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Mixed-lubrication models comprising of Patir and Cheng's [1,2] average Reynolds equation and Greenwood and Tripp's [3] asperity interaction formulations have hitherto been widely used in predicting piston-ring performance. In this paper a number of models have been developed to allow mixed-lubrication of both Newtonian and shear thinning fluids to be simulated. Lubricating action usually involves two anisotropic solid surfaces of statistically different profiles. Various forms of the average Reynolds equation and the asperity interaction models require parameters representing the composite surface roughness and profile parameters at the contact. Here a strategy for determining these equivalent composite parameters is presented. Mathematical simulations indicate that when the composite RMS and composite summit RMS roughness of the contact approach the same value, the performance of the mix-lubrication model becomes dominated by the asperity interaction formulation.