An analytical model and non-parametric kernel density estimation approach are proposed for probability distribution calculation of distribution system reliability indices.In view of the fact that the time for work and repair of the system components is exponentially and non-exponentially distributed，analytical characterization for the reliability indices of the distribution network is conducted from the system level and the nodal layer using the random function，respectively.Furthermore，by referring to the non-parametric kernel density estimation technology，the probability distribution calculation is implemented for the expression of the reliability indices random function.With this method，it can be seen that taking into account that the time for work and repair of components will make the estimation results closer to engineering practice.Simulation results of RBTS-BUS6system show that the proposed method is effective.