Grouped per Configuration - Standard Gompertz Model - Revision history

Lisa Hacker at 21:23, 18 September 2023

2023-09-18T21:23:38Z

← Older revision		Revision as of 21:23, 18 September 2023
Line 1:		Line 1:
	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [~~[Gompertz_Models\|~~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>

David J. Groebel at 18:58, 29 May 2014

2014-05-29T18:58:20Z

← Older revision		Revision as of 18:58, 29 May 2014
Line 38:		Line 38:
	<li>The data is entered in cumulative format and the estimated standard Gompertz parameters are shown in the following figure.		<li>The data is entered in cumulative format and the estimated standard Gompertz parameters are shown in the following figure.

	[[Image:rga7.6.png\|center\|~~400px~~\|Entered data and the estimated Standard Gompertz parameters.]]		[[Image:rga7.6.png\|center\|600px\|Entered data and the estimated Standard Gompertz parameters.]]
	</li>		</li>
	<li>The initial reliability at <math>T=0\,\!</math> is equal to:		<li>The initial reliability at <math>T=0\,\!</math> is equal to:
Line 50:		Line 50:
	<li>The reliability at the ninth stage can be calculated using the Quick Calculation Pad (QCP) as shown in the figure below.		<li>The reliability at the ninth stage can be calculated using the Quick Calculation Pad (QCP) as shown in the figure below.

	[[Image:rga7.7.png\|center\|~~400px~~\|Calculate the reliability at the end of the ninth stage with 90% confidence bounds.]]		[[Image:rga7.7.png\|center\|450px\|Calculate the reliability at the end of the ninth stage with 90% confidence bounds.]]

	The estimated reliability at the end of the ninth stage is equal to 91.92%. However, the lower limit at the 90% 1-sided confidence bound is equal to 82.15%. Therefore, the required goal of 85% reliability at a 90% confidence level has not been met.		The estimated reliability at the end of the ninth stage is equal to 91.92%. However, the lower limit at the 90% 1-sided confidence bound is equal to 82.15%. Therefore, the required goal of 85% reliability at a 90% confidence level has not been met.
	</li>		</li>
	</ol>		</ol>

David J. Groebel at 18:49, 29 May 2014

2014-05-29T18:49:38Z

← Older revision		Revision as of 18:49, 29 May 2014
Line 1:		Line 1:
	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [[Gompertz_Models\|Reliability Growth and Repairable System Analysis Reference ~~book~~]]''.		''This example appears in the [[Gompertz_Models\|Reliability Growth and Repairable System Analysis Reference]]''.
	</noinclude>		</noinclude>

Line 42:		Line 42:
	<li>The initial reliability at <math>T=0\,\!</math> is equal to:		<li>The initial reliability at <math>T=0\,\!</math> is equal to:

	::<math>\begin{align}		:<math>\begin{align}
	{{R}_{T=0}}= & a\cdot b \\		{{R}_{T=0}}= & a\cdot b \\
	= & 0.9497\cdot 0.5249 \\		= & 0.9497\cdot 0.5249 \\

Chris Kahn at 23:33, 31 January 2014

2014-01-31T23:33:22Z

← Older revision		Revision as of 23:33, 31 January 2014
Line 5:		Line 5:
	A new design is put through a reliability growth test. The requirement is that after the ninth stage the design will exhibit an 85% reliability with a 90% confidence level. Given the data in the following table, do the following:		A new design is put through a reliability growth test. The requirement is that after the ninth stage the design will exhibit an 85% reliability with a 90% confidence level. Given the data in the following table, do the following:

	~~:1)~~ Estimate the parameters of the standard Gompertz model.		#Estimate the parameters of the standard Gompertz model.
	~~:2)~~ What is the initial reliability at <math>T=0\,\!</math> ?		#What is the initial reliability at <math>T=0\,\!</math> ?
	~~:3)~~ Determine the reliability at the end of the ninth stage and check to see whether the goal has been met.		#Determine the reliability at the end of the ninth stage and check to see whether the goal has been met.

	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
Line 35:		Line 35:

	'''Solution'''		'''Solution'''
			<ol>
	~~:1)~~ The data is entered in cumulative format and the estimated standard Gompertz parameters are shown in the following figure.		<li>The data is entered in cumulative format and the estimated standard Gompertz parameters are shown in the following figure.

	[[Image:rga7.6.png\|center\|400px\|Entered data and the estimated Standard Gompertz parameters.]]		[[Image:rga7.6.png\|center\|400px\|Entered data and the estimated Standard Gompertz parameters.]]
			</li>
	~~:2)~~ The initial reliability at <math>T=0\,\!</math> is equal to:		<li>The initial reliability at <math>T=0\,\!</math> is equal to:

	::<math>\begin{align}		::<math>\begin{align}
Line 47:		Line 47:
	= & 0.4985		= & 0.4985
	\end{align}\,\!</math>		\end{align}\,\!</math>
			</li>
	~~:3)~~ The reliability at the ninth stage can be calculated using the Quick Calculation Pad (QCP) as shown in the figure below.		<li>The reliability at the ninth stage can be calculated using the Quick Calculation Pad (QCP) as shown in the figure below.

	[[Image:rga7.7.png\|center\|400px\|Calculate the reliability at the end of the ninth stage with 90% confidence bounds.]]		[[Image:rga7.7.png\|center\|400px\|Calculate the reliability at the end of the ninth stage with 90% confidence bounds.]]

	The estimated reliability at the end of the ninth stage is equal to 91.92%. However, the lower limit at the 90% 1-sided confidence bound is equal to 82.15%. Therefore, the required goal of 85% reliability at a 90% confidence level has not been met.		The estimated reliability at the end of the ninth stage is equal to 91.92%. However, the lower limit at the 90% 1-sided confidence bound is equal to 82.15%. Therefore, the required goal of 85% reliability at a 90% confidence level has not been met.
			</li>
			</ol>

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

2014-01-21T20:35:24Z

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

New page

<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Gompertz_Models|Reliability Growth and Repairable System Analysis Reference book]]''.
</noinclude>

A new design is put through a reliability growth test. The requirement is that after the ninth stage the design will exhibit an 85% reliability with a 90% confidence level. Given the data in the following table, do the following:

:1) Estimate the parameters of the standard Gompertz model.
:2) What is the initial reliability at <math>T=0\,\!</math> ?
:3) Determine the reliability at the end of the ninth stage and check to see whether the goal has been met.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Grouped per Configuration Data'''
!Stage
!Number of Units
!Number of Failures
|-
|1|| 10|| 5
|-
|2|| 8|| 3
|-
|3|| 9|| 3
|-
|4|| 9|| 2
|-
|5|| 10|| 2
|-
|6|| 10|| 1
|-
|7|| 10|| 1
|-
|8|| 10|| 1
|-
|9|| 10|| 1
|}

'''Solution'''

:1) The data is entered in cumulative format and the estimated standard Gompertz parameters are shown in the following figure.

[[Image:rga7.6.png|center|400px|Entered data and the estimated Standard Gompertz parameters.]]

:2) The initial reliability at <math>T=0\,\!</math> is equal to:

::<math>\begin{align}
{{R}_{T=0}}= & a\cdot b \\
= & 0.9497\cdot 0.5249 \\
= & 0.4985
\end{align}\,\!</math>

:3) The reliability at the ninth stage can be calculated using the Quick Calculation Pad (QCP) as shown in the figure below.

[[Image:rga7.7.png|center|400px|Calculate the reliability at the end of the ninth stage with 90% confidence bounds.]]

The estimated reliability at the end of the ninth stage is equal to 91.92%. However, the lower limit at the 90% 1-sided confidence bound is equal to 82.15%. Therefore, the required goal of 85% reliability at a 90% confidence level has not been met.