Abstract: Thin stiffened shell structures are widely employed in aerospace, mechanical, chemical, and civil engineering owing to their superior load-bearing capacity and manufacturing simplicity. However, their buckling loads are highly sensitive to random initial geometric imperfections arising from fabrication, machining and assembly. Existing approaches are difficult to balance the universality, accuracy and efficiency when determining the random buckling load and reliability assessment of reinforced cylindrical thin shells. To this end, this study introduces a highly universal direct probability integral method (DPIM) to quantify the uncertainty of buckling load and evaluate the instability probability of stiffened cylindrical thin shells with random initial geometric imperfections. First, a random field model of initial geometric imperfections for stiffened cylindrical thin shells is established, and the expansion optimal linear estimation method is adopted to simulate the random field; a perimeter invariant constraint is introduced to ensure that the generated imperfections are physically consistent with engineering practice. Second, based on DPIM with an adaptive point-selection strategy, the criteria selecting linear and nonlinear buckling analyses are suggested, achieving the probabilistic distribution of buckling loads and instability probability of stiffened cylindrical thin shells with random initial geometric imperfections. Finally, the results are compared with those obtained by Monte Carlo simulation (MCS) and quasi-MCS, demonstrating the high accuracy and efficiency of the proposed method. The influences of geometric imperfection random field parameters on the stochastic buckling load and instability probability are revealed.