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Electricity distribution companies are in-charge-of supplying stable electric energy to urban customers over a wide geographical area. In these distribution networks, large number of Distribution-Transformers (DTs) are installed on towers or in electric-rooms with the ratings below 1000 kVA, which are the most important assets of distribution companies. Periodic maintenance and test services are not economically feasible for all in-operation transformers. Hence, estimating the remaining useful life and scheduling the maintenance times of DTs are of great technical and economic importance. An analytical approach is presented in this paper for predicting lifetime of DTs based on degree of polymerization. An appropriate Machine-Learning (ML) algorithm trained by measured data is selected for forecasting driven load according to the ambient temperature and humidity and day-hour schedules. The relation of Hot-Spot-Temperature in IEC60076∼7 is modified based on the measured data for accounting unbalanced-loading. Neutral-current is predicted using a trained ML-model. Another approach is proposed for determining times of oil filtering services aiming to minimize the maintenance cost and maximizing the remaining life. The proposed lifetime estimation method is validated by comparing its results with the damaged DT data of a sample network chosen as the case studies for this research, i.e., Bushehr province, Iran. [ABSTRACT FROM AUTHOR]