Implementing the concept of a “smart furnace transformer” should stipulate its information support throughout its life cycle. This requires improving techniques for estimating the transformer’s health and forecasting its remaining useful life (RUL). A brief review of the problem being solved has shown that the known RUL estimation techniques include processing the results of measuring the facility state parameters using various mathematical methods. Data processing techniques (deep learning, SOLA, etc.) are used, but there is no information on their application in online monitoring systems. Herewith, fast (shock) changes in the resource caused by the failures and subsequent recoveries of the facility’s health have not been considered. This reduces the RUL forecasting accuracy for the repairable equipment, including transformers. It is especially relevant to consider the impact of sudden state changes when it comes to furnace transformers due to a cumulative wear effect determined by their frequent connections to the grid (up to 100 times a day). The proposed approach is based on calculating the RUL by analytical dependencies, considering the failures and recoveries of the facility state. For the first time, an engineering RUL forecasting technique has been developed, based on the online diagnostic monitoring data results provided in the form of time series. The equipment’s relative failure tolerance index, calculated with analytical dependencies, has first been used in RUL forecasting. As a generalized indicator, a relative failure tolerance index considering the facility’s state change dynamics has been proposed. The application of the RUL forecasting technique based on the results of dissolved gas analysis of a ladle furnace unit’s transformer is demonstrated. The changes in the transformer state during the operation period from 2014 to 2022 have been studied. The RUL was calculated in the intensive aging interval; the winding dismantling results were demonstrated, which confirmed developing destructive processes in the insulation. The key practical result of the study is reducing accidents and increasing the service life of the arc and ladle furnace transformers. The techno-economic effect aims to ensure process continuity and increase the metallurgical enterprise’s output (we cannot quantify this effect since it depends on the performance of a particular enterprise). It is recommended to use the technique to forecast the RUL of repairable facilities equipped with online monitoring systems.