Metal magnetic memory(MMM) testing has been widely used to detect welded joints. However, load levels, environmental magnetic field, and measurement noises make the MMM data dispersive and bring difficulty to quantitative evaluation. In order to promote the development of quantitative MMM reliability assessment, a new MMM model is presented for welded joints. Steel Q235 welded specimens are tested along the longitudinal and horizontal lines by TSC-2M-8 instrument in the tensile fatigue experiments. The X-ray testing is carried out synchronously to verify the MMM results. It is found that MMM testing can detect the hidden crack earlier than X-ray testing. Moreover, the MMM gradient vector sum Kvs is sensitive to the damage degree, especially at early and hidden damage stages. Considering the dispersion of MMM data, the Kvs statistical law is investigated, which shows that Kvs obeys Gaussian distribution. So Kvs is the suitable MMM parameter to establish reliability model of welded joints. At last, the original quantitative MMM reliability model is first presented based on the improved stress strength interference theory. It is shown that the reliability degree R gradually decreases with the decreasing of the residual life ratio T, and the maximal error between prediction reliability degree R1 and verification reliability degree R2 is 9.15%. This presented method provides a novel tool of reliability testing and evaluating in practical engineering for welded joints.