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A method is proposed to prioritize the repair or replacement of out-of-service transformers that feed a heavily meshed secondary grid. Priority assigned to the restoration of a specific transformer is based on the risk reduction that results from this replacement. Risk is defined as the reduction in the probable number of customers out of service should the transformer return to service. This measure of risk addresses the possibility of network collapse following feeder failures (occasioned by load-induced failure of transformers or feeders) and local customer impact on the secondary network. The prediction of risk makes extensive use of load predictions for feeder sections, network transformers, and secondary mains. A software tool has been developed to implement the equations proposed in this paper. This software gives system planners and operators the ability to quickly and economically select the next transformer to be repaired or replaced.