Simulation Based Bounds Example - Revision history

Lisa Hacker at 18:58, 18 September 2023

2023-09-18T18:58:53Z

← Older revision		Revision as of 18:58, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [[~~Introduction to Confidence Bounds]~~] ~~article~~.''		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference] and [https://help.reliasoft.com/reference/accelerated_life_testing_data_analysis Accelerated life testing reference].''

Richard House at 05:02, 23 August 2012

2012-08-23T05:02:16Z

← Older revision		Revision as of 05:02, 23 August 2012
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	</noinclude>'''Comparing Parameter Estimation Methods Using Simulation Based Bounds'''		</noinclude>'''Comparing Parameter Estimation Methods Using Simulation Based Bounds'''

	The purpose of this example is to determine the best parameter estimation method for a sample of ten units with complete time-to-failure data for each unit (i.e., no censoring). The data set follows a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> hours.		The purpose of this example is to determine the best parameter estimation method for a sample of ten units with complete time-to-failure data for each unit (i.e., no censoring). The data set follows a Weibull distribution with <math>\beta =2\,\!</math> and <math>\eta =100\,\!</math> hours.

	The confidence bounds for the data set could be obtained by using [[Weibull++ SimuMatic\|'''Weibull++''''s SimuMatic]] utility. To obtain the results, use the following settings in SimuMatic.		The confidence bounds for the data set could be obtained by using [[Weibull++ SimuMatic\|'''Weibull++''''s SimuMatic]] utility. To obtain the results, use the following settings in SimuMatic.

	:# On the Main tab, choose the '''2P-Weibull''' distribution and enter the given parameters (i.e., <math>\beta =2</math> and <math>\eta =100</math> hours)		:# On the Main tab, choose the '''2P-Weibull''' distribution and enter the given parameters (i.e., <math>\beta =2\,\!</math> and <math>\eta =100\,\!</math> hours)
	:# On the Censoring tab, select the '''No censoring''' option.		:# On the Censoring tab, select the '''No censoring''' option.
	:# On the Settings tab, set the number of data sets to '''1,000''' and the number of data points to '''10'''.		:# On the Settings tab, set the number of data sets to '''1,000''' and the number of data points to '''10'''.

Melinda Caroline at 03:19, 17 August 2012

2012-08-17T03:19:30Z

← Older revision		Revision as of 03:19, 17 August 2012
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	</noinclude>'''Comparing Parameter Estimation Methods Using Simulation Based Bounds'''		</noinclude>'''Comparing Parameter Estimation Methods Using Simulation Based Bounds'''

	The purpose of this example is to determine the best parameter estimation method for a sample of ten units with complete time-to-failure data for each unit (i.e., no censoring). The data set follows a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> hr.		The purpose of this example is to determine the best parameter estimation method for a sample of ten units with complete time-to-failure data for each unit (i.e., no censoring). The data set follows a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> hours.

	The confidence bounds for the data set could be obtained by using [[Weibull++ SimuMatic\|'''Weibull++''''s SimuMatic]] utility. To obtain the results, use the following settings in SimuMatic.		The confidence bounds for the data set could be obtained by using [[Weibull++ SimuMatic\|'''Weibull++''''s SimuMatic]] utility. To obtain the results, use the following settings in SimuMatic.

	:# On the Main tab, choose the '''2P-Weibull''' distribution and enter the given parameters (i.e., <math>\beta =2</math> and <math>\eta =100</math> hr)		:# On the Main tab, choose the '''2P-Weibull''' distribution and enter the given parameters (i.e., <math>\beta =2</math> and <math>\eta =100</math> hours)
	:# On the Censoring tab, select the '''No censoring''' option.		:# On the Censoring tab, select the '''No censoring''' option.
	:# On the Settings tab, set the number of data sets to '''1,000''' and the number of data points to '''10'''.		:# On the Settings tab, set the number of data sets to '''1,000''' and the number of data points to '''10'''.

Richard House at 07:57, 7 August 2012

2012-08-07T07:57:24Z

← Older revision		Revision as of 07:57, 7 August 2012
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	The following plot shows the simulation-based confidence bounds for the RRX parameter estimation method, as well as the expected variation due to sampling error.		The following plot shows the simulation-based confidence bounds for the RRX parameter estimation method, as well as the expected variation due to sampling error.


	[[Image:SimuMatic RRX.png\|center\|500px\|'''RRX''']]		[[Image:SimuMatic RRX.png\|center\|500px\|'''RRX''']]


	Create another SimuMatic folio and generate a second data using the same settings, but this time, select the RRY analysis method on the Analysis tab. The following plot shows the result.		Create another SimuMatic folio and generate a second data using the same settings, but this time, select the RRY analysis method on the Analysis tab. The following plot shows the result.


	[[Image:SimuMatic RRY.png\|center\|500px\|'''RRY''']]		[[Image:SimuMatic RRY.png\|center\|500px\|'''RRY''']]


	The following plot shows the results using the MLE analysis method.		The following plot shows the results using the MLE analysis method.


	[[Image:SimuMatic MLE.png\|center\|500px\|'''MLE''']]		[[Image:SimuMatic MLE.png\|center\|500px\|'''MLE''']]


	The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds.		The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds.

	This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.		This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.

Kate Racaza at 04:46, 6 August 2012

2012-08-06T04:46:18Z

← Older revision		Revision as of 04:46, 6 August 2012
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	The purpose of this example is to determine the best parameter estimation method for a sample of ten units with complete time-to-failure data for each unit (i.e., no censoring). The data set follows a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> hr.		The purpose of this example is to determine the best parameter estimation method for a sample of ten units with complete time-to-failure data for each unit (i.e., no censoring). The data set follows a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> hr.

	The confidence bounds for the data set could be obtained by using '''Weibull++''''s SimuMatic utility. To obtain the results, use the following settings in SimuMatic.		The confidence bounds for the data set could be obtained by using [[Weibull++ SimuMatic\|'''Weibull++''''s SimuMatic]] utility. To obtain the results, use the following settings in SimuMatic.

	:# On the Main tab, choose the '''2P-Weibull''' distribution and enter the given parameters (i.e., <math>\beta =2</math> and <math>\eta =100</math> hr)		:# On the Main tab, choose the '''2P-Weibull''' distribution and enter the given parameters (i.e., <math>\beta =2</math> and <math>\eta =100</math> hr)

Kate Racaza: updated example

2012-08-06T04:44:10Z

updated example

← Older revision		Revision as of 04:44, 6 August 2012
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	''~~'Comparing Parameter Estimation Methods Using Simulation Based~~ Bounds'''		<noinclude>{{Banner Weibull Examples}}
			''This example appears in the [[Introduction to Confidence Bounds]] article.''

	The purpose of this example is to determine the best parameter estimation method for a sample of ten units following a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> and with complete time-to-failure data for each unit (i.e. no censoring). The number of generated data sets is set to 1,000. The SimuMatic inputs are shown next.

	~~[[Image: SimuMatic Parameters.png\|thumb\|center\|500px]]~~		</noinclude>'''Comparing Parameter Estimation Methods Using Simulation Based Bounds'''

	~~[[Image: SimuMatic Censoring~~.~~png\|thumb\|center\|500px]]~~		The purpose of this example is to determine the best parameter estimation method for a sample of ten units with complete time-to-failure data for each unit (i.e., no censoring). The data set follows a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> hr.

	~~[[Image:~~ SimuMatic ~~Number of Data Sets~~.~~png\|thumb\|center\|500px]]~~		The confidence bounds for the data set could be obtained by using '''Weibull++''''s SimuMatic utility. To obtain the results, use the following settings in SimuMatic.

			:# On the Main tab, choose the '''2P-Weibull''' distribution and enter the given parameters (i.e., <math>\beta =2</math> and <math>\eta =100</math> hr)
			:# On the Censoring tab, select the '''No censoring''' option.
			:# On the Settings tab, set the number of data sets to '''1,000''' and the number of data points to '''10'''.
			:# On the Analysis tab, choose the '''RRX''' analysis method and set the confidence bounds to '''90'''.

	The ~~parameters are estimated using~~ RRX, ~~RRY and MLE. The plotted results generated by SimuMatic are shown next~~.		The following plot shows the simulation-based confidence bounds for the RRX parameter estimation method, as well as the expected variation due to sampling error.

	~~:Using RRX:~~

	[[Image:SimuMatic RRX.png~~\|thumb~~\|center\|500px\|'''RRX''']]		[[Image:SimuMatic RRX.png\|center\|500px\|'''RRX''']]

	~~<br>~~

	~~:Using~~ RRY:		Create another SimuMatic folio and generate a second data using the same settings, but this time, select the RRY analysis method on the Analysis tab. The following plot shows the result.

	~~[[Image:SimuMatic RRY.png\|thumb\|center\|500px\|'''RRY''']]~~

	~~<br>~~		[[Image:SimuMatic RRY.png\|center\|500px\|'''RRY''']]

	~~:Using~~ MLE:
			The following plot shows the results using the MLE analysis method.

	~~<br> [[Image:SimuMatic MLE.png\|thumb\|center\|500px\|'''MLE''']]~~

	~~<br>~~ The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds~~. The previous figures also show the simulation-based bounds, as well as the expected variation due to sampling error~~.		[[Image:SimuMatic MLE.png\|center\|500px\|'''MLE''']]


			The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds.

	This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.		This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.

Kate Racaza: moved Template:Example: Comparing Parameter Estimation Methods Using Simulation Based Bounds to Simulation Based Bounds Example: incorrect namespace

2012-08-06T04:23:54Z

moved Template:Example: Comparing Parameter Estimation Methods Using Simulation Based Bounds to Simulation Based Bounds Example: incorrect namespace

← Older revision	Revision as of 04:23, 6 August 2012
(No difference)

Richard House at 02:17, 6 August 2012

2012-08-06T02:17:57Z

← Older revision		Revision as of 02:17, 6 August 2012
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	<br> The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds. The previous figures also show the simulation-based bounds, as well as the expected variation due to sampling error.		<br> The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds. The previous figures also show the simulation-based bounds, as well as the expected variation due to sampling error.

	~~<br>~~ This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.		This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.

Chris Kahn at 14:09, 25 June 2012

2012-06-25T14:09:20Z

← Older revision		Revision as of 14:09, 25 June 2012
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	The purpose of this example is to determine the best parameter estimation method for a sample of ten units following a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> and with complete time-to-failure data for each unit (i.e. no censoring). The number of generated data sets is set to 1,000. The SimuMatic inputs are shown next.		The purpose of this example is to determine the best parameter estimation method for a sample of ten units following a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> and with complete time-to-failure data for each unit (i.e. no censoring). The number of generated data sets is set to 1,000. The SimuMatic inputs are shown next.

	[[Image: SimuMatic Parameters.png\|thumb\|center\|~~250px~~]]		[[Image: SimuMatic Parameters.png\|thumb\|center\|500px]]

	[[Image: SimuMatic Censoring.png\|thumb\|center\|~~250px~~]]		[[Image: SimuMatic Censoring.png\|thumb\|center\|500px]]

	[[Image: SimuMatic Number of Data Sets.png\|thumb\|center\|~~250px~~]]		[[Image: SimuMatic Number of Data Sets.png\|thumb\|center\|500px]]


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	:Using RRX:		:Using RRX:

	[[Image:SimuMatic RRX.png\|thumb\|center\|~~250px~~\|'''RRX''']]		[[Image:SimuMatic RRX.png\|thumb\|center\|500px\|'''RRX''']]

	<br>		<br>
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	:Using RRY:		:Using RRY:

	[[Image:SimuMatic RRY.png\|thumb\|center\|~~250px~~\|'''RRY''']]		[[Image:SimuMatic RRY.png\|thumb\|center\|500px\|'''RRY''']]

	<br>		<br>
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	:Using MLE:		:Using MLE:

	<br> [[Image:SimuMatic MLE.png\|thumb\|center\|~~250px~~\|'''MLE''']]		<br> [[Image:SimuMatic MLE.png\|thumb\|center\|500px\|'''MLE''']]

	<br> The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds. The previous figures also show the simulation-based bounds, as well as the expected variation due to sampling error.		<br> The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds. The previous figures also show the simulation-based bounds, as well as the expected variation due to sampling error.

	<br> This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.		<br> This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.

Nicolette Young at 17:51, 25 April 2012

2012-04-25T17:51:28Z

← Older revision		Revision as of 17:51, 25 April 2012
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	The purpose of this example is to determine the best parameter estimation method for a sample of ten units following a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> and with complete time-to-failure data for each unit (i.e. no censoring). The number of generated data sets is set to 1,000. The SimuMatic inputs are shown next.		The purpose of this example is to determine the best parameter estimation method for a sample of ten units following a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> and with complete time-to-failure data for each unit (i.e. no censoring). The number of generated data sets is set to 1,000. The SimuMatic inputs are shown next.

	[[Image: SimuMatic Parameters.png\|thumb\|center\|~~400px~~]]		[[Image: SimuMatic Parameters.png\|thumb\|center\|250px]]

	[[Image: SimuMatic Censoring.png\|thumb\|center\|~~400px~~]]		[[Image: SimuMatic Censoring.png\|thumb\|center\|250px]]

	[[Image: SimuMatic Number of Data Sets.png\|thumb\|center\|~~400px~~]]		[[Image: SimuMatic Number of Data Sets.png\|thumb\|center\|250px]]