Due to relatively low design standards, distribution lines are vulnerable to typhoons damage, often resulting in pole collapse and line breakage. Traditional reliability models based on the stress-strength interference (SSI) theory typically approximate that the random variable of line load and wind speed follow the same distribution, thereby neglecting the correlation between load randomness and wind speed probability distribution. To improve model accuracy, the SSI theory is used to analyze the impact of line and pole parameters on line-breaking probability. Then the proposed breakage probability model considering wind speed probability distribution is compared with traditional reliability models, showing that conventional approaches fail to accurately capture the forced response of the load profile. Finally, a breakage probability improvement model considering wind speed probability distribution is proposed using a quadratic functional relationship between load and wind speed. Compared with the models that only consider load randomness, the improved model can more accurately capture the forced response of the load profile, while also achieving second-level computational efficiency. This provides a basis for fast and accurate damage warning and emergency repair for distribution lines under typhoon disasters.