A simulation-based investigation of the staircase method for fatigue strength testing

A critical evaluation of the statistics of the fatigue strength distribution as determined by the staircase (or up-and-down) method is presented. The effects of test parameters (namely, step size and sample size) were analyzed using numerical simulation to determine the accuracy of fatigue strength standard deviation calculations using traditional staircase statistics, resulting in a quantification of standard deviation bias as a function of step size and sample size. A non-linear correction was formulated to mitigate this standard deviation bias inherent in small-sample tests. In addition, the simulation was used to investigate the effectiveness of a bootstrapping algorithm on standard deviation estimates. The bootstrapping algorithm was found to significantly reduce the potential of large standard deviation errors in small-sample tests. Together, the use of the non-linear correction factor and the bootstrapping algorithm may allow an improved method to estimate the statistics of a material’s fatigue strength distribution using a small-sample staircase test strategy.