In the age of Industry 4.0, the capability of health management is critical to the design and maintenance of gas turbines. This work presents a probabilistic method to estimate the low-cycle fatigue (LCF) life of a gas turbine compressor vane carrier (CVC) under varying operating conditions. Sensitivity analysis based on finite element analysis (FEA) indicates that an operating cycle can be characterized by three predominant contributors to the LCF damage of the CVC among multiple parameters of an operating cycle. Two surrogate models mapping these three features to equivalent stresses are then built for fast computation of the LCF damage. Miner's rule is applied in a probabilistic way to calculate the distribution of accumulated LCF damage over varying operating cycles. Finally, the probabilistic LCF life of the CVC is assessed using real operational data. The proposed approach includes two novel solutions: 1) a new data processing technique inspired by the cumulative sum (CUSUM) control chart to identify the first ramp-up period as well as the shutdown period of each cycle from noisy operational data; 2) the sequential convolution strategy adapted from Miner's rule to compute the probability distribution of accumulated LCF damage (and hence LCF life) from the single-cycle damage distribution, and an approximative quick estimation method to reduce computational expense. Both the offline application for design and online implementation for predictive maintenance show that the expected LCF life at a critical location of the CVC is significantly longer than the deterministically assessed life.