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| ==Generalized Eyring Relationship==
| | #REDIRECT [[Eyring_Relationship#Generalized_Eyring_Relationship]] |
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| ===Introduction===
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| <br>
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| The generalized Eyring relationship is used when temperature and a second non-thermal stress (e.g. voltage) are the accelerated stresses of a test and their interaction is also of interest. This relationship is given by:
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| <br>
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| ::<math>L(V,U)=\frac{1}{V}{{e}^{A+\tfrac{B}{V}+CU+D\tfrac{U}{V}}}</math>
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| <br>
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| :where:
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| <br>
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| • is the temperature (in absolute units ).
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| • <math>U</math> is the non-thermal stress (i.e. voltage, vibration, etc.).
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| <math>A,B,C,D</math> are the parameters to be determined.
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| <br>
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| The Eyring relationship is a simple case of the generalized Eyring relationship where <math>C=D=0</math> and <math>{{A}_{Eyr}}=-{{A}_{GEyr}}.</math>
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| Note that the generalized Eyring relationship includes the interaction term of <math>U</math> and <math>V</math> as described by the <math>D\tfrac{U}{V}</math> term. In other words, this model can estimate the effect of changing one of the factors depending on the level of the other factor.
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| {{gen-eyring acceleration factor}}
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| {{generalized eyring-exponential}}
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| {{generalized eyring-weibull}}
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| {{generalized eyring-log}}
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| ===Example===
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| <br>
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| The following data set represents failure times (in hours) obtained from an electronics epoxy packaging accelerated life test performed to understand the synergy between temperature and humidity and estimate the <math>B10</math> life at the use conditions of <math>T=350K</math> and <math>H=0.3</math> . The data set is modeled using the lognormal distribution and the generalized Eyring model.
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| <br>
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| [[Image:altaproject.png|thumb|center|400px| ]] | |
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| [[Image:altaaccelerated.png|thumb|center|400px| ]]
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| [[Image:altatimes2fail.png|thumb|center|400px|]]
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| [[Image:tempNhumin.png|thumb|center|400px|]]
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| [[Image:406-1-2.png|thumb|center|400px|]]
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| <math></math>
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| The probability plot at the use conditions is shown next.
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| <br>
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| [[Image:plotfolio426.png|thumb|center|400px|]]
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| <br>
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| The <math>B10</math> information is estimated to be 3004.63 hours, as shown next.
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| <br>
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| [[Image:tempBX.png|thumb|center|400px|]]
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| <br>
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