New method for estimating fatigue life three-parameter P-S-N curves

From the scatter nature of fatigue data at different stress levels, it is well known that the variances of fatigue life logarithms are different, which is out of Gauss-Markov assumptions. At the case, the conventional least square method (LSM) cannot provide an optimal estimation for three parameter P-S-N curves in statistics. The weighted least square method (WLSM), however, is a best linear unbiased estimator (BLUE) for this heteroscedastic linear regression. Therefore, based on the WLSM and Bootstrap method, a new method is presented to estimate the three parameter P-S-N curves of fatigue life. Bootstrap method is employed to determine the covariance matrix, which simplify the iterative procedure for computing weight matrix in WLSM. The applications in Aluminum alloy LY12CZ, 45 Carbon steel and 40CrNiMo steel show how the presented method is implemented. From the result comparison of the presented method and the conventional LSM, it is concluded that the conventional LSM might give a dangerous estimation due to ignoring the Gauss-Markov assumptions, but the presented method can give a rational estimation due to its BLUE, especially as the increase of the sample size, the mean estimation of the presented method converges to the real mean and the variances of regression coefficients are minimum.