Axial Flux Permanent Magnet (AFPM) machines with ironless rotors are an attractive and recently studied solution in low-speed applications, due to their potentially high power/weight ratio, high aspect ratio, and high efficiency. Nevertheless, these machines are prone to be affected by manufacturing tolerance during its fabrication process and consequently, the magnets may move freely inside the rotor structure. This work presents a statistical analysis of manufacturing tolerances of an AFPM machine with an ironless rotor, considering several magnet fault types. A computationally efficient superposition method is developed and implemented to obtain both the cogging torque and rated torque considering several tolerance combinations with acceptable accuracy. The results obtained from a statistical analysis of 10,000 designs of a two-stator one rotor tooth coil winding AFPM (TCW-AFPM) machine allowed us to identify the parameters with the most impact on relevant performance indicators and disclosed a substantial increase in cogging and ripple torque when unavoidable combined tolerances are present.