Arrhenius-Lognormal Model for Interval Data with Activation Energy: Difference between revisions
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{{Reference Example| | {{Reference Example|{{Banner ALTA Reference Examples}}}} | ||
This example | This example validates the results for the Arrhenius-lognormal model for interval data, with a given activation energy. | ||
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where ''T'' is the temperature; <math>\beta_{1}\,\!</math> is the activation energy; 11605 is calculated from the reciprocal of the Boltzmann constant. This function can be written in the following way: | where ''T'' is the temperature; <math>\beta_{1}\,\!</math> is the activation energy; and 11605 is calculated from the reciprocal of the Boltzmann constant. This function can be written in the following way: | ||
::<math>e^{\mu'} = e^{\alpha_{0}+ \frac {\alpha_{1}}{T}}\,\!</math> | ::<math>e^{\mu'} = e^{\alpha_{0}+ \frac {\alpha_{1}}{T}}\,\!</math> | ||
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The above equation is the general log-linear model in ALTA. In ALTA, the coefficients are denoted by <math>\alpha_{i}\,\!</math>. We can see <math>\beta_{0} = \alpha_{0}\,\!</math> and <math>\beta_{1} = \frac{\alpha_{1}}{11605}\,\!</math>. | The above equation is the general log-linear model in ALTA. In ALTA, the coefficients are denoted by <math>\alpha_{i}\,\!</math>. We can see <math>\beta_{0} = \alpha_{0}\,\!</math> and <math>\beta_{1} = \frac{\alpha_{1}}{11605}\,\!</math>. | ||
In fact, the above model also | In fact, the above model can also be expressed using the traditional Arrhenius model: | ||
::<math>e^{\mu'} = e^{\alpha_{0}+ \frac {\alpha_{1}}{T}} = C \times e^{\frac{B}{T}}\,\!</math> | ::<math>e^{\mu'} = e^{\alpha_{0}+ \frac {\alpha_{1}}{T}} = C \times e^{\frac{B}{T}}\,\!</math> | ||
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{{Reference_Example_Heading4|ALTA}} | {{Reference_Example_Heading4|ALTA}} | ||
We can use the "Alter One Parameter (and Recalculate)" utility in ALTA to enter the value for <math>\alpha_{1}\,\!</math> = 9284, as shown next. | |||
[[Image: Arrhenius Log alter parameters.png|center]] | |||
The following picture shows the results. | |||
[[Image: Arrhenius Log alter parameters results.png|center]] | |||
The probability plot with confidence interval at the use temperature level is shown next. This plot is similar to the plot shown in the book. The confidence interval for the reliability at the use stress level (the line at the far right side of the plot) is very tight since the activation energy is given. | |||
[[Image: Arrhenius Log alter parameters plot.png|center|550px]] |
Latest revision as of 18:19, 28 September 2015
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