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In this manuscript, a generalized net-section-collapse (NSC) failure criterion of circumferentially cracked pipes with multiple arbitrary-shaped cracks is presented. This generalized NSC formulation is capable of predicting the NSC moment of a pipe with multiple arbitrary-shaped cracks distributed around the circumference of the pipe, regardless of whether they are distributed symmetrically or not. The case in which internal cracks straddle the compressive zone is accounted for in the present formulation. Closed form solutions are provided for the maximum moments of pipes containing multiple cracks with idealized shapes, namely constant depth, semi-elliptical and parabolic crack profiles. Through a series of examples, the results show the effectiveness and accuracy of the method. Using this method, quantification of the effect of the crack profile uncertainty on the maximum bending moment sustained by a cracked pipe is evaluated. It is demonstrated that while the uncertainty associated with the surface roughness of the crack profile has little to no effect on the maximum bending moment, irregular shape profiles have, not surprisingly, a large effect on the estimation of the maximum bending moment. In fact, it is mathematically shown that the uncertainty associated with the maximum bending moment is proportional to the magnitude of the crack profile uncertainty and inversely proportional to the square root of the uncertainty sampling size (i.e. surface roughness vs. irregular crack profile).