RGA SimuMatic Example - Revision history

Lisa Hacker at 20:55, 18 September 2023

2023-09-18T20:55:04Z

← Older revision		Revision as of 20:55, 18 September 2023
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [~~[Simulation_with_RGA_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 20:29, 2 June 2014

2014-06-02T20:29:32Z

← Older revision		Revision as of 20:29, 2 June 2014
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [[Simulation_with_RGA_Models\|Reliability Growth and Repairable System Analysis Reference ~~book~~]]''.		''This example appears in the [[Simulation_with_RGA_Models\|Reliability Growth and Repairable System Analysis Reference]]''.
	</noinclude>		</noinclude>

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	#Estimate the 1-sided 90% lower confidence bound on time for an MTBF of 1,000 hours.		#Estimate the 1-sided 90% lower confidence bound on time for an MTBF of 1,000 hours.
	#Estimate the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test.		#Estimate the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test.


	'''Solution'''		'''Solution'''
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	<li>The next figure shows the SimuMatic window with all the appropriate inputs for creating the data sets.		<li>The next figure shows the SimuMatic window with all the appropriate inputs for creating the data sets.

	[[Image:rga14.8.png~~\|thumb~~\|center\|~~400px\|The Main tab of the SimuMatic window.~~]]		[[Image:rga14.8.png\|center\|450px]]


	:The next three figures show the settings in the Analysis, Test Design and Results tab of the SimuMatic window in order to obtain the desired outputs.		The next three figures show the settings in the Analysis, Test Design and Results tab of the SimuMatic window in order to obtain the desired outputs.

	[[Image:rga14.9.png~~\|thumb~~\|center\|~~400px\|The '''Analysis''' tab of the SimuMatic window.~~]]		[[Image:rga14.9.png\|center\|450px]]

	[[Image:rga14.9.5.png~~\|thumb~~\|center\|~~400px\|The '''Test Design''' tab of the SimuMatic window.~~]]		[[Image:rga14.9.5.png\|center\|450px]]

	[[Image:rga14.10.png~~\|thumb~~\|center\|~~400px\|The '''Results''' tab of the SimuMatic window.~~]]		[[Image:rga14.10.png\|center\|450px]]

			The following figure displays the results of the simulation. The columns labeled "Beta" and "Lambda" contain the different parameters obtained by calculating each data set generated via simulation for the 1,000 data sets. The "DMTBF" column contains the instantaneous MTBF at 15,000 hours (the end of test time), given the parameters obtained by calculating each data set generated via simulation. The "T(IMTBF=1000 Hr)" column contains the time required for the MTBF to reach 1,000 hours, given the parameters obtained from the simulation.

	:The following figure displays the results of the simulation. The columns labeled "Beta" and "Lambda" contain the different parameters obtained by calculating each data set generated via simulation for the 1,000 data sets. The "DMTBF" column contains the instantaneous MTBF at 15,000 hours (the end of test time), given the parameters obtained by calculating each data set generated via simulation. The "T(IMTBF=1000 Hr)" column contains the time required for the MTBF to reach 1,000 hours, given the parameters obtained from the simulation.		[[Image:rga14.11.png\|center\|600px]]

	[[Image:rga14.11.png~~\|thumb~~\|center\|~~450px\|Simulation results using SimuMatic.~~]]


	<li>The next figure shows the plot of the instantaneous MTBF with the 90% confidence bounds.		<li>The next figure shows the plot of the instantaneous MTBF with the 90% confidence bounds.

	[[Image:rga14.12.png~~\|thumb~~\|center\|450px~~\|Instantaneous MTBF with 90% confidence bounds.~~]]		[[Image:rga14.12.png\|center\|450px]]

	</li>		</li>
	<li>The 1-sided 90% lower confidence bound on time, assuming MTBF = 1,000 hours, can be obtained from the results of the simulation. In the "Sorted" data sheet, this is the target DMTBF value that corresponds to 10.00%, as shown in the next figure. Therefore the 1-sided 90% lower confidence bound on time is 12,642.21 hours.		<li>The 1-sided 90% lower confidence bound on time, assuming MTBF = 1,000 hours, can be obtained from the results of the simulation. In the "Sorted" data sheet, this is the target DMTBF value that corresponds to 10.00%, as shown in the next figure. Therefore the 1-sided 90% lower confidence bound on time is 12,642.21 hours.

	[[Image:rga14.13.png~~\|thumb~~\|center\|~~450px\|The 1-sided 90% lower confidence bound on time assuming 1,000 hours MTBF.~~]]		[[Image:rga14.13.png\|center\|600px]]

	</li>		</li>
	<li>The next figure shows the 1-sided 90% lower confidence bound on time in the instantaneous MTBF plot. This is indicated by the target lines on the plot.		<li>The next figure shows the 1-sided 90% lower confidence bound on time in the instantaneous MTBF plot. This is indicated by the target lines on the plot.

	[[Image:rga14.14.png~~\|thumb~~\|center\|450px~~\|Instantaneous MTBF with the target.~~]]		[[Image:rga14.14.png\|center\|450px]]

	</li>		</li>
	<li>The 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is again obtained from the "Sorted" data sheet by looking at the value in the "IMTBF(15,000)" column that corresponds to 10.00%. As seen in the simulation results shown above, the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is 605.93 hours.</li>		<li>The 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is again obtained from the "Sorted" data sheet by looking at the value in the "IMTBF(15,000)" column that corresponds to 10.00%. As seen in the simulation results shown above, the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is 605.93 hours.</li>

Chris Kahn at 00:21, 24 April 2014

2014-04-24T00:21:22Z

← Older revision		Revision as of 00:21, 24 April 2014
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	<li>The next figure shows the SimuMatic window with all the appropriate inputs for creating the data sets.		<li>The next figure shows the SimuMatic window with all the appropriate inputs for creating the data sets.

	[[Image:rga14.8.png\|thumb\|center\|~~450px~~\|The Main tab of the SimuMatic window.]]		[[Image:rga14.8.png\|thumb\|center\|400px\|The Main tab of the SimuMatic window.]]


	:The next three figures show the settings in the Analysis, Test Design and Results tab of the SimuMatic window in order to obtain the desired outputs.		:The next three figures show the settings in the Analysis, Test Design and Results tab of the SimuMatic window in order to obtain the desired outputs.

	[[Image:rga14.9.png\|thumb\|center\|~~450px~~\|The '''Analysis''' tab of the SimuMatic window.]]		[[Image:rga14.9.png\|thumb\|center\|400px\|The '''Analysis''' tab of the SimuMatic window.]]

	[[Image:rga14.9.5.png\|thumb\|center\|~~450px~~\|The '''Test Design''' tab of the SimuMatic window.]]		[[Image:rga14.9.5.png\|thumb\|center\|400px\|The '''Test Design''' tab of the SimuMatic window.]]

	[[Image:rga14.10.png\|thumb\|center\|~~450px~~\|The '''Results''' tab of the SimuMatic window.]]		[[Image:rga14.10.png\|thumb\|center\|400px\|The '''Results''' tab of the SimuMatic window.]]

Chris Kahn at 18:25, 6 February 2014

2014-02-06T18:25:36Z

Kate Racaza at 18:40, 4 February 2014

2014-02-04T18:40:05Z

← Older revision		Revision as of 18:40, 4 February 2014
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	<noinclude>{{Banner RGA Examples~~}}{{Navigation box~~}}		<noinclude>{{Banner RGA Examples}}
	''~~These examples appear~~ in the [[Simulation_with_RGA_Models\|Reliability Growth and Repairable System Analysis Reference book]]''.		''This example appears in the [[Simulation_with_RGA_Models\|Reliability Growth and Repairable System Analysis Reference book]]''.
	</noinclude>		</noinclude>

Kate Racaza: Created page with '{{Banner RGA Examples}}{{Navigation box}} ''These examples appear in the [[Simulation_with_RGA_Models|Reliability Growth and Repairable System Analysis Reference book]…'

2014-01-29T19:21:59Z

Created page with '<noinclude>{{Banner RGA Examples}}{{Navigation box}} ''These examples appear in the [[Simulation_with_RGA_Models|Reliability Growth and Repairable System Analysis Reference book]…'

New page

<noinclude>{{Banner RGA Examples}}{{Navigation box}}
''These examples appear in the [[Simulation_with_RGA_Models|Reliability Growth and Repairable System Analysis Reference book]]''.
</noinclude>

A manufacturer wants to design a reliability growth test for a redesigned product, in order to achieve an MTBF of 1,000 hours. Simulation is chosen to estimate the 1-sided 90% confidence bound on the required time to achieve the goal MTBF of 1,000 hours and the 1-sided 90% lower confidence bound on the MTBF at the end of the test time. The total test time is expected to be 15,000 hours. Based on historical data for the previous version, the expected beta and lambda parameters of the test are 0.5 and 0.3, respectively. Do the following:

:1) Generate 1,000 data sets using SimuMatic along with the required output.
:2) Plot the instantaneous MTBF vs. time with the 90% confidence bounds.
:3) Estimate the 1-sided 90% lower confidence bound on time for an MTBF of 1,000 hours.
:4) Estimate the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test.

'''Solution'''

1) The next figure shows the SimuMatic window with all the appropriate inputs for creating the data sets.

[[Image:rga14.8.png|thumb|center|450px|The Main tab of the SimuMatic window.]]

:The next three figures show the settings in the Analysis, Test Design and Results tab of the SimuMatic window in order to obtain the desired outputs.

[[Image:rga14.9.png|thumb|center|450px|The '''Analysis''' tab of the SimuMatic window.]]

[[Image:rga14.9.5.png|thumb|center|450px|The '''Test Design''' tab of the SimuMatic window.]]

[[Image:rga14.10.png|thumb|center|450px|The '''Results''' tab of the SimuMatic window.]]

:The following figure displays the results of the simulation. The columns labeled "Beta" and "Lambda" contain the different parameters obtained by calculating each data set generated via simulation for the 1,000 data sets. The "DMTBF" column contains the instantaneous MTBF at 15,000 hours (the end of test time), given the parameters obtained by calculating each data set generated via simulation. The "T(IMTBF=1000 Hr)" column contains the time required for the MTBF to reach 1,000 hours, given the parameters obtained from the simulation.

[[Image:rga14.11.png|thumb|center|450px|Simulation results using SimuMatic.]]

2) The next figure shows the plot of the instantaneous MTBF with the 90% confidence bounds.

[[Image:rga14.12.png|thumb|center|450px|Instantaneous MTBF with 90% confidence bounds.]]

3) The 1-sided 90% lower confidence bound on time, assuming MTBF = 1,000 hours, can be obtained from the results of the simulation. In the "Sorted" data sheet, this is the target DMTBF value that corresponds to 10.00%, as shown in the next figure. Therefore the 1-sided 90% lower confidence bound on time is 12,642.21 hours.

[[Image:rga14.13.png|thumb|center|450px|The 1-sided 90% lower confidence bound on time assuming 1,000 hours MTBF.]]

4) The next figure shows the 1-sided 90% lower confidence bound on time in the instantaneous MTBF plot. This is indicated by the target lines on the plot.

[[Image:rga14.14.png|thumb|center|450px|Instantaneous MTBF with the target.]]

5) The 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is again obtained from the "Sorted" data sheet by looking at the value in the "IMTBF(15,000)" column that corresponds to 10.00%. As seen in the simulation results shown above, the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is 605.93 hours.

← Older revision		Revision as of 18:25, 6 February 2014
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	A manufacturer wants to design a reliability growth test for a redesigned product, in order to achieve an MTBF of 1,000 hours. Simulation is chosen to estimate the 1-sided 90% confidence bound on the required time to achieve the goal MTBF of 1,000 hours and the 1-sided 90% lower confidence bound on the MTBF at the end of the test time. The total test time is expected to be 15,000 hours. Based on historical data for the previous version, the expected beta and lambda parameters of the test are 0.5 and 0.3, respectively. Do the following:		A manufacturer wants to design a reliability growth test for a redesigned product, in order to achieve an MTBF of 1,000 hours. Simulation is chosen to estimate the 1-sided 90% confidence bound on the required time to achieve the goal MTBF of 1,000 hours and the 1-sided 90% lower confidence bound on the MTBF at the end of the test time. The total test time is expected to be 15,000 hours. Based on historical data for the previous version, the expected beta and lambda parameters of the test are 0.5 and 0.3, respectively. Do the following:

	~~:1)~~ Generate 1,000 data sets using SimuMatic along with the required output.		#Generate 1,000 data sets using SimuMatic along with the required output.
	~~:2)~~ Plot the instantaneous MTBF vs. time with the 90% confidence bounds.		#Plot the instantaneous MTBF vs. time with the 90% confidence bounds.
	~~:3)~~ Estimate the 1-sided 90% lower confidence bound on time for an MTBF of 1,000 hours.		#Estimate the 1-sided 90% lower confidence bound on time for an MTBF of 1,000 hours.
	~~:4)~~ Estimate the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test.		#Estimate the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test.


	'''Solution'''		'''Solution'''
			<ol>
	1) The next figure shows the SimuMatic window with all the appropriate inputs for creating the data sets.		<li>The next figure shows the SimuMatic window with all the appropriate inputs for creating the data sets.

	[[Image:rga14.8.png\|thumb\|center\|450px\|The Main tab of the SimuMatic window.]]		[[Image:rga14.8.png\|thumb\|center\|450px\|The Main tab of the SimuMatic window.]]
Line 32:		Line 32:


	2) The next figure shows the plot of the instantaneous MTBF with the 90% confidence bounds.		<li>The next figure shows the plot of the instantaneous MTBF with the 90% confidence bounds.

	[[Image:rga14.12.png\|thumb\|center\|450px\|Instantaneous MTBF with 90% confidence bounds.]]		[[Image:rga14.12.png\|thumb\|center\|450px\|Instantaneous MTBF with 90% confidence bounds.]]

			</li>
	3) The 1-sided 90% lower confidence bound on time, assuming MTBF = 1,000 hours, can be obtained from the results of the simulation. In the "Sorted" data sheet, this is the target DMTBF value that corresponds to 10.00%, as shown in the next figure. Therefore the 1-sided 90% lower confidence bound on time is 12,642.21 hours.		<li>The 1-sided 90% lower confidence bound on time, assuming MTBF = 1,000 hours, can be obtained from the results of the simulation. In the "Sorted" data sheet, this is the target DMTBF value that corresponds to 10.00%, as shown in the next figure. Therefore the 1-sided 90% lower confidence bound on time is 12,642.21 hours.

	[[Image:rga14.13.png\|thumb\|center\|450px\|The 1-sided 90% lower confidence bound on time assuming 1,000 hours MTBF.]]		[[Image:rga14.13.png\|thumb\|center\|450px\|The 1-sided 90% lower confidence bound on time assuming 1,000 hours MTBF.]]

			</li>
	4) The next figure shows the 1-sided 90% lower confidence bound on time in the instantaneous MTBF plot. This is indicated by the target lines on the plot.		<li>The next figure shows the 1-sided 90% lower confidence bound on time in the instantaneous MTBF plot. This is indicated by the target lines on the plot.

	[[Image:rga14.14.png\|thumb\|center\|450px\|Instantaneous MTBF with the target.]]		[[Image:rga14.14.png\|thumb\|center\|450px\|Instantaneous MTBF with the target.]]

			</li>
	5) The 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is again obtained from the "Sorted" data sheet by looking at the value in the "IMTBF(15,000)" column that corresponds to 10.00%. As seen in the simulation results shown above, the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is 605.93 hours.		<li>The 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is again obtained from the "Sorted" data sheet by looking at the value in the "IMTBF(15,000)" column that corresponds to 10.00%. As seen in the simulation results shown above, the 1-sided 90% lower confidence bound on the instantaneous MTBF at the end of the test is 605.93 hours.</li>