Robustness analysis for the global exponential stability of fuzzy bidirectional associative memory cellular neural network (FBAMCNN) is explored in this paper. By applying Gronwall-Bellman lemma and other inequality techniques, the range limits of both time-varying delays and the intensity of noise that FBAMCNN can withstand to maintain globally exponentially stable is estimated. It means that if the intensities of interference are larger than the bounds we derived, then the perturbed system may lose global exponential stability. Several instances are given to support our main results.