The Rafita asteroid family is an S-type group located in the middle main belt, on the right-hand side of the 3J:-1A mean-motion resonance. The proximity of this resonance to the family left-hand side in the semimajor axis caused many former family members to be lost. As a consequence, the family shape in the (a, 1/D) domain is quite asymmetrical, with a preponderance of objects on the right-hand side of the distribution. The Rafita family is also characterized by a leptokurtic distribution in inclination, which allows the use of methods of family age estimation recently introduced for other leptokurtic families such as Astrid, Hansa, Gallia and Barcelona. In this work, we propose a new method based on the behaviour of an asymmetry coefficient function of the distribution in the (a, 1/D) plane to date incomplete asteroid families such as Rafita. By monitoring the time behaviour of this coefficient for asteroids simulating the initial conditions at the time of the family formation, we were able to estimate that the Rafita family should have an age of 490 ± 200 Myr, in good agreement with results from independent methods such as Monte Carlo simulations of Yarkovsky and YORP dynamical induced evolution and the time behaviour of the kurtosis of the sin (i) distribution. Asteroids from the Rafita family can reach orbits similar to 8 per cent of the currently known near-Earth objects. During the final 10 Myr of the simulation, 1 per cent of the simulated objects are present in NEO space, and thus would be comparable to objects in the present-day NEO population.