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A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of a fatigue crack can result in catastrophic failure, particularly in the case of aircraft. When many growing fatigue cracks interact with one another it is known as widespread fatigue damage. A crack growth equation can be used to ...
In a 1961 paper, P. C. Paris introduced the idea that the rate of crack growth may depend on the stress intensity factor. [4] Then in their 1963 paper, Paris and Erdogan indirectly suggested the equation with the aside remark "The authors are hesitant but cannot resist the temptation to draw the straight line slope 1/4 through the data" after reviewing data on a log-log plot of crack growth ...
This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either Miner's rule to calculate the fatigue damage, or in a crack growth equation to calculate the crack increments. [2] Both methods give an estimate of the fatigue life of a component.
In statistical prediction, the coverage probability is the probability that a prediction interval will include an out-of-sample value of the random variable. The coverage probability can be defined as the proportion of instances where the interval surrounds an out-of-sample value as assessed by long-run frequency. [2]
Provided the data are strictly positive, a better measure of relative accuracy can be obtained based on the log of the accuracy ratio: log(F t / A t) This measure is easier to analyze statistically and has valuable symmetry and unbiasedness properties.
That is, a prediction of 80% that correctly proved true would receive a score of ln(0.8) = −0.22. This same prediction also assigns 20% likelihood to the opposite case, and so if the prediction proves false, it would receive a score based on the 20%: ln(0.2) = −1.6. The goal of a forecaster is to maximize the score and for the score to be ...
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution.