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Tukey’s  g -and- h  distribution is a generalized implicit distribution based on the transformation of normal distribution, which has a stronger fault-tolerant capability for the fitting of life data distribution. In this paper, the  P-S-N  curve is modelled through its corresponding location-scale model with quantile expression, so as to improve the life prediction accuracy of mechanical parts in reliability design. Two groups of life experiment data concerning G20CrNi2Mo bearing steel and 104 rolling bearing are used to verify the proposed model. The mean square error (MSE) of experimental data and simulation data is taken as the objective function, and the parameter estimation of the model is realized with the whale optimization algorithm (WOA). The results show that the proposed approach could accurately express the trend of life varying with different loads, and the quantile expression of life data can be realized conveniently.

Quantile S-N Curve and its Application based on Tukey’s g-and-h Distribution and Whale Optimization Algorithm