A reliability enhancement scheme for an electric distribution system is impossible to be cost-effective without the guidance of accurate reliability index estimations. As one of the widely used basic reliability indices, average interruption duration is of foremost concern, due to being a straightforward indicator of the electric power supply quality in the aspect of customer satisfaction to the incident response capability of electric utilities to outage events. This paper proposed an analytical distribution system reliability evaluation method that allows for considering stochastic load point interruption durations together with stipulated network reconfiguration constraints. Through case studies on the Roy Billinton Reliability Test System, advantages of the proposed method over a traditional section technique-based reliability evaluation method are discussed. The proposed method is validated to yield more realistic estimations in the case of considering stochastic interruption durations and post-fault network reconfigurations, thus is expected to be capable of supporting economical system reliability-enhancing decision-making.