The depth of anaesthesia estimation has been of a great interest in recent decades. We present a new methodology to quantify the depth of anaesthesia by quantifying the power-law correlations of the EEG signal. Extraction of useful information about the nonlinear dynamics of the brain during anaesthesia has been proposed with the optimum fractal scaling exponent. This optimum solution is based on the best domain of box sizes in the detrended fluctuation analysis (DFA) algorithm which have meaningful changes at different depth of anaesthesia. The experimental results confirm that our new algorithm on the raw EEG data can clearly discriminate between aware to moderate and deep anaesthesia levels and have robust relations with the well known depth of anaesthesia index (BIS). Moreover, it significantly reduces the computational complexity and results in a faster reaction to the transients in patients' consciousness levels