Closed-form solution based on peak probability density function for statistical fatigue life prediction under Broad-Band random loading

•Analytical method for fast spectral fatigue-life prediction under random loading is proposed.•Fatigue prediction is based on the stress power spectral density and the Rice peak distribution.•The novel closed-form solution employs special HyperGeometric function.•HyperGeometric solution possesses higher accuracy than other methods based on the peak distribution.•Straightforward engineering applicability of obtained results is achieved.