First of all

randomness of fatigue loading

fatigue life and fatigue strength are classified into three types of random-constant amplitude

random-variable amplitude and random-stochastic time history

respectively.Then

according to Miner's two-dimensional Probabilistic Rule

a new reliability-based prediction procedure of fatigue life is established for the structural component subjected to one-dimensional and two-dimensional cyclic loadings of variable amplitude or stochastic time history.Meanwhile

the probability distribution of α in Statistical Miner Rule is derived.The verification of the obtained results by means of variable amplitude experiment at data of fatigue life shows that the new prediction procedure is very accurate.In the end

an example is presented in detail

which indicates that this new procedure is of simplicity and of feasibility in engineering application.