Template:Generalized eyring relationship

Introduction
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:


 * $$L(V,U)=\frac{1}{V}{{e}^{A+\tfrac{B}{V}+CU+D\tfrac{U}{V}}}$$


 * where:

•	   is the temperature (in absolute units ).

•	 $$U$$ is the non-thermal stress (i.e. voltage, vibration, etc.). $$A,B,C,D$$ are the parameters to be determined.

The Eyring relationship is a simple case of the generalized Eyring relationship where $$C=D=0$$  and  $${{A}_{Eyr}}=-{{A}_{GEyr}}.$$ Note that the generalized Eyring relationship includes the interaction term of $$U$$  and  $$V$$  as described by the  $$D\tfrac{U}{V}$$  term. In other words, this model can estimate the effect of changing one of the factors depending on the level of the other factor.

Example
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 $$B10$$  life at the use conditions of  $$T=350K$$  and  $$H=0.3$$. The data set is modeled using the lognormal distribution and the generalized Eyring model.









$$$$

The probability plot at the use conditions is shown next.

The $$B10$$  information is estimated to be 3004.63 hours, as shown next.