Reconfigurable Intelligent Surface (RIS) and Rate Splitting Multiple Access (RSMA) technologies are two emerging communication techniques with broad prospects in future wireless systems. Active RIS (ARIS) has the advantage of overcoming the effects of multiplicative fading compared to Passive RIS (PRIS). The paper addresses the outage performance of ARIS-assisted RSMA systems under random deployment. Under Nakagami-m small-scale fading model in downlink, multiple users are randomly distributed within a semicircular region around ARIS and sorted by the distances between the users and ARIS. Taking the optimal phase shift for the furthest user as the entry point, a moment matching approach is employed to derive the shape and scale parameters associated with the cascaded channel power characteristic for each RSMA user. We derive a closed-form expression for the outage performance of the users, analyze the effect of the power splitting coefficients on the Outage Probability (OP), and obtain the diversity order and an expression for the approximate OP. Simulation results show that the OP of a non-perfect phase-shifted user under ARIS-assistance is re duced by 58% compared to the passive RIS-assisted system under a power budget of 50 dBm and a moderate amount of RIS elements. In addition, the power consumption of the user with the optimal phase shift is reduced by 53 dBm.