Template:Example:GLL - Revision history

Kate Racaza: Redirected page to General Log-Linear Relationship Example

2012-08-14T02:22:33Z

Redirected page to General Log-Linear Relationship Example

← Older revision		Revision as of 02:22, 14 August 2012
Line 1:		Line 1:
	~~==GLL Example==~~		#REDIRECT [[General_Log-Linear_Relationship_Example]]

	~~Consider the data summarized in the following tables. These data illustrate a typical three-stress type accelerated test.~~

	~~<center>'''Stress Profile Summary'''</center>~~
	[[~~Image:ALTA11t1.png\|center\|350px\|]]~~


	~~<center>'''Failure Data'''</center>~~
	~~[[Image:ALTA11t2.png\|center\|450px\|]]~~

	The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.

	~~[[Image:StressTransformation.gif\|center\|400px\|]]~~

	~~The GLL relationship then becomes:~~

	~~::<math>\eta ={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}+{{\alpha }_{2}}\ln ({{V}_{2}})+{{\alpha }_{3}}{{V}_{3}}}}</math>~~

	~~The resulting relationship after performing these transformations is:~~

	~~::<math>\begin{align}~~
	& \eta = & {{e}^{{{\alpha }_{0}}}}{{e}^{{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}}}{{e}^{{{\alpha }_{2}}\ln ({{V}_{2}})}}{{e}^{{{\alpha }_{3}}{{V}_{3}}}} =\ & {{e}^{{{\alpha }_{0}}}}{{e}^{{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}}}V_{2}^{{{\alpha }_{2}}}{{e}^{{{\alpha }_{3}}{{V}_{3}}}}
	~~\end{align}</math>~~

	Therefore, the parameter <math>B</math> of the Arrhenius relationship is equal to the log-linear coefficient <math>{{\alpha }_{1}}</math> , and the parameter <math>n</math> of the inverse power relationship is equal to ( <math>-{{\alpha }_{2}}</math> ). Therefore <math>\eta </math> can also be written as:

	~~::<math>\eta ={{e}^{{{\alpha }_{0}}}}{{e}^{\tfrac{B}{{{V}_{1}}}}}V_{2}^{n}{{e}^{{{\alpha }_{3}}{{V}_{3}}}}</math>~~

	~~The activation energy of the Arrhenius relationship can be calculated by multiplying B with Boltzmann's constant.~~

	~~The best fit values for the parameters in this case are:~~

	~~::<math>\begin{align}~~
	~~\beta = & 3.7483;\text{ }{{\alpha }_{0}}=-6.0220;\text{ }{{\alpha }_{1}}=5776.9341 \\~~
	~~{{\alpha }_{2}}= &~~ -~~1.4340;\text{ }{{\alpha }_{3}}=0.6242.~~
	~~\end{align}</math>~~

	~~Once the parameters are estimated, further analysis on the data can be performed. First, using ALTA, a Weibull probability plot of the data can be obtained, as shown next.~~

	~~[[Image:ALTA11.1.gif\|thumb\|center\|550px\|Weibull probability plot for all covariates.]]~~

	Several types of information about the model as well as the data can be obtained from a probability plot. For example, the choice of an underlying distribution and the assumption of a common slope (shape parameter) can be examined. In this example, the linearity of the data supports the use of the Weibull distribution. In addition, the data appear parallel on this plot, therefore reinforcing the assumption of a common beta. Further statistical analysis can and should be performed for these purposes as well.
	The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.

	~~[[Image:ALTA11.2.gif\|thumb\|center\|550px\|Effects of temperature on life.]]~~


	~~[[Image:ALTA11.3.gif\|thumb\|center\|550px\|Effects of voltage on life.]]~~

	The effects of the two different operation types on life can be observed in the next figure. It can be seen that the on/off cycling has a greater effect on the life of the product in terms of accelerating failure than the continuous operation. In other words, a higher reliability can be achieved by running the product continuously.

	~~[[Image:ALTA11.4.gif\|thumb\|center\|550px\|Effect of operation type on life.~~]]

Richard House at 05:37, 9 August 2012

2012-08-09T05:37:54Z

← Older revision		Revision as of 05:37, 9 August 2012
Line 39:		Line 39:
	Once the parameters are estimated, further analysis on the data can be performed. First, using ALTA, a Weibull probability plot of the data can be obtained, as shown next.		Once the parameters are estimated, further analysis on the data can be performed. First, using ALTA, a Weibull probability plot of the data can be obtained, as shown next.

	[[Image:ALTA11.1.gif\|thumb\|center\|~~450px~~\|Weibull probability plot for all covariates.]]		[[Image:ALTA11.1.gif\|thumb\|center\|550px\|Weibull probability plot for all covariates.]]

	Several types of information about the model as well as the data can be obtained from a probability plot. For example, the choice of an underlying distribution and the assumption of a common slope (shape parameter) can be examined. In this example, the linearity of the data supports the use of the Weibull distribution. In addition, the data appear parallel on this plot, therefore reinforcing the assumption of a common beta. Further statistical analysis can and should be performed for these purposes as well.		Several types of information about the model as well as the data can be obtained from a probability plot. For example, the choice of an underlying distribution and the assumption of a common slope (shape parameter) can be examined. In this example, the linearity of the data supports the use of the Weibull distribution. In addition, the data appear parallel on this plot, therefore reinforcing the assumption of a common beta. Further statistical analysis can and should be performed for these purposes as well.
	The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.		The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.

	[[Image:ALTA11.2.gif\|thumb\|center\|~~500px~~\|Effects of temperature on life.]]		[[Image:ALTA11.2.gif\|thumb\|center\|550px\|Effects of temperature on life.]]


	[[Image:ALTA11.3.gif\|thumb\|center\|~~500px~~\|Effects of voltage on life.]]		[[Image:ALTA11.3.gif\|thumb\|center\|550px\|Effects of voltage on life.]]

	The effects of the two different operation types on life can be observed in the next figure. It can be seen that the on/off cycling has a greater effect on the life of the product in terms of accelerating failure than the continuous operation. In other words, a higher reliability can be achieved by running the product continuously.		The effects of the two different operation types on life can be observed in the next figure. It can be seen that the on/off cycling has a greater effect on the life of the product in terms of accelerating failure than the continuous operation. In other words, a higher reliability can be achieved by running the product continuously.

	[[Image:ALTA11.4.gif\|thumb\|center\|~~500px~~\|Effect of operation type on life.]]		[[Image:ALTA11.4.gif\|thumb\|center\|550px\|Effect of operation type on life.]]

Richard House: /* GLL Example */

2012-08-09T05:36:56Z

GLL Example

← Older revision		Revision as of 05:36, 9 August 2012
Line 1:		Line 1:
	==GLL Example==		==GLL Example==
	~~<br>~~
	Consider the data summarized in the following tables. These data illustrate a typical three-stress type accelerated test.		Consider the data summarized in the following tables. These data illustrate a typical three-stress type accelerated test.
	~~<br>~~
	~~<br>~~
	<center>'''Stress Profile Summary'''</center>		<center>'''Stress Profile Summary'''</center>
	[[Image:ALTA11t1.png\|center\|~~300px~~\|]]		[[Image:ALTA11t1.png\|center\|350px\|]]
	~~<br>~~

	<center>'''Failure Data'''</center>		<center>'''Failure Data'''</center>
	[[Image:ALTA11t2.png\|center\|~~350px~~\|]]		[[Image:ALTA11t2.png\|center\|450px\|]]

	~~<br>~~
	The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.		The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.
	~~<br>~~
	~~[[Image:StressTransformation.gif\|thumb\|center\|400px\|]]~~

	~~<br>~~		[[Image:StressTransformation.gif\|center\|400px\|]]

	The GLL relationship then becomes:		The GLL relationship then becomes:

	~~<br>~~
	::<math>\eta ={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}+{{\alpha }_{2}}\ln ({{V}_{2}})+{{\alpha }_{3}}{{V}_{3}}}}</math>		::<math>\eta ={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}+{{\alpha }_{2}}\ln ({{V}_{2}})+{{\alpha }_{3}}{{V}_{3}}}}</math>

	~~<br>~~
	The resulting relationship after performing these transformations is:		The resulting relationship after performing these transformations is:

	~~<br>~~
	::<math>\begin{align}		::<math>\begin{align}
	& \eta = & {{e}^{{{\alpha }_{0}}}}{{e}^{{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}}}{{e}^{{{\alpha }_{2}}\ln ({{V}_{2}})}}{{e}^{{{\alpha }_{3}}{{V}_{3}}}} =\ & {{e}^{{{\alpha }_{0}}}}{{e}^{{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}}}V_{2}^{{{\alpha }_{2}}}{{e}^{{{\alpha }_{3}}{{V}_{3}}}}		& \eta = & {{e}^{{{\alpha }_{0}}}}{{e}^{{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}}}{{e}^{{{\alpha }_{2}}\ln ({{V}_{2}})}}{{e}^{{{\alpha }_{3}}{{V}_{3}}}} =\ & {{e}^{{{\alpha }_{0}}}}{{e}^{{{\alpha }_{1}}\tfrac{1}{{{V}_{1}}}}}V_{2}^{{{\alpha }_{2}}}{{e}^{{{\alpha }_{3}}{{V}_{3}}}}
	\end{align}</math>		\end{align}</math>

	~~<br>~~
	Therefore, the parameter <math>B</math> of the Arrhenius relationship is equal to the log-linear coefficient <math>{{\alpha }_{1}}</math> , and the parameter <math>n</math> of the inverse power relationship is equal to ( <math>-{{\alpha }_{2}}</math> ). Therefore <math>\eta </math> can also be written as:		Therefore, the parameter <math>B</math> of the Arrhenius relationship is equal to the log-linear coefficient <math>{{\alpha }_{1}}</math> , and the parameter <math>n</math> of the inverse power relationship is equal to ( <math>-{{\alpha }_{2}}</math> ). Therefore <math>\eta </math> can also be written as:

	~~<br>~~
	::<math>\eta ={{e}^{{{\alpha }_{0}}}}{{e}^{\tfrac{B}{{{V}_{1}}}}}V_{2}^{n}{{e}^{{{\alpha }_{3}}{{V}_{3}}}}</math>		::<math>\eta ={{e}^{{{\alpha }_{0}}}}{{e}^{\tfrac{B}{{{V}_{1}}}}}V_{2}^{n}{{e}^{{{\alpha }_{3}}{{V}_{3}}}}</math>

	~~<br>~~
	The activation energy of the Arrhenius relationship can be calculated by multiplying B with Boltzmann's constant.		The activation energy of the Arrhenius relationship can be calculated by multiplying B with Boltzmann's constant.
	~~<br>~~
	The best fit values for the parameters in this case are:		The best fit values for the parameters in this case are:

	~~<br>~~
	::<math>\begin{align}		::<math>\begin{align}
	\beta = & 3.7483;\text{ }{{\alpha }_{0}}=-6.0220;\text{ }{{\alpha }_{1}}=5776.9341 \\		\beta = & 3.7483;\text{ }{{\alpha }_{0}}=-6.0220;\text{ }{{\alpha }_{1}}=5776.9341 \\
Line 47:		Line 37:
	\end{align}</math>		\end{align}</math>

	~~<br>~~
	Once the parameters are estimated, further analysis on the data can be performed. First, using ALTA, a Weibull probability plot of the data can be obtained, as shown next.		Once the parameters are estimated, further analysis on the data can be performed. First, using ALTA, a Weibull probability plot of the data can be obtained, as shown next.
	~~<br>~~

	~~<br>~~
	[[Image:ALTA11.1.gif\|thumb\|center\|450px\|Weibull probability plot for all covariates.]]		[[Image:ALTA11.1.gif\|thumb\|center\|450px\|Weibull probability plot for all covariates.]]
	~~<br>~~
	~~<br>~~
	Several types of information about the model as well as the data can be obtained from a probability plot. For example, the choice of an underlying distribution and the assumption of a common slope (shape parameter) can be examined. In this example, the linearity of the data supports the use of the Weibull distribution. In addition, the data appear parallel on this plot, therefore reinforcing the assumption of a common beta. Further statistical analysis can and should be performed for these purposes as well.		Several types of information about the model as well as the data can be obtained from a probability plot. For example, the choice of an underlying distribution and the assumption of a common slope (shape parameter) can be examined. In this example, the linearity of the data supports the use of the Weibull distribution. In addition, the data appear parallel on this plot, therefore reinforcing the assumption of a common beta. Further statistical analysis can and should be performed for these purposes as well.
	The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.		The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.
	~~<br>~~
	[[Image:ALTA11.2.gif\|thumb\|center\|500px\|Effects of temperature on life.]]		[[Image:ALTA11.2.gif\|thumb\|center\|500px\|Effects of temperature on life.]]
	~~<br>~~
	~~<br>~~
	[[Image:ALTA11.3.gif\|thumb\|center\|500px\|Effects of voltage on life.]]		[[Image:ALTA11.3.gif\|thumb\|center\|500px\|Effects of voltage on life.]]
	~~<br>~~
	~~<br>~~
	The effects of the two different operation types on life can be observed in the next figure. It can be seen that the on/off cycling has a greater effect on the life of the product in terms of accelerating failure than the continuous operation. In other words, a higher reliability can be achieved by running the product continuously.		The effects of the two different operation types on life can be observed in the next figure. It can be seen that the on/off cycling has a greater effect on the life of the product in terms of accelerating failure than the continuous operation. In other words, a higher reliability can be achieved by running the product continuously.

	~~<br>~~
	[[Image:ALTA11.4.gif\|thumb\|center\|500px\|Effect of operation type on life.]]		[[Image:ALTA11.4.gif\|thumb\|center\|500px\|Effect of operation type on life.]]
	~~<br>~~

Richard House: /* GLL Example */

2012-08-01T08:52:04Z

GLL Example

← Older revision		Revision as of 08:52, 1 August 2012
Line 52:		Line 52:

	<br>		<br>
	[[Image:ALTA11.1.gif\|thumb\|center\|~~150px~~\|Weibull probability plot for all covariates.]]		[[Image:ALTA11.1.gif\|thumb\|center\|450px\|Weibull probability plot for all covariates.]]
	<br>		<br>
	<br>		<br>
Line 58:		Line 58:
	The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.		The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.
	<br>		<br>
	[[Image:ALTA11.2.gif\|thumb\|center\|~~200px~~\|Effects of temperature on life.]]		[[Image:ALTA11.2.gif\|thumb\|center\|500px\|Effects of temperature on life.]]
	<br>		<br>
	<br>		<br>
	[[Image:ALTA11.3.gif\|thumb\|center\|~~200px~~\|Effects of voltage on life.]]		[[Image:ALTA11.3.gif\|thumb\|center\|500px\|Effects of voltage on life.]]
	<br>		<br>
	<br>		<br>
Line 67:		Line 67:

	<br>		<br>
	[[Image:ALTA11.4.gif\|thumb\|center\|~~200px~~\|Effect of operation type on life.]]		[[Image:ALTA11.4.gif\|thumb\|center\|500px\|Effect of operation type on life.]]
	<br>		<br>

Richard House: /* GLL Example */

2012-08-01T08:50:21Z

GLL Example

← Older revision		Revision as of 08:50, 1 August 2012
Line 14:		Line 14:
	The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.		The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.
	<br>		<br>
	[[Image:StressTransformation.gif\|thumb\|center\|~~300px~~\|]]		[[Image:StressTransformation.gif\|thumb\|center\|400px\|]]

	<br>		<br>

Richard House: /* GLL Example */

2012-08-01T08:49:52Z

GLL Example

← Older revision		Revision as of 08:49, 1 August 2012
Line 5:		Line 5:
	<br>		<br>
	<center>'''Stress Profile Summary'''</center>		<center>'''Stress Profile Summary'''</center>
	[[Image:ALTA11t1.png\|center\|~~200px~~\|]]		[[Image:ALTA11t1.png\|center\|300px\|]]
	<br>		<br>

	<center>'''Failure Data'''</center>		<center>'''Failure Data'''</center>
	[[Image:ALTA11t2.png\|center\|~~250px~~\|]]		[[Image:ALTA11t2.png\|center\|350px\|]]

	<br>		<br>
	The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.		The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.
	<br>		<br>
	[[Image:StressTransformation.gif\|thumb\|center\|~~200px~~\|]]		[[Image:StressTransformation.gif\|thumb\|center\|300px\|]]

	<br>		<br>

Kate Racaza: /* GLL Example */

2012-07-03T13:56:23Z

GLL Example

← Older revision		Revision as of 13:56, 3 July 2012
Line 4:		Line 4:
	<br>		<br>
	<br>		<br>
	<center>~~<h3>~~Stress Profile Summary~~</h3>~~</center>		<center>'''Stress Profile Summary'''</center>
	[[Image:ALTA11t1.png\|center\|200px\|]]		[[Image:ALTA11t1.png\|center\|200px\|]]
	<br>		<br>

	<center>~~<h3>~~Failure Data~~</h3>~~</center>		<center>'''Failure Data'''</center>
	[[Image:ALTA11t2.png\|center\|250px\|]]		[[Image:ALTA11t2.png\|center\|250px\|]]

Chuck Smith: /* GLL Example */

2012-04-26T15:42:41Z

GLL Example

← Older revision		Revision as of 15:42, 26 April 2012
Line 5:		Line 5:
	<br>		<br>
	<center><h3>Stress Profile Summary</h3></center>		<center><h3>Stress Profile Summary</h3></center>
	[[Image:ALTA11t1.png\|center\|~~400px~~\|]]		[[Image:ALTA11t1.png\|center\|200px\|]]
	<br>		<br>

	<center><h3>Failure Data</h3></center>		<center><h3>Failure Data</h3></center>
	[[Image:ALTA11t2.png\|center\|~~500px~~\|]]		[[Image:ALTA11t2.png\|center\|250px\|]]

	<br>		<br>
	The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.		The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.
	<br>		<br>
	[[Image:StressTransformation.gif\|thumb\|center\|~~400px~~\|]]		[[Image:StressTransformation.gif\|thumb\|center\|200px\|]]

	<br>		<br>
Line 52:		Line 52:

	<br>		<br>
	[[Image:ALTA11.1.gif\|thumb\|center\|~~300px~~\|Weibull probability plot for all covariates.]]		[[Image:ALTA11.1.gif\|thumb\|center\|150px\|Weibull probability plot for all covariates.]]
	<br>		<br>
	<br>		<br>
Line 58:		Line 58:
	The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.		The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.
	<br>		<br>
	[[Image:ALTA11.2.gif\|thumb\|center\|~~400px~~\|Effects of temperature on life.]]		[[Image:ALTA11.2.gif\|thumb\|center\|200px\|Effects of temperature on life.]]
	<br>		<br>
	<br>		<br>
	[[Image:ALTA11.3.gif\|thumb\|center\|~~400px~~\|Effects of voltage on life.]]		[[Image:ALTA11.3.gif\|thumb\|center\|200px\|Effects of voltage on life.]]
	<br>		<br>
	<br>		<br>
Line 67:		Line 67:

	<br>		<br>
	[[Image:ALTA11.4.gif\|thumb\|center\|~~400px~~\|Effect of operation type on life.]]		[[Image:ALTA11.4.gif\|thumb\|center\|200px\|Effect of operation type on life.]]
	<br>		<br>

Nicolette Young: /* GLL Example */

2012-04-03T17:27:29Z

GLL Example

← Older revision		Revision as of 17:27, 3 April 2012
Line 4:		Line 4:
	<br>		<br>
	<br>		<br>
	<center>Stress Profile Summary</center>		<center><h3>Stress Profile Summary</h3></center>
	[[Image:ALTA11t1.png\|center\|400px\|]]		[[Image:ALTA11t1.png\|center\|400px\|]]
	<br>		<br>

	<center>Failure Data</center>		<center><h3>Failure Data</h3></center>
	[[Image:ALTA11t2.png\|center\|500px\|]]		[[Image:ALTA11t2.png\|center\|500px\|]]

Line 14:		Line 14:
	The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.		The data in the second table are analyzed assuming a Weibull distribution, an Arrhenius life-stress relationship for temperature and an inverse power life-stress relationship for voltage. No transformation is performed on the operation type. The operation type variable is treated as an indicator variable, taking the discrete values of 0 and 1, for on/off and continuous operation, respectively. The following figure, shows the stress types and their transformations as in ALTA.
	<br>		<br>
	[[Image:StressTransformation.gif\|thumb\|center\|~~300px~~\|]]		[[Image:StressTransformation.gif\|thumb\|center\|400px\|]]

	<br>		<br>
Line 58:		Line 58:
	The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.		The Life vs. Stress plot is a very common plot for the analysis of accelerated data. Life vs. Stress plots can be very useful in assessing the effect of each stress on a product's failure. In this case, since the life is a function of three stresses, three different plots can be created. Such plots are created by holding two of the stresses constant at the desired use level, and varying the remaining one. The use stress levels for this example are 328K for temperature and 10V for voltage. For the operation type, a decision has to be made by the engineers as to whether they implement on/off or continuous operation. The next two figures display the effects of temperature and voltage on the life of the product.
	<br>		<br>
	[[Image:ALTA11.2.gif\|thumb\|center\|~~300px~~\|Effects of temperature on life.]]		[[Image:ALTA11.2.gif\|thumb\|center\|400px\|Effects of temperature on life.]]
	<br>		<br>
	<br>		<br>
	[[Image:ALTA11.3.gif\|thumb\|center\|~~300px~~\|Effects of voltage on life.]]		[[Image:ALTA11.3.gif\|thumb\|center\|400px\|Effects of voltage on life.]]
	<br>		<br>
	<br>		<br>
Line 67:		Line 67:

	<br>		<br>
	[[Image:ALTA11.4.gif\|thumb\|center\|~~300px~~\|Effect of operation type on life.]]		[[Image:ALTA11.4.gif\|thumb\|center\|400px\|Effect of operation type on life.]]
	<br>		<br>

Nikki Helms: /* GLL Example */

2012-03-30T21:55:06Z

GLL Example

← Older revision		Revision as of 21:55, 30 March 2012
Line 9:		Line 9:

	<center>Failure Data</center>		<center>Failure Data</center>
	[[Image:ALTA11t2.png\|center\|~~400px~~\|]]		[[Image:ALTA11t2.png\|center\|500px\|]]

	<br>		<br>