► A new parameter, S b, is proposed for composition studies in cosmic ray surface arrays. ► The discrimination capability ( η) of S b between proton and iron maximizes for b ∼ 3. ► If muon contribution is enhanced, optimal b is still 3 and η increases. ► A major advantage is that S 3 is almost independent on zenith angle. ► Composition accuracy using S 3 is of the same order than that from X max. A new family of parameters intended for composition studies in cosmic ray surface array detectors is proposed. The application of this technique to different array layout designs has been analyzed. The parameters make exclusive use of surface data combining the information from the total signal at each triggered detector and the array geometry. They are sensitive to the combined effects of the different muon and electromagnetic components on the lateral distribution function of proton and iron initiated showers at any given primary energy. Analytical and numerical studies have been performed in order to assess the reliability, stability and optimization of these parameters. Experimental uncertainties, the underestimation of the muon component in the shower simulation codes, intrinsic fluctuations and reconstruction errors are considered and discussed in a quantitative way. The potential discrimination power of these parameters, under realistic experimental conditions, is compared on a simplified, albeit quantitative way, with that expected from other surface and fluorescence estimators.