Monte Carlo Simulation Example - Revision history

Lisa Hacker at 18:56, 18 September 2023

2023-09-18T18:56:56Z

← Older revision		Revision as of 18:56, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[Risk_Analysis_and_Probabilistic_Design_with_Monte_Carlo_Simulation\|~~Life ~~Data Analysis Reference book]~~]''.		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.

Lisa Hacker at 17:58, 23 May 2023

2023-05-23T17:58:03Z

← Older revision		Revision as of 17:58, 23 May 2023
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	</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example that demonstrates how to obtain the joint ''pdf'' of random variables is available in the [~~http~~://help.~~synthesis8~~.com/~~weibull_alta11~~/user-defined_equation_example.htm Weibull++~~/ALTA Help~~ file]. A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).		</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example that demonstrates how to obtain the joint ''pdf'' of random variables is available in the [https://help.reliasoft.com/weibull23/content/user-defined_equation_example.htm Weibull++ help file].

	'''Monte Carlo Simulation: A Hinge Length Example'''		'''Monte Carlo Simulation: A Hinge Length Example'''

Richard House at 15:59, 11 August 2017

2017-08-11T15:59:05Z

← Older revision		Revision as of 15:59, 11 August 2017
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	</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example that demonstrates how to obtain the joint ''pdf'' of random variables is available in the [http://help.synthesis8.com/~~weibull_alta8~~/user-defined_equation_example.htm Weibull++/ALTA Help file]. A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).		</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example that demonstrates how to obtain the joint ''pdf'' of random variables is available in the [http://help.synthesis8.com/weibull_alta11/user-defined_equation_example.htm Weibull++/ALTA Help file]. A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).

	'''Monte Carlo Simulation: A Hinge Length Example'''		'''Monte Carlo Simulation: A Hinge Length Example'''

Richard House at 18:52, 26 September 2012

2012-09-26T18:52:03Z

← Older revision		Revision as of 18:52, 26 September 2012
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	\text{2}\text{.0273} & \text{2}\text{.0354} & \text{30}\text{.1343} & \text{35}\text{.2666} \\		\text{2}\text{.0273} & \text{2}\text{.0354} & \text{30}\text{.1343} & \text{35}\text{.2666} \\
	\text{1}\text{.984} & \text{1}\text{.9908} & \text{30}\text{.0423} & \text{35}\text{.7111} \\		\text{1}\text{.984} & \text{1}\text{.9908} & \text{30}\text{.0423} & \text{35}\text{.7111} \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>

	'''Solution'''		'''Solution'''
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	\hat{\mu }=2.0146 & \hat{\mu }=2.0096 & \hat{\mu }=30.0981 & \hat{\mu }=34.8149 \\		\hat{\mu }=2.0146 & \hat{\mu }=2.0096 & \hat{\mu }=30.0981 & \hat{\mu }=34.8149 \\
	\hat{\sigma }=0.0181 & \hat{\sigma }=0.0249 & \hat{\sigma }=0.1762 & \hat{\sigma }=0.7121 \\		\hat{\sigma }=0.0181 & \hat{\sigma }=0.0249 & \hat{\sigma }=0.1762 & \hat{\sigma }=0.7121 \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>

	Next, perform a Monte Carlo simulation to estimate the probability that (A+B+C) will be greater than D. To do this, choose the '''User Defined''' distribution and enter its equation as follows. (Click the '''Insert Data Source''' button to insert the data sheets that contain the measurements for the components.)		Next, perform a Monte Carlo simulation to estimate the probability that (A+B+C) will be greater than D. To do this, choose the '''User Defined''' distribution and enter its equation as follows. (Click the '''Insert Data Source''' button to insert the data sheets that contain the measurements for the components.)

Kate Racaza at 21:19, 26 August 2012

2012-08-26T21:19:39Z

← Older revision		Revision as of 21:19, 26 August 2012
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	</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example, that demonstrates how to obtain the joint ''pdf'' of random variables, is available in the [http://help.synthesis8.com/weibull_alta8/user-defined_equation_example.htm Weibull++/ALTA Help file]. A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).		</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example that demonstrates how to obtain the joint ''pdf'' of random variables is available in the [http://help.synthesis8.com/weibull_alta8/user-defined_equation_example.htm Weibull++/ALTA Help file]. A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).

	'''Monte Carlo Simulation: A Hinge Length Example'''		'''Monte Carlo Simulation: A Hinge Length Example'''

Richard House at 07:56, 7 August 2012

2012-08-07T07:56:50Z

Chris Kahn at 04:22, 2 August 2012

2012-08-02T04:22:14Z

← Older revision		Revision as of 04:22, 2 August 2012
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	[[Image:Rsik Analysis Example Monte Carlo D.png~~\|thumb~~\|center\|550px\| ]]		[[Image:Rsik Analysis Example Monte Carlo D.png\|center\|550px\| ]]


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	[[Image:Rsik Analysis Example Selected Life Comparison Plot.png~~\|thumb~~\|center\|550px\| ]]		[[Image:Rsik Analysis Example Selected Life Comparison Plot.png\|center\|550px\| ]]


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	[[Image:Rsik Analysis Example Selected Life Comparison Result.png~~\|thumb~~\|center\|550px\| ]]		[[Image:Rsik Analysis Example Selected Life Comparison Result.png\|center\|550px\| ]]

Kate Racaza at 02:33, 1 August 2012

2012-08-01T02:33:22Z

← Older revision		Revision as of 02:33, 1 August 2012
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	Click '''Generate''' to create a data sheet that contains the generated data points. Rename the new data sheet to "Simulated (A+B+C)."		Click '''Generate''' to create a data sheet that contains the generated data points. Rename the new data sheet to "Simulated A+B+C."

	Follow the same procedure to generate 100 data points to represent the D measurements. Rename the new data sheet to "Simulated D."		Follow the same procedure to generate 100 data points to represent the D measurements. Rename the new data sheet to "Simulated D."
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	Analyze the two data sets, "Simulated (A+B+C)" and "Simulated D," using the normal distribution and the RRX analysis method.		Analyze the two data sets, "Simulated A+B+C" and "Simulated D," using the normal distribution and the RRX analysis method.

	Next, open the Life Comparison tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets.		Next, open the Life Comparison tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets.
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	The following report shows that the probability that (A+B+C) will be greater than D is 16.033%. (Note that the results may vary because of the randomness in the simulation.)		The following report shows that the probability that "Simulated A+B+C" will be greater than "Simulated D" is 16.033%. (Note that the results may vary because of the randomness in the simulation.)


	[[Image:Rsik Analysis Example Selected Life Comparison Result.png\|thumb\|center\|550px\| ]]		[[Image:Rsik Analysis Example Selected Life Comparison Result.png\|thumb\|center\|550px\| ]]

Kate Racaza at 02:09, 1 August 2012

2012-08-01T02:09:03Z

← Older revision		Revision as of 02:09, 1 August 2012
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	'''Solution'''		'''Solution'''

	In a Weibull++ standard folio, enter the parts dimensions measurements of each component into a separate data sheets. Analyze each data sheet using the normal distribution and the RRX analysis method. The parameters are:		In a Weibull++ standard folio, enter the parts dimensions measurements of each component into separate data sheets. Analyze each data sheet using the normal distribution and the RRX analysis method. The parameters are:


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	On the ~~Setting~~ tab, set the number of data points to '''100''', as shown next.		On the Settings tab, set the number of data points to '''100''', as shown next.

Kate Racaza at 02:05, 1 August 2012

2012-08-01T02:05:05Z

← Older revision		Revision as of 02:05, 1 August 2012
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''~~User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following~~ example ~~uses~~ the Life ~~Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example, that demonstrates how to obtain the joint '~~'~~pdf~~'~~' of random variables, is available in the [http://help.synthesis8.com/weibull_alta8/user-defined_equation_example.htm Weibull++/ALTA Help file]~~.		''This example appears in the [[Risk_Analysis_and_Probabilistic_Design_with_Monte_Carlo_Simulation\|Life Data Analysis Reference book]]''.

	A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).
			</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example, that demonstrates how to obtain the joint ''pdf'' of random variables, is available in the [http://help.synthesis8.com/weibull_alta8/user-defined_equation_example.htm Weibull++/ALTA Help file]. A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).

← Older revision		Revision as of 07:56, 7 August 2012
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	</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example, that demonstrates how to obtain the joint ''pdf'' of random variables, is available in the [http://help.synthesis8.com/weibull_alta8/user-defined_equation_example.htm Weibull++/ALTA Help file]. A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).		</noinclude>Monte Carlo simulation can be used to perform simple relationship-based simulations. This type of simulation has many applications in probabilistic design, risk analysis, quality control, etc. The Monte Carlo utility includes a ''User Defined'' distribution feature that allows you to specify an equation relating different random variables. The following example uses the Life Comparison tool to compare the ''pdf'' of two user-defined distributions. A variation of the example, that demonstrates how to obtain the joint ''pdf'' of random variables, is available in the [http://help.synthesis8.com/weibull_alta8/user-defined_equation_example.htm Weibull++/ALTA Help file]. A demonstration on how to perform the example using ReliaSoft's advanced stochastic event simulation software, [http://reno.reliasoft.com '''RENO'''], is also available ([http://www.reliasoft.com/reno/examples/renoexr3/index.htm view it in html]).


	'''Monte Carlo Simulation: A Hinge Length Example'''		'''Monte Carlo Simulation: A Hinge Length Example'''

	A hinge is made up of four components A, B, C, D, as shown next. Seven units of each component were taken from the assembly line and measurements (in cm) were recorded.		A hinge is made up of four components A, B, C, D, as shown next. Seven units of each component were taken from the assembly line and measurements (in cm) were recorded.


	[[Image:WB.23 lda26.1.png\|center\|250px\| ]]		[[Image:WB.23 lda26.1.png\|center\|250px\| ]]


	The following table shows the measurements. Determine the probability that D will fall out of specifications.		The following table shows the measurements. Determine the probability that D will fall out of specifications.


	::<center><math>\begin{matrix}		::<center><math>\begin{matrix}
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	\text{1}\text{.984} & \text{1}\text{.9908} & \text{30}\text{.0423} & \text{35}\text{.7111} \\		\text{1}\text{.984} & \text{1}\text{.9908} & \text{30}\text{.0423} & \text{35}\text{.7111} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	'''Solution'''		'''Solution'''

	In a Weibull++ standard folio, enter the parts dimensions measurements of each component into separate data sheets. Analyze each data sheet using the normal distribution and the RRX analysis method. The parameters are:		In a Weibull++ standard folio, enter the parts dimensions measurements of each component into separate data sheets. Analyze each data sheet using the normal distribution and the RRX analysis method. The parameters are:


	::<center><math>\begin{matrix}		::<center><math>\begin{matrix}
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	\hat{\sigma }=0.0181 & \hat{\sigma }=0.0249 & \hat{\sigma }=0.1762 & \hat{\sigma }=0.7121 \\		\hat{\sigma }=0.0181 & \hat{\sigma }=0.0249 & \hat{\sigma }=0.1762 & \hat{\sigma }=0.7121 \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	Next, perform a Monte Carlo simulation to estimate the probability that (A+B+C) will be greater than D. To do this, choose the '''User Defined''' distribution and enter its equation as follows. (Click the '''Insert Data Source''' button to insert the data sheets that contain the measurements for the components.)		Next, perform a Monte Carlo simulation to estimate the probability that (A+B+C) will be greater than D. To do this, choose the '''User Defined''' distribution and enter its equation as follows. (Click the '''Insert Data Source''' button to insert the data sheets that contain the measurements for the components.)


	[[Image:Rsik Analysis Example Monte Carlo Setting.png\|center\|550px\| ]]		[[Image:Rsik Analysis Example Monte Carlo Setting.png\|center\|550px\| ]]


	On the Settings tab, set the number of data points to '''100''', as shown next.		On the Settings tab, set the number of data points to '''100''', as shown next.


	[[Image:Rsik Analysis Example Monte Carlo Number of Points.png\|center\|550px\| ]]		[[Image:Rsik Analysis Example Monte Carlo Number of Points.png\|center\|550px\| ]]


	Click '''Generate''' to create a data sheet that contains the generated data points. Rename the new data sheet to "Simulated A+B+C."		Click '''Generate''' to create a data sheet that contains the generated data points. Rename the new data sheet to "Simulated A+B+C."

	Follow the same procedure to generate 100 data points to represent the D measurements. Rename the new data sheet to "Simulated D."		Follow the same procedure to generate 100 data points to represent the D measurements. Rename the new data sheet to "Simulated D."


	[[Image:Rsik Analysis Example Monte Carlo D.png\|center\|550px\| ]]		[[Image:Rsik Analysis Example Monte Carlo D.png\|center\|550px\| ]]


	Analyze the two data sets, "Simulated A+B+C" and "Simulated D," using the normal distribution and the RRX analysis method.		Analyze the two data sets, "Simulated A+B+C" and "Simulated D," using the normal distribution and the RRX analysis method.

	Next, open the Life Comparison tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets.		Next, open the Life Comparison tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets.


	[[Image:Rsik Analysis Example Selected Life Comparison Plot.png\|center\|550px\| ]]		[[Image:Rsik Analysis Example Selected Life Comparison Plot.png\|center\|550px\| ]]


	The following report shows that the probability that "Simulated A+B+C" will be greater than "Simulated D" is 16.033%. (Note that the results may vary because of the randomness in the simulation.)		The following report shows that the probability that "Simulated A+B+C" will be greater than "Simulated D" is 16.033%. (Note that the results may vary because of the randomness in the simulation.)


	[[Image:Rsik Analysis Example Selected Life Comparison Result.png\|center\|550px\| ]]		[[Image:Rsik Analysis Example Selected Life Comparison Result.png\|center\|550px\| ]]