The safety assessment and reliability analysis are the two critical factors that affect the design of a complex structured system. In this paper, safety assessment model is used and the radiation dose of radionuclides are evaluated. The model is developed based on single dumping mode of disposal. In the present paper, radioactive carbon (¹⁴C) is considered as it delivered the maximum concentration in ground water. To consider variability in the model parameters, a probabilistic methodology is adopted. One of the efficient probabilistic methods, collocation based stochastic response surface methodology (CSRSM) is used. In this method, the complex analytical equations are approximated by a higher order polynomial (using polynomial chaos expansion (PCE)). Groundwater velocity, thickness of unsaturated zone, dispersivity and distribution coefficient are considered as random variables. Third order polynomial gave the best fit for the model and an R² of 0.99 is obtained for a third order polynomial. Reliability analysis was carried out and the probability of failure of annual radiation dose of ¹⁴C (radioactive carbon) radionuclide exceeding the permissible limits was estimated for different scenarios. The results show that the probability of failure of the system is very low and the multi barrier system is safe.