The effect of velocity slip with viscosity variation between porous rough circular stepped plates with couple stress fluid is examined. A stochastic random variable having a non-zero mean, variance, and skewness is used to model a more general type of surface roughness equation also the modified Reynolds equation accounting for pressure dependent viscosity is analytically derived. The numerical solution obtained for the non-dimensionless pressure, load carrying capacity and time. It is observed that the impact of roughness and viscosity variation using a couple stress fluid between circular stepped plates has been discussed. These effects improved the ability of load carrying capacity as compared to the corresponding Newtonian case.