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| =Cumulative Damage Power Relationship=
| | #REDIRECT [[Time-Varying_Stress_Models#Cumulative_Damage_Power_Relationship]] |
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| This section presents a generalized formulation of the cumulative damage model where stress can be any function of time and the life-stress relationship is based on the power relationship. Given a time-varying stress <math>x(t)</math> and assuming the power law relationship, the life-stress relationship is given by:
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| <br>
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| ::<math>L(x(t))={{\left( \frac{a}{x(t)} \right)}^{n}}</math>
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| <br>
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| In ALTA, the above relationship is actually presented in a format consistent with the general log-linear (GLL) relationship for the power law relationship:
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| ::<math>L(x(t))={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\ln \left( x(t) \right)}}</math>
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| <br>
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| Therefore, instead of displaying <math>a</math> and <math>n</math> as the calculated parameters, the following reparameterization is used:
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| <br>
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| ::<math>\begin{align}
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| {{\alpha }_{0}}=\ & \ln ({{a}^{n}}) \\
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| {{\alpha }_{1}}=\ & -n
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| \end{align}</math>
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| <br>
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| {{cd power exponential}}
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| {{cd power weibull}}
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| {{cd power lognormal}}
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