Interval Data Example - Revision history

Kate Racaza at 01:54, 15 August 2012

2012-08-15T01:54:48Z

← Older revision		Revision as of 01:54, 15 August 2012
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	~~===Interval Data Example===~~		<noinclude>{{Banner ALTA Examples}}</noinclude>
	~~A sample~~ of ~~and~~ electronic device ~~was~~ tested in two ~~testing~~ chambers set at different ~~temperatures and monitored on a weekly basis~~. The test ~~was~~ performed continuously for 15 weeks. ~~50 units were put in~~ each ~~chamber~~. The goal of the test is to estimate the 90% lower bound on the <math>B10</math> life (in hours) of the electronic device. The ~~following figure represents~~ the test ~~results~~, ~~it shows~~ the ~~test results entered in ALTA in an~~ interval data format. The normal use condition is assumed to be 300K.
			100 units of an electronic device are tested using two test chambers. Each test chamber contains 50 units and is set to a different temperature. The test is performed continuously for 15 weeks, but monitored only on a weekly basis; therefore, the exact times at which the units failed are unknown. For each failed unit, the only information available is whether or not it failed between inspections.

			The goal of the test is to estimate the 90% lower bound on the <math>B10</math> life (in hours) of the electronic device. The data obtained from the test are recorded in an ALTA standard folio, using the interval data format, as shown next. The normal use condition is assumed to be 300K.


	[[Image:chapter14_80.gif\|center\|650px\|]]		[[Image:chapter14_80.gif\|center\|650px\|]]

	~~====Solution====~~
	Assuming that the failure times of the ~~devices~~ follow a Weibull distribution and that the Arrhenius model is an adequate life-stress relationship, we obtain the following ~~estimated model~~ parameters:		Assuming that the failure times of the device follow a Weibull distribution and that the Arrhenius model is an adequate life-stress relationship, we obtain the following estimates for the parameters:


	::<math>\begin{align}		::<math>\begin{align}
Line 13:		Line 18:
	\end{align}</math>		\end{align}</math>

	~~The next figure show the probability lines at the different stress levels along with the extrapolated use level probability line.~~

	[[Image:intervaldataproblines.gif~~\|thumb~~\|center\|550px\|Probability lines at the different test stress levels with the extrapolated use level probability line.]]		The next figure show the probability lines at the different stress levels, along with the extrapolated use level probability line.

			[[Image:intervaldataproblines.gif\|center\|550px\|Probability lines at the different test stress levels with the extrapolated use level probability line.]]

	The following ~~is the life versus stress~~ plot ~~showing~~ the <math>B10</math> life line.		The following Life vs. Stress plot shows the <math>B10</math> life line.

	[[Image:ch14-23.gif~~\|thumb~~\|center\|550px\|Life vs. Stress with the ''B''10 life line (bottom).]]		[[Image:ch14-23.gif\|center\|550px\|Life vs. Stress with the ''B''10 life line (bottom).]]

	The 90% lower bound on the <math>B10</math> life can be estimated as follows.		The 90% lower bound on the <math>B10</math> life can be estimated as follows.

	[[Image:intervalb10qcp.gif\|center\|400px\|]]		[[Image:intervalb10qcp.gif\|center\|400px\|]]

Kate Racaza: moved Template:Interval Data Example to Interval Data Example: incorrect namespace

2012-08-15T01:15:09Z

moved Template:Interval Data Example to Interval Data Example: incorrect namespace

← Older revision	Revision as of 01:15, 15 August 2012
(No difference)

Richard House at 06:54, 9 August 2012

2012-08-09T06:54:37Z

← Older revision		Revision as of 06:54, 9 August 2012
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	A sample of and electronic device was tested in two testing chambers set at different temperatures and monitored on a weekly basis. The test was performed continuously for 15 weeks. 50 units were put in each chamber. The goal of the test is to estimate the 90% lower bound on the <math>B10</math> life (in hours) of the electronic device. The following figure represents the test results, it shows the test results entered in ALTA in an interval data format. The normal use condition is assumed to be 300K.		A sample of and electronic device was tested in two testing chambers set at different temperatures and monitored on a weekly basis. The test was performed continuously for 15 weeks. 50 units were put in each chamber. The goal of the test is to estimate the 90% lower bound on the <math>B10</math> life (in hours) of the electronic device. The following figure represents the test results, it shows the test results entered in ALTA in an interval data format. The normal use condition is assumed to be 300K.

	~~<br>~~		[[Image:chapter14_80.gif\|center\|650px\|]]
	[[Image:chapter14_80.gif~~\|thumb~~\|center\|650px\|]]
	~~<br>~~

	====Solution====		====Solution====
	Assuming that the failure times of the devices follow a Weibull distribution and that the Arrhenius model is an adequate life-stress relationship, we obtain the following estimated model parameters:		Assuming that the failure times of the devices follow a Weibull distribution and that the Arrhenius model is an adequate life-stress relationship, we obtain the following estimated model parameters:


	::<math>\begin{align}		::<math>\begin{align}
Line 16:		Line 13:
	\end{align}</math>		\end{align}</math>

			The next figure show the probability lines at the different stress levels along with the extrapolated use level probability line.

	~~The next figure show the probability~~ lines at the different stress levels ~~along~~ with the extrapolated use level probability line.		[[Image:intervaldataproblines.gif\|thumb\|center\|550px\|Probability lines at the different test stress levels with the extrapolated use level probability line.]]

	~~<br>~~
	~~[[Image:intervaldataproblines.gif\|thumb\|center\|500px\|Probability lines at the different test stress levels with the extrapolated use level probability line.]]~~
	~~<br>~~
	The following is the life versus stress plot showing the <math>B10</math> life line.		The following is the life versus stress plot showing the <math>B10</math> life line.

	~~<br>~~		[[Image:ch14-23.gif\|thumb\|center\|550px\|Life vs. Stress with the ''B''10 life line (bottom).]]
	[[Image:ch14-23.gif\|thumb\|center\|~~500px~~\|Life vs. Stress with the ''B''10 life line (bottom).]]
	~~<br>~~
	The 90% lower bound on the <math>B10</math> life can be estimated as follows.		The 90% lower bound on the <math>B10</math> life can be estimated as follows.
	~~<br>~~
	~~<br>~~		[[Image:intervalb10qcp.gif\|center\|400px\|]]
	[[Image:intervalb10qcp.gif~~\|thumb~~\|center\|400px\|]]
	~~<br>~~
	~~<math></math>~~

Chris Kahn: /* Interval Data Example */

2012-06-25T13:12:11Z

Interval Data Example

← Older revision		Revision as of 13:12, 25 June 2012
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	<br>		<br>
	[[Image:chapter14_80.gif\|thumb\|center\|~~200px~~\|]]		[[Image:chapter14_80.gif\|thumb\|center\|650px\|]]
	<br>		<br>

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	<br>		<br>
	[[Image:intervaldataproblines.gif\|thumb\|center\|~~200px~~\|Probability lines at the different test stress levels with the extrapolated use level probability line.]]		[[Image:intervaldataproblines.gif\|thumb\|center\|500px\|Probability lines at the different test stress levels with the extrapolated use level probability line.]]
	<br>		<br>
	The following is the life versus stress plot showing the <math>B10</math> life line.		The following is the life versus stress plot showing the <math>B10</math> life line.

	<br>		<br>
	[[Image:ch14-23.gif\|thumb\|center\|~~200px~~\|Life vs. Stress with the ''B''10 life line (bottom).]]		[[Image:ch14-23.gif\|thumb\|center\|500px\|Life vs. Stress with the ''B''10 life line (bottom).]]
	<br>		<br>
	The 90% lower bound on the <math>B10</math> life can be estimated as follows.		The 90% lower bound on the <math>B10</math> life can be estimated as follows.
	<br>		<br>
	<br>		<br>
	[[Image:intervalb10qcp.gif\|thumb\|center\|~~200px~~\|]]		[[Image:intervalb10qcp.gif\|thumb\|center\|400px\|]]
	<br>		<br>
	<math></math>		<math></math>

Chuck Smith: /* Interval Data Example */

2012-04-25T23:26:56Z

Interval Data Example

← Older revision		Revision as of 23:26, 25 April 2012
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	<br>		<br>
	[[Image:chapter14_80.gif\|thumb\|center\|~~400px~~\|]]		[[Image:chapter14_80.gif\|thumb\|center\|200px\|]]
	<br>		<br>

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	<br>		<br>
	[[Image:intervaldataproblines.gif\|thumb\|center\|~~400px~~\|Probability lines at the different test stress levels with the extrapolated use level probability line.]]		[[Image:intervaldataproblines.gif\|thumb\|center\|200px\|Probability lines at the different test stress levels with the extrapolated use level probability line.]]
	<br>		<br>
	The following is the life versus stress plot showing the <math>B10</math> life line.		The following is the life versus stress plot showing the <math>B10</math> life line.

	<br>		<br>
	[[Image:ch14-23.gif\|thumb\|center\|~~400px~~\|Life vs. Stress with the ''B''10 life line (bottom).]]		[[Image:ch14-23.gif\|thumb\|center\|200px\|Life vs. Stress with the ''B''10 life line (bottom).]]
	<br>		<br>
	The 90% lower bound on the <math>B10</math> life can be estimated as follows.		The 90% lower bound on the <math>B10</math> life can be estimated as follows.
	<br>		<br>
	<br>		<br>
	[[Image:intervalb10qcp.gif\|thumb\|center\|~~400px~~\|]]		[[Image:intervalb10qcp.gif\|thumb\|center\|200px\|]]
	<br>		<br>
	<math></math>		<math></math>

Athanasios Gerokostopoulos: Created page with '===Interval Data Example=== A sample of and electronic device was tested in two testing chambers set at different temperatures and monitored on a weekly basis. The test was perfo…'

2012-03-21T17:52:16Z

Created page with '===Interval Data Example=== A sample of and electronic device was tested in two testing chambers set at different temperatures and monitored on a weekly basis. The test was perfo…'

New page

===Interval Data Example===
A sample of and electronic device was tested in two testing chambers set at different temperatures and monitored on a weekly basis. The test was performed continuously for 15 weeks. 50 units were put in each chamber. The goal of the test is to estimate the 90% lower bound on the <math>B10</math> life (in hours) of the electronic device. The following figure represents the test results, it shows the test results entered in ALTA in an interval data format. The normal use condition is assumed to be 300K.

 
[[Image:chapter14_80.gif|thumb|center|400px|]]
 

====Solution====
Assuming that the failure times of the devices follow a Weibull distribution and that the Arrhenius model is an adequate life-stress relationship, we obtain the following estimated model parameters:

::<math>\begin{align}
\beta =\ & 3.425937 \\
B=\ & 1488.412639 \\
C=\ & 24.059577
\end{align}</math>

The next figure show the probability lines at the different stress levels along with the extrapolated use level probability line.

 
[[Image:intervaldataproblines.gif|thumb|center|400px|Probability lines at the different test stress levels with the extrapolated use level probability line.]]
 
The following is the life versus stress plot showing the <math>B10</math> life line.

 
[[Image:ch14-23.gif|thumb|center|400px|Life vs. Stress with the ''B''10 life line (bottom).]]
 
The 90% lower bound on the <math>B10</math> life can be estimated as follows.
 
 
[[Image:intervalb10qcp.gif|thumb|center|400px|]]
 
<math></math>