Electricity distribution systems are dynamically expanded in anticipation of new demands. Cost and reliability are the most important factors in finding the optimal plans for network expansion. Recently, implementation of incentive reliability regulations has accentuated the role of reliability considerations in distribution systems studies. This is because such incentive schemes create a direct link between distribution companies' revenues and their service reliability. Thus, these schemes have changed the role of reliability from a technical constraint to an economic factor. In this occasion, distribution companies require new techniques to incorporate the effects of incentive reliability...