Creepage discharges are a main cause of insulation damage in power transformers during repeated tests or during operation. In this paper, a hazardous region in the insulation structure of power transformers (the interface between solid and liquid insulation at the top edge of a high-voltage electrode) is considered, and the impact of a very important factor of the surface discharge initiation and propagation (the tangential component of the electric field) on the strength of the insulation structure is investigated in power transformers. Insulation system reliability against this tangential component is presented as a safety factor. Two methods based on cumulative stress characteristics and breakdown probability are proposed for safety factor calculation and for the recognition of weak insulation regions. These methods provide essential information on insulation system design and optimization for reducing insulation deteriorations. A case study is performed on the insulation structure of a power transformer that failed during a test at the Iran Transfo Corporation. The redesigned transformer has shown no test failures in the past 10 years.