Operational Testing Example - Revision history

Lisa Hacker at 21:35, 18 September 2023

2023-09-18T21:35:09Z

← Older revision		Revision as of 21:35, 18 September 2023
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [~~[Operational Testing\|~~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 20:05, 2 June 2014

2014-06-02T20:05:25Z

← Older revision		Revision as of 20:05, 2 June 2014
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	<li>The entered operational testing data and the estimated parameters are given below.		<li>The entered operational testing data and the estimated parameters are given below.

	[[File:OperationalTestData.png\|center\|~~650px\|Estimated parameters for operational testing data.~~]]		[[File:OperationalTestData.png\|center\|600px]]

	The assumption of <math>\beta = 1\,\!</math> can be verified by looking at the confidence bounds on <math>\beta\,\!</math> via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on <math>\beta\,\!</math> are shown next.		The assumption of <math>\beta = 1\,\!</math> can be verified by looking at the confidence bounds on <math>\beta\,\!</math> via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on <math>\beta\,\!</math> are shown next.

	[[File:OTBeta=1.png\|center\|~~400px\|Confidence bounds on Beta.~~]]		[[File:OTBeta=1.png\|center\|450px]]

	Since the confidence bounds on <math>\beta\,\!</math> include one, then you can fail to reject the hypothesis that <math>\beta = 1\,\!</math>.		Since the confidence bounds on <math>\beta\,\!</math> include one, then you can fail to reject the hypothesis that <math>\beta = 1\,\!</math>.
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	<li>The projected MTBF and growth potential values can be displayed via the Growth Potential MTBF plot.		<li>The projected MTBF and growth potential values can be displayed via the Growth Potential MTBF plot.

	[[File:OTGPMTBFPlot.png\|center\|~~650px\|Growth Potential MTBF plot for operational testing.~~]]		[[File:OTGPMTBFPlot.png\|center\|450px]]

	The plot shows that the projected MTBF equals 42.3824 hours, and the growth potential MTBF equals 62.9518 hours.		The plot shows that the projected MTBF equals 42.3824 hours, and the growth potential MTBF equals 62.9518 hours.
	</li>		</li>
	</ol>		</ol>

Chris Kahn at 18:44, 14 May 2014

2014-05-14T18:44:51Z

← Older revision		Revision as of 18:44, 14 May 2014
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	The assumption of <math>\beta = 1\,\!</math> can be verified by looking at the confidence bounds on <math>\beta\,\!</math> via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on <math>\beta\,\!</math> are shown next.		The assumption of <math>\beta = 1\,\!</math> can be verified by looking at the confidence bounds on <math>\beta\,\!</math> via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on <math>\beta\,\!</math> are shown next.

	[[File:OTBeta=1.png\|center\|Confidence bounds on Beta.]]		[[File:OTBeta=1.png\|center\|400px\|Confidence bounds on Beta.]]

	Since the confidence bounds on <math>\beta\,\!</math> include one, then you can fail to reject the hypothesis that <math>\beta = 1\,\!</math>.		Since the confidence bounds on <math>\beta\,\!</math> include one, then you can fail to reject the hypothesis that <math>\beta = 1\,\!</math>.

Chris Kahn: moved Example - Operational Testing to Operational Testing Example over redirect

2014-04-24T18:31:03Z

moved Example - Operational Testing to Operational Testing Example over redirect

← Older revision	Revision as of 18:31, 24 April 2014
(No difference)

Chris Kahn: moved Operational Testing Example to Example - Operational Testing

2014-04-24T18:16:59Z

moved Operational Testing Example to Example - Operational Testing

← Older revision	Revision as of 18:16, 24 April 2014
(No difference)

Chris Kahn at 22:53, 23 April 2014

2014-04-23T22:53:55Z

← Older revision		Revision as of 22:53, 23 April 2014
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	#After estimating the parameters, verify the assumption of <math>\beta = 1\,\!</math>.		#After estimating the parameters, verify the assumption of <math>\beta = 1\,\!</math>.
	#Estimate the ~~demonstrated~~ MTBF of the system.		#Estimate the instantaneous MTBF of the system at the end of the test (demonstrated MTBF).
	#Estimate the MTBF that can be expected after the BD failure modes are addressed (projected MTBF) and the maximum MTBF that can be achieved if all BD modes that exist in the system were discovered and fixed according to the current maintenance strategy (growth potential MTBF).		#Estimate the MTBF that can be expected after the BD failure modes are addressed (projected MTBF) and the maximum MTBF that can be achieved if all BD modes that exist in the system were discovered and fixed according to the current maintenance strategy (growth potential MTBF).

Chris Kahn at 22:26, 23 April 2014

2014-04-23T22:26:14Z

← Older revision		Revision as of 22:26, 23 April 2014
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	</li>		</li>
	<li>From #1, the demonstrated MTBF (DMTBF) equals 33.7097 Hr.		<li>From #1, the demonstrated MTBF (DMTBF) equals 33.7097 hours.
	</li>		</li>

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	[[File:OTGPMTBFPlot.png\|center\|650px\|Growth Potential MTBF plot for operational testing.]]		[[File:OTGPMTBFPlot.png\|center\|650px\|Growth Potential MTBF plot for operational testing.]]

	~~From the~~ plot the projected MTBF equals 42.3824 ~~Hr. The~~ growth potential MTBF equals 62.9518 Hr.		The plot shows that the projected MTBF equals 42.3824 hours, and the growth potential MTBF equals 62.9518 hours.
	</li>		</li>
	</ol>		</ol>

Chris Kahn at 22:21, 23 April 2014

2014-04-23T22:21:44Z

← Older revision		Revision as of 22:21, 23 April 2014
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	The assumption of <math>\beta = 1\,\!</math> can be verified by looking at the confidence bounds on <math>\beta\,\!</math> via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on <math>\beta\,\!</math> are shown next.		The assumption of <math>\beta = 1\,\!</math> can be verified by looking at the confidence bounds on <math>\beta\,\!</math> via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on <math>\beta\,\!</math> are shown next.

	[[File:OTBeta=1.png\|center~~\|650px~~\|Confidence bounds on Beta.]]		[[File:OTBeta=1.png\|center\|Confidence bounds on Beta.]]

	Since the confidence bounds on <math>\beta\,\!</math> include one, then you can fail to reject the hypothesis that <math>\beta = 1\,\!</math>.		Since the confidence bounds on <math>\beta\,\!</math> include one, then you can fail to reject the hypothesis that <math>\beta = 1\,\!</math>.

Chris Kahn at 22:19, 23 April 2014

2014-04-23T22:19:49Z

← Older revision		Revision as of 22:19, 23 April 2014
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	</noinclude>		</noinclude>

	Consider two systems ~~are~~ placed into operational testing. The data for each system is given below. Do the following:		Consider two systems that have been placed into operational testing. The data for each system are given below. Do the following:

	#After estimating the parameters, verify the assumption of <math>\beta = 1\,\!</math>.		#After estimating the parameters, verify the assumption of <math>\beta = 1\,\!</math>.
	#Estimate the demonstrated MTBF of the system.		#Estimate the demonstrated MTBF of the system.
	#~~What~~ are ~~the~~ projected MTBF and ~~growth potential~~ MTBF of the system if the ~~delayed fixes are to be implemented?~~		#Estimate the MTBF that can be expected after the BD failure modes are addressed (projected MTBF) and the maximum MTBF that can be achieved if all BD modes that exist in the system were discovered and fixed according to the current maintenance strategy (growth potential MTBF).

	{\|width="350" border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|width="350" border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
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	\|End Time (Hr)\|\| 504\|\| 541		\|End Time (Hr)\|\| 504\|\| 541
	\|-		\|-
	\|rowspan="23"\|Failure Times (Hr)\|\| 21 BD43\|\| 83 BD37		\|rowspan="23"\|Failure Times (Hr) and<br>Failure Modes\|\| 21 BD43\|\| 83 BD37
	\|-		\|-
	\|29 A42\|\| 83 BD43		\|29 A42\|\| 83 BD43
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	\|}		\|}

	The BD modes are implemented at the end of the test and assume a fixed effectiveness factor equal to 0.6.		The BD modes are implemented at the end of the test and assume a fixed effectiveness factor equal to 0.6 (i.e., 40% of the failure intensity will remain after the fixes are implemented).

	'''Solution'''		'''Solution'''
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	<li>The entered operational testing data and the estimated parameters are given below.		<li>The entered operational testing data and the estimated parameters are given below.

	[[File:OperationalTestData.png\|center\|~~400px~~\|Estimated parameters for operational testing data.]]		[[File:OperationalTestData.png\|center\|650px\|Estimated parameters for operational testing data.]]

	The assumption of <math>\beta = 1\,\!</math> can be ~~checked~~ by looking at the confidence bounds on <math>\beta\,\!</math> via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on <math>\beta\,\!</math> are shown next.		The assumption of <math>\beta = 1\,\!</math> can be verified by looking at the confidence bounds on <math>\beta\,\!</math> via the Quick Calculation Pad (QCP). The 90% 2-sided Crow confidence bounds on <math>\beta\,\!</math> are shown next.

	[[File:OTBeta=1.png\|center\|~~400px~~\|Confidence bounds on Beta.]]		[[File:OTBeta=1.png\|center\|650px\|Confidence bounds on Beta.]]

	Since the confidence bounds on <math>\beta\,\!</math> include one, then you can fail to reject the hypothesis that <math>\beta = 1\,\!</math>.		Since the confidence bounds on <math>\beta\,\!</math> include one, then you can fail to reject the hypothesis that <math>\beta = 1\,\!</math>.
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	<li>The projected MTBF and growth potential values can be displayed via the Growth Potential MTBF plot.		<li>The projected MTBF and growth potential values can be displayed via the Growth Potential MTBF plot.

	[[File:OTGPMTBFPlot.png\|center\|~~400px~~\|Growth Potential MTBF plot for operational testing.]]		[[File:OTGPMTBFPlot.png\|center\|650px\|Growth Potential MTBF plot for operational testing.]]

	From the plot the projected MTBF equals 42.3824 Hr. The growth potential MTBF equals 62.9518 Hr.		From the plot the projected MTBF equals 42.3824 Hr. The growth potential MTBF equals 62.9518 Hr.
	</li>		</li>
	</ol>		</ol>

David J. Groebel at 23:15, 22 April 2014

2014-04-22T23:15:50Z

← Older revision		Revision as of 23:15, 22 April 2014
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	From the plot the projected MTBF equals 42.3824 Hr. The growth potential MTBF equals 62.9518 Hr.		From the plot the projected MTBF equals 42.3824 Hr. The growth potential MTBF equals 62.9518 Hr.
	</li>		</li>
			</ol>