The risk of cascading blackouts greatly relies on failure probabilities of individual components in power grids. To quantify how component failure probabilities (CFP) influences blackout risk (BR), this paper proposes a sample-induced semi-analytic approach to characterize the relationship between CFP and BR. To this end, we first give a generic component failure probability function (CoFPF) to describe CFP with varying parameters or forms. Then the exact relationship between BR and CoFPFs is built on the abstract Markov-sequence model of cascading outages. Leveraging a set of samples generated by blackout simulations, we further establish a sample-induced semi-analytic mapping between the unbiased estimation of BR and CoFPFs. Finally, we derive an efficient algorithm that can directly calculate the unbiased estimation of BR when the CoFPFs change. Since no additional simulations are required, the algorithm is computationally scalable and efficient. Numerical experiments well confirm the theory and the algorithm.
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