable System Analysis Reference]~~]''.		''This example appears in the [https://help.reliasoft.com/reference/reliability_growth_and_repairable_system_analysis Reliability growth reference]''.
	</noinclude>		</noinclude>

Chris Kahn at 16:45, 14 May 2014

2014-05-14T16:45:12Z

← Older revision		Revision as of 16:45, 14 May 2014
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	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|+'''Grouped ~~failure times data~~'''		\|+'''Grouped Failure Times Data'''
	!Run Number		!Run Number
	!Cumulative Failures		!Cumulative Failures

David J. Groebel at 00:11, 23 April 2014

2014-04-23T00:11:48Z

← Older revision		Revision as of 00:11, 23 April 2014
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [[Crow-AMSAA (NHPP)\|Reliability Growth and Repairable System Analysis Reference ~~book~~]]''.		''This example appears in the [[Crow-AMSAA (NHPP)\|Reliability Growth and Repairable System Analysis Reference]]''.
	</noinclude>		</noinclude>

Kate Racaza: Created page with '{{Banner RGA Examples}} ''This example appears in the Reliability Growth and Repairable System Analysis Reference book''. Consider …'

2014-01-31T17:38:08Z

Created page with '<noinclude>{{Banner RGA Examples}} ''This example appears in the Reliability Growth and Repairable System Analysis Reference book''. </noinclude> Consider …'

New page

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Crow-AMSAA (NHPP)|Reliability Growth and Repairable System Analysis Reference book]]''.
</noinclude>

Consider the grouped failure times data given in the following table. Solve for the Crow-AMSAA parameters using MLE.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Grouped failure times data'''
!Run Number
!Cumulative Failures
!End Time(hours)
!<math>\ln{(T_i)}\,\!</math>
!<math>\ln{(T_i)^2}\,\!</math>
!<math>\ln{(\theta_i)}\,\!</math>
!<math>\ln{(T_i)}\cdot\ln{(\theta_i)}\,\!</math>
|-
|1|| 2|| 200|| 5.298|| 28.072|| 0.693|| 3.673
|-
|2|| 3|| 400|| 5.991 ||35.898|| 1.099|| 6.582
|-
|3|| 4|| 600|| 6.397|| 40.921|| 1.386|| 8.868
|-
|4|| 11|| 3000|| 8.006|| 64.102|| 2.398 ||19.198
|-
| || ||Sum =||25.693 ||168.992||5.576||38.321
|}

'''Solution'''

Using RGA, the value of <math>\hat{\beta }\,\!</math>, which must be solved numerically, is 0.6315. Using this value, the estimator of <math>\lambda \,\!</math> is:

:<math>\begin{align}
\hat{\lambda } = & \frac{11}{3,{{000}^{0.6315}}} \\
= & 0.0701
\end{align}\,\!</math>

Therefore, the intensity function becomes:

:<math>\hat{\rho }(T)=0.0701\cdot 0.6315\cdot {{T}^{-0.3685}}\,\!</math>