At present, the most reliable fatigue design for structures subjected to service loading is considered to be one based on fatigue strength diagrams. These diagrams would have to be obtained from actual service loading fatigue tests or random loading fatigue tests simulating service loading. However, it would take a very long time to complete the necessary experiments, so long as to be impossible. In the previous paper, the authors proposed a new method of developing fatigue strength diagrams under random loading conditions. This method combines random loading test plus an equation, and promises to reduce by 95-99 percent the time required for ordinary random loading fatigue tests with the Weibull distribution. In this paper, using the proposed method, fatigue strength diagrams for butt and fillet welds of mild steel were obtained for load-controlled axial pulsating tension random loading with the Weibull distribution. Shape coefficient in the Weibull distribution was chosen to be 0.75, 1.0 and 1.25. Strength diagrams with these welds were also derived by means of UKDOE Guidance and AWS Code. The main results obtained in this study are as follows. 1) Fatigue strength diagrams, represented by shape coefficients as a parameter, are approximated by paralell straight lines in semi-log coordinate. 2) Fatigue strength decreases by about ten precent or fatigue life about one-hundredth as shape coefficient increases by 0.25, from 0.75 to 1.25. 3) Strength diagrams for both welds, obtained by those two organizations, lead to divergent final designs.