An analytical calculation method for the reliability sensitivity indexes of distribution systems is proposed to explicitly quantify the impact of various influence factors on system reliability. Firstly, the analytical calculation formulas for the reliability indexes of distribution systems are derived based on the fault incidence matrix (FIM). Secondly, the factors that affect system reliability are divided into two categories: quantifiable parameter factors and non-quantifiable network structure factors. The sensitivity indexes for the quantifiable parameter factors are derived using the direct partial derivation of the reliability calculation formulas. The sensitivity indexes for the non-quantifiable network structure factors are derived using the transformation of FIMs. Finally, the accuracy and efficiency of the proposed sensitivity calculation method are verified by applying them to an IEEE 6-bus RBTS system. This paper sums up the factors that influence system reliability in detail and gives the explicit analytical calculation method for the sensitivity of each factor. Repetitive calculation of the reliability index can be avoided during the sensitivity analysis. The bottleneck that affects the reliability level of distribution systems can be identified efficiently, and valuable information and guidance can be provided to enhance the reliability of distribution systems.