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As long as the relative crack depth is small, a crack closure straight line model may be used, while the crack closure parabolic line should be used in the case of a deep crack.
The starting point is a straight line model f(X) = β1 X.
For each of the 54 regions a straight line model Y t = α + β t + ϵ is assumed for the life expectancy Y t at year t.
The question then arises why not work with a straight line model (5) log p | log (1 − q ) = α + θ log (1 − q ).
The model mentioned by these authors is equivalent to our straight line model of Section Shape of the time-varying covariate.
The extension of the straight line model are power functions β1 X p. The values of p are chosen from the set S = {-2,-1,-0.5,0,0.5,1,2,3} where X denotes log(X).
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Hung et al. [7] and Divorra et al. [8, 9] independently addressed this limitation with the variable block size ME&MC by introducing additional wedge-like partitions where a MB is segmented using a straight line modelled by two parameters: orientation angle θ and distance ρ from the centre of the MB.
An intersecting straight lines model was used by Shibayama et al. for detecting phenophases in the Subarctic [ 29].
As mentioned earlier, model-assisted estimation would then become appropriate and the full power of linear, non-linear and multiple regression may be employed in the place of the simple straight-line model shown in Eqs.
The model, purposely kept simple for ease of use as a design tool, is found to capture trends in the fatigue data not predicted using traditional straight-line models on a mean stress versus alternating stress constant-life plot.
As far as dense range data is concerned, [13] describes straight-line model-based methods, RGBD cameras being exploited only to extract distance information.
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