Mechanical Components Example - Revision history

Lisa Hacker at 02:56, 16 August 2012

2012-08-16T02:56:53Z

← Older revision		Revision as of 02:56, 16 August 2012
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	The value of <math>\beta</math> is not the only indicator for the observed behavior. As you can see from the data ~~that was~~ obtained from the test, the times-to-failure at all three stress levels fall within the same ranges. Another way to observe this is by looking at the Life vs. Stress plot. The following plot shows the scale parameter, <math>\eta </math>, and the mean life. As you can see, the life ( <math>\eta </math> and the mean life) are almost invariant with stress.		The value of <math>\beta</math> is not the only indicator for the observed behavior. As you can see from the data obtained from the test, the times-to-failure at all three stress levels fall within the same ranges. Another way to observe this is by looking at the Life vs. Stress plot. The following plot shows the scale parameter, <math>\eta </math>, and the mean life. As you can see, the life ( <math>\eta </math> and the mean life) are almost invariant with stress.

	[[Image:new_arrhexample.gif\|center\|550px\|Eta and Mean Life vs. Stress.]]		[[Image:new_arrhexample.gif\|center\|550px\|Eta and Mean Life vs. Stress.]]

Lisa Hacker at 02:55, 16 August 2012

2012-08-16T02:55:29Z

← Older revision		Revision as of 02:55, 16 August 2012
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	The parameters of the Arrhenius Weibull model were estimated using the ALTA standard folio. The results are:		The parameters of the Arrhenius-Weibull model were estimated using the ALTA standard folio. The results are:

Lisa Hacker at 02:44, 16 August 2012

2012-08-16T02:44:19Z

← Older revision		Revision as of 02:44, 16 August 2012
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	<noinclude>{{Banner ALTA Examples}}</noinclude>		<noinclude>{{Banner ALTA Examples}}</noinclude>
	A mechanical component was put into an accelerated life test with temperature as the stress type. The objective is to fit the Arrhenius-Weibull ~~relationship~~ model to the observed data and analyze the result of the test. The following times-to-failure data were observed.		A mechanical component was put into an accelerated life test with temperature as the stress type. The objective is to fit the Arrhenius-Weibull model to the observed data and analyze the result of the test. The following times-to-failure data were observed.

Kate Racaza at 01:04, 15 August 2012

2012-08-15T01:04:59Z

← Older revision		Revision as of 01:04, 15 August 2012
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	The value of <math>\beta</math> is not the only indicator for the observed behavior. As you can see from the data that was obtained from the test, the times-to-failure at all three stress levels fall within the same ranges. Another way to observe this is by looking at the ~~Arrhenius~~ plot. The following plot shows the scale parameter, <math>\eta </math>, and the mean life. As you can see, the life ( <math>\eta </math> and the mean life) are almost invariant with stress.		The value of <math>\beta</math> is not the only indicator for the observed behavior. As you can see from the data that was obtained from the test, the times-to-failure at all three stress levels fall within the same ranges. Another way to observe this is by looking at the Life vs. Stress plot. The following plot shows the scale parameter, <math>\eta </math>, and the mean life. As you can see, the life ( <math>\eta </math> and the mean life) are almost invariant with stress.

	[[Image:new_arrhexample.gif\|center\|550px\|Eta and Mean Life vs. Stress.]]		[[Image:new_arrhexample.gif\|center\|550px\|Eta and Mean Life vs. Stress.]]

Kate Racaza: updated example

2012-08-15T00:52:04Z

updated example

← Older revision		Revision as of 00:52, 15 August 2012
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	~~===Mechanical Components Example===~~		<noinclude>{{Banner ALTA Examples}}</noinclude>
	A mechanical component was put into an accelerated test with temperature as the ~~accelerated~~ stress. The following times-to-failure were observed.		A mechanical component was put into an accelerated life test with temperature as the stress type. The objective is to fit the Arrhenius-Weibull relationship model to the observed data and analyze the result of the test. The following times-to-failure data were observed.


	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
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	\|}		\|}

	~~1) Determine the parameters of the Arrhenius-Weibull model.~~

	~~2) What is your observation?~~		The parameters of the Arrhenius Weibull model were estimated using the ALTA standard folio. The results are:

	~~====Solution====~~

	~~The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:~~

	::<math>\begin{align}		::<math>\begin{align}
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	\end{align}</math>		\end{align}</math>

	~~A small value for <math>B</math> was estimated. The following observations can then be made:~~

	*Life is not accelerated with temperature, or		The estimate shows a small value for <math>\beta</math>. The following observations can then be made:

			:* Life is not accelerated with temperature, or

			:* The stress increments were not sufficient, or

	*the ~~stress increments~~ were ~~not sufficient, or~~		:* The stress values used in the test were well within the "specification limits" for the product (see discussion [[Introduction to Accelerated Life Testing#Stresses & Stress Levels\|here]]).

	*the test stresses were well within the "specification limits" for the product (see discussion [[Introduction to Accelerated Life Testing#Stresses & Stress Levels\|here]]).

	~~A small~~ value ~~for~~ <math>B</math> is not the only ~~indication~~ for ~~this~~ behavior. ~~One~~ can ~~also observe~~ from the data that ~~at all three stress levels~~, the times-to-failure ~~are~~ within the same ~~range~~. Another way to observe this is by looking at the Arrhenius plot. The scale parameter, <math>\eta </math> , and the mean life are ~~plotted next~~.		The value of <math>\beta</math> is not the only indicator for the observed behavior. As you can see from the data that was obtained from the test, the times-to-failure at all three stress levels fall within the same ranges. Another way to observe this is by looking at the Arrhenius plot. The following plot shows the scale parameter, <math>\eta </math>, and the mean life. As you can see, the life ( <math>\eta </math> and the mean life) are almost invariant with stress.

	[[Image:new_arrhexample.gif~~\|thumb~~\|center\|550px\|Eta and Mean Life vs. Stress.]]		[[Image:new_arrhexample.gif\|center\|550px\|Eta and Mean Life vs. Stress.]]

	~~It can be seen that life ( <math>\eta </math> , and the mean life) is almost invariant with stress.~~

Kate Racaza: moved Template:Mechanical Components Example to Mechanical Components Example: incorrect namespace

2012-08-15T00:35:06Z

moved Template:Mechanical Components Example to Mechanical Components Example: incorrect namespace

← Older revision	Revision as of 00:35, 15 August 2012
(No difference)

Richard House: /* Solution */

2012-08-09T06:48:27Z

Solution

← Older revision		Revision as of 06:48, 9 August 2012
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	The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:		The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:

	::<math>\beta =1.771460,\text{ }B=86.183591,\text{ }C=1170.423770.</math>		::<math>\begin{align}
			\beta =1.771460,\text{ }B=86.183591,\text{ }C=1170.423770.
			\end{align}</math>

	A small value for <math>B</math> was estimated. The following observations can then be made:		A small value for <math>B</math> was estimated. The following observations can then be made:

Richard House: /* Solution */

2012-08-09T06:47:41Z

Solution

← Older revision		Revision as of 06:47, 9 August 2012
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	The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:		The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:

	<math>\beta =1.771460,\text{ }B=86.183591,\text{ }C=1170.423770.</math>		::<math>\beta =1.771460,\text{ }B=86.183591,\text{ }C=1170.423770.</math>

	A small value for <math>B</math> was estimated. The following observations can then be made:		A small value for <math>B</math> was estimated. The following observations can then be made:

Richard House: /* Mechanical Components Example */

2012-08-09T06:47:26Z

Mechanical Components Example

← Older revision		Revision as of 06:47, 9 August 2012
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	A mechanical component was put into an accelerated test with temperature as the accelerated stress. The following times-to-failure were observed.		A mechanical component was put into an accelerated test with temperature as the accelerated stress. The following times-to-failure were observed.

			{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	{\|~~style=~~ border="1" align="center"
	!343 K		!343 K
	!363 K		!363 K
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	\|}		\|}

	~~<br>~~
	1) Determine the parameters of the Arrhenius-Weibull model.		1) Determine the parameters of the Arrhenius-Weibull model.
	~~<br>~~

	2) What is your observation?		2) What is your observation?


	~~<br>~~
	====Solution====		====Solution====


	The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:		The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:

			<math>\beta =1.771460,\text{ }B=86.183591,\text{ }C=1170.423770.</math>

	<math>~~\beta =1.771460,\text{ }~~B~~=86.183591,\text{ }C=1170.423770.~~</math>		A small value for <math>B</math> was estimated. The following observations can then be made:

			*Life is not accelerated with temperature, or

	~~A small value for <math>B</math> was estimated. The following observations can then be made:~~		*the stress increments were not sufficient, or

	~~<br>~~		*the test stresses were well within the "specification limits" for the product (see discussion [[Introduction to Accelerated Life Testing#Stresses & Stress Levels\|here]]).
	~~• Life is not accelerated with temperature, or~~
	~~<br>~~
	~~• the stress increments were not sufficient, or~~
	~~<br>~~
	• the test stresses were well within the "specification limits" for the product (see discussion [[Introduction to Accelerated Life Testing#Stresses & Stress Levels\|here]]).

	~~<br>~~
	A small value for <math>B</math> is not the only indication for this behavior. One can also observe from the data that at all three stress levels, the times-to-failure are within the same range. Another way to observe this is by looking at the Arrhenius plot. The scale parameter, <math>\eta </math> , and the mean life are plotted next.		A small value for <math>B</math> is not the only indication for this behavior. One can also observe from the data that at all three stress levels, the times-to-failure are within the same range. Another way to observe this is by looking at the Arrhenius plot. The scale parameter, <math>\eta </math> , and the mean life are plotted next.
	~~<br>~~
	~~<br>~~		[[Image:new_arrhexample.gif\|thumb\|center\|550px\|Eta and Mean Life vs. Stress.]]
	[[Image:new_arrhexample.gif\|thumb\|center\|~~500px~~\|Eta and Mean Life vs. Stress.]]
	~~<br>~~

	It can be seen that life ( <math>\eta </math> , and the mean life) is almost invariant with stress.		It can be seen that life ( <math>\eta </math> , and the mean life) is almost invariant with stress.

Chris Kahn: /* Solution */

2012-06-25T13:08:36Z

Solution

← Older revision		Revision as of 13:08, 25 June 2012
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	<br>		<br>
	<br>		<br>
	[[Image:new_arrhexample.gif\|thumb\|center\|~~200px~~\|Eta and Mean Life vs. Stress.]]		[[Image:new_arrhexample.gif\|thumb\|center\|500px\|Eta and Mean Life vs. Stress.]]
	<br>		<br>

	It can be seen that life ( <math>\eta </math> , and the mean life) is almost invariant with stress.		It can be seen that life ( <math>\eta </math> , and the mean life) is almost invariant with stress.