For　vibration　response　signals　with　mean　stress,　a　Rayleigh　function　with　a　multiplier　was　used　to　fit　the　probability　distribution　of　stress　amplitude　corrected　to　vibration　response　signals　with　zero　mean　stress.　An　equation　was　developed　by　the　obtained　S-N　curves　for　welded　1Cr18Ni9Ti　stainless　steel　connections　with　stress　ratios　of　−1,　0.1,　and　0.5,　respectively,　to　convert　the　stress　amplitudes　of　cyclic　loadings　with　different　mean　stress　to　stress　amplitudes　with　zero　mean　stress　for　the　same　fatigue　life.　Based　on　the　S-N　curve　of　material　with　a　stress　ratio　of　−1　and　the　Miner　linear　damage　accumulation　theory,　a　vibration　fatigue　life　prediction　method　was　proposed.　The　results　of　the　random　vibration　fatigue　test　with　non-zero　mean　stress　on　the　pipeline　of　the　launch　vehicle　have　verified　the　accuracy　of　the　proposed　method.　©　2024