Advances in medical research and intelligent modeling techniques have led to developments in anaesthesia management. The present study aims to estimate the depth of anaesthesia using cognitive signal processing and intelligent modeling techniques. The neurophysiological signal that reflects the cognitive state of anaesthetic drugs is the electroencephalogram signal. The information available from electroencephalogram signals during anaesthesia is extracted from the relative wave energy features of those signals. Discrete wavelet transform is used to decompose electroencephalogram signals into four levels and the relative wave energy is computed from approximate and detailed coefficients of the signal sub-bands. Relative wave energy is extracted to determine the degree of importance of different electroencephalogram frequency bands associated with different anaesthetic phases, for example, the awake, induction, maintenance, and recovery phases. The Kruskal-Wallis statistical test is applied to relative wave energy features to check the discriminative capability of the relative wave energy features classified as awake, light anaesthesia, moderate anaesthesia, and deep anaesthesia. A novel depth of anaesthesia index is generated by implementing an adaptive neuro-fuzzy inference system based on a fuzzy c-means clustering algorithm which uses relative wave energy features as inputs. Finally, the generated depth of anaesthesia index is compared with a commercially available depth of anaesthesia monitor, the Bispectral index.