Stress-Strength Parameter Uncertainty Example - Revision history

Lisa Hacker at 18:53, 18 September 2023

2023-09-18T18:53:58Z

← Older revision		Revision as of 18:53, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[Stress-Strength_Analysis#Example_1\|~~Life ~~Data Analysis Reference book]~~]''.		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.

	</noinclude>		</noinclude>

Nicolette Young at 21:49, 23 December 2015

2015-12-23T21:49:32Z

← Older revision		Revision as of 21:49, 23 December 2015
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	Next, open the Stress-Strength tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets:		Next, open the Stress-Strength tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets:

	[[Image:Stress-Strength Example 1 pdf curve.png\|center\|~~650px~~]]		[[Image:Stress-Strength Example 1 pdf curve.png\|center\|750px]]

	Since the warranty is 1 year/15,000 miles, all the vehicles with mileage larger than 15,000 should not be considered in the calculation. To do this, go to the Setup page of the control panel and select the '''Override auto-calculated limits''' check box. Set the value of the upper limit to '''15,000''' as shown next.		Since the warranty is 1 year/15,000 miles, all the vehicles with mileage larger than 15,000 should not be considered in the calculation. To do this, go to the Setup page of the control panel and select the '''Override auto-calculated limits''' check box. Set the value of the upper limit to '''15,000''' as shown next.

Nicolette Young at 21:49, 23 December 2015

2015-12-23T21:49:08Z

← Older revision		Revision as of 21:49, 23 December 2015
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	Next, open the Stress-Strength tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets:		Next, open the Stress-Strength tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets:

	[[Image:Stress-Strength Example 1 pdf curve.png\|center\|~~550px~~]]		[[Image:Stress-Strength Example 1 pdf curve.png\|center\|650px]]

	Since the warranty is 1 year/15,000 miles, all the vehicles with mileage larger than 15,000 should not be considered in the calculation. To do this, go to the Setup page of the control panel and select the '''Override auto-calculated limits''' check box. Set the value of the upper limit to '''15,000''' as shown next.		Since the warranty is 1 year/15,000 miles, all the vehicles with mileage larger than 15,000 should not be considered in the calculation. To do this, go to the Setup page of the control panel and select the '''Override auto-calculated limits''' check box. Set the value of the upper limit to '''15,000''' as shown next.

Richard House at 07:51, 7 August 2012

2012-08-07T07:51:37Z

← Older revision		Revision as of 07:51, 7 August 2012
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	The following table gives the data for the mileage distribution per year (stress):		The following table gives the data for the mileage distribution per year (stress):

	{\| ~~cellspacing~~="0" ~~border~~="1" style="~~margin~~: ~~1em auto~~;" ~~class~~="~~wikitable~~"		{\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|-		\|-
	\| align="center" style="background: none repeat scroll 0% 0% rgb(240, 240, 240);" colspan="2" \| '''Stress: Usage Mileage Distribution'''<br>		\| align="center" style="background: none repeat scroll 0% 0% rgb(240, 240, 240);" colspan="2" \| '''Stress: Usage Mileage Distribution'''<br>
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	<br> The following table gives the data for the miles-to-failure distribution (strength):		<br> The following table gives the data for the miles-to-failure distribution (strength):

	{\| ~~cellspacing~~="0" ~~border~~="1" style="~~margin~~: ~~1em auto~~;" ~~class~~="~~wikitable~~"		{\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|-		\|-
	\| align="center" style="background: none repeat scroll 0% 0% rgb(240, 240, 240);" colspan="2" \| '''Strength: Failure Mileage Distribution'''<br>		\| align="center" style="background: none repeat scroll 0% 0% rgb(240, 240, 240);" colspan="2" \| '''Strength: Failure Mileage Distribution'''<br>
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	\|}		\|}

			'''Solution'''
	~~<br>~~ '''Solution'''

	First, estimate the stress and strength distributions using the given data. Enter the stress and strength data into two separate data sheets and analyze each data sheet using the lognormal distribution and MLE analysis method. The parameters of the stress distribution are estimated to be log-mean = 9.411844 and log-std = 0.098741.		First, estimate the stress and strength distributions using the given data. Enter the stress and strength data into two separate data sheets and analyze each data sheet using the lognormal distribution and MLE analysis method. The parameters of the stress distribution are estimated to be log-mean = 9.411844 and log-std = 0.098741.

Richard House at 05:52, 6 August 2012

2012-08-06T05:52:40Z

← Older revision		Revision as of 05:52, 6 August 2012
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	First, estimate the stress and strength distributions using the given data. Enter the stress and strength data into two separate data sheets and analyze each data sheet using the lognormal distribution and MLE analysis method. The parameters of the stress distribution are estimated to be log-mean = 9.411844 and log-std = 0.098741.		First, estimate the stress and strength distributions using the given data. Enter the stress and strength data into two separate data sheets and analyze each data sheet using the lognormal distribution and MLE analysis method. The parameters of the stress distribution are estimated to be log-mean = 9.411844 and log-std = 0.098741.


	[[Image:Stress-Strength Example 1 Stress-Distribution.png\|center\|550px]]		[[Image:Stress-Strength Example 1 Stress-Distribution.png\|center\|550px]]


	The parameters of the strength distribution are estimated to be log-mean = 9.681503 and log-std = 0.083494.		The parameters of the strength distribution are estimated to be log-mean = 9.681503 and log-std = 0.083494.


	[[Image:Stress-Strength Example 1 Strength-Distribution.png\|center\|550px]]		[[Image:Stress-Strength Example 1 Strength-Distribution.png\|center\|550px]]


	Next, open the Stress-Strength tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets:		Next, open the Stress-Strength tool and choose to compare the two data sheets. The following picture shows the ''pdf'' curves of the two data sets:


	[[Image:Stress-Strength Example 1 pdf curve.png\|center\|550px]]		[[Image:Stress-Strength Example 1 pdf curve.png\|center\|550px]]


	Since the warranty is 1 year/15,000 miles, all the vehicles with mileage larger than 15,000 should not be considered in the calculation. To do this, go to the Setup page of the control panel and select the '''Override auto-calculated limits''' check box. Set the value of the upper limit to '''15,000''' as shown next.		Since the warranty is 1 year/15,000 miles, all the vehicles with mileage larger than 15,000 should not be considered in the calculation. To do this, go to the Setup page of the control panel and select the '''Override auto-calculated limits''' check box. Set the value of the upper limit to '''15,000''' as shown next.

			[[Image:Stress-Strength Example 1 Calculation Settings.png\|center\|250px]]
	[[Image:Stress-Strength Example 1 Calculation Settings.png\|center\|~~550px~~]]


	Recalculate the results. The estimated reliability for vehicles less than 15,000 miles per year is 98.84%. The associated confidence bounds are estimated from the variance of the distribution parameters. With larger samples for the stress and strength data, the width of the bounds will be narrower.		Recalculate the results. The estimated reliability for vehicles less than 15,000 miles per year is 98.84%. The associated confidence bounds are estimated from the variance of the distribution parameters. With larger samples for the stress and strength data, the width of the bounds will be narrower.

	[[Image:Stress-Strength Example 1 Calculation Results.png\|center\|~~550px~~]]		[[Image:Stress-Strength Example 1 Calculation Results.png\|center\|250px]]

Richard House at 05:51, 6 August 2012

2012-08-06T05:51:36Z

← Older revision		Revision as of 05:51, 6 August 2012
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	[[Image:Stress-Strength Example 1 Stress-Distribution.png~~\|thumb~~\|center\|550px]]		[[Image:Stress-Strength Example 1 Stress-Distribution.png\|center\|550px]]


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	[[Image:Stress-Strength Example 1 Strength-Distribution.png~~\|thumb~~\|center\|550px]]		[[Image:Stress-Strength Example 1 Strength-Distribution.png\|center\|550px]]


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	[[Image:Stress-Strength Example 1 pdf curve.png~~\|thumb~~\|center\|550px]]		[[Image:Stress-Strength Example 1 pdf curve.png\|center\|550px]]


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	[[Image:Stress-Strength Example 1 Calculation Settings.png~~\|thumb~~\|center\|550px]]		[[Image:Stress-Strength Example 1 Calculation Settings.png\|center\|550px]]


	Recalculate the results. The estimated reliability for vehicles less than 15,000 miles per year is 98.84%. The associated confidence bounds are estimated from the variance of the distribution parameters. With larger samples for the stress and strength data, the width of the bounds will be narrower.		Recalculate the results. The estimated reliability for vehicles less than 15,000 miles per year is 98.84%. The associated confidence bounds are estimated from the variance of the distribution parameters. With larger samples for the stress and strength data, the width of the bounds will be narrower.

	[[Image:Stress-Strength Example 1 Calculation Results.png~~\|thumb~~\|center\|550px]]		[[Image:Stress-Strength Example 1 Calculation Results.png\|center\|550px]]

Kate Racaza: increased image size

2012-07-30T04:41:39Z

increased image size

← Older revision		Revision as of 04:41, 30 July 2012
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	[[Image:Stress-Strength Example 1 Stress-Distribution.png\|thumb\|center\|~~450px~~]]		[[Image:Stress-Strength Example 1 Stress-Distribution.png\|thumb\|center\|550px]]


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	[[Image:Stress-Strength Example 1 Strength-Distribution.png\|thumb\|center\|~~450px~~]]		[[Image:Stress-Strength Example 1 Strength-Distribution.png\|thumb\|center\|550px]]


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	[[Image:Stress-Strength Example 1 pdf curve.png\|thumb\|center\|~~450px~~]]		[[Image:Stress-Strength Example 1 pdf curve.png\|thumb\|center\|550px]]


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	[[Image:Stress-Strength Example 1 Calculation Settings.png\|thumb\|center\|~~450px~~]]		[[Image:Stress-Strength Example 1 Calculation Settings.png\|thumb\|center\|550px]]


	Recalculate the results. The estimated reliability for vehicles less than 15,000 miles per year is 98.84%. The associated confidence bounds are estimated from the variance of the distribution parameters. With larger samples for the stress and strength data, the width of the bounds will be narrower.		Recalculate the results. The estimated reliability for vehicles less than 15,000 miles per year is 98.84%. The associated confidence bounds are estimated from the variance of the distribution parameters. With larger samples for the stress and strength data, the width of the bounds will be narrower.

	[[Image:Stress-Strength Example 1 Calculation Results.png\|thumb\|center\|~~450px~~]]		[[Image:Stress-Strength Example 1 Calculation Results.png\|thumb\|center\|550px]]

Kate Racaza at 04:17, 30 July 2012

2012-07-30T04:17:57Z

← Older revision		Revision as of 04:17, 30 July 2012
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [[Stress-Strength_Analysis#~~Example1~~\|Life Data Analysis Reference book]]''.		''This example appears in the [[Stress-Strength_Analysis#Example_1\|Life Data Analysis Reference book]]''.


	</noinclude>		</noinclude>

	Assume that we are going to use stress-strength analysis to estimate the reliability of a component used in a vehicle. The stress is the usage mileage distribution and the strength is the miles-to-failure distribution of the component. The warranty is 1 year or 15,000 miles, whichever is earlier. The goal is to estimate the reliability of the component within the warranty period (1 year/15,000 miles).		Assume that we are going to use stress-strength analysis to estimate the reliability of a component used in a vehicle. The stress is the usage mileage distribution and the strength is the miles-to-failure distribution of the component. The warranty is 1 year or 15,000 miles, whichever is earlier. The goal is to estimate the reliability of the component within the warranty period (1 year/15,000 miles).

Kate Racaza: updated example

2012-07-30T04:12:13Z

updated example

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Harry Guo: Created page with '{{Example: Stress-Strength Analysis with Parameter Uncertainty}}'

2012-02-27T21:52:48Z

Created page with '{{Example: Stress-Strength Analysis with Parameter Uncertainty}}'

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