The high-voltage circuit breaker (HV CB) constitutes an important repairable asset in power systems. Due to its great number in the power network and strategic role in the successful operation of power systems, it is important to ensure its reliability. This paper deals with the estimation of the failure process of CBs considering the impact of age, operation intensity, corrective maintenance, and examination. A general model that integrates the above factors' effects is proposed, which can be reduced to many specific models like virtual age models, scale models, the two combinations, and their regression analysis. The model estimation under the condition of random censoring population data is illustrated, including parameters, reliability indicators, the cumulative intensity function, and goodness-of-fit tests. Moreover, a general procedure to stepwise select valuable effect functions into the general model is presented, thereby obtaining a specific formulation fitting the given data. The above works are applied to a real case to discuss the most probable failure process of the given HV CBs.