Survival analysis plays a critical role in understanding time-to-event data, especially in medical research. In this paper, we focus on modeling and analyzing survival times of breast cancer patients using the Nadarajah-Haghighi distribution under a general progressive Type-II censoring scheme. We aim to estimate key survival metrics, including the survival function and hazard rate, along with the model parameters. Using the classical approach, maximum likelihood estimates for the parameters are obtained via the Newton-Raphson method, and confidence intervals are approximated using the Fisher information matrix. In the Bayesian framework, we derive parameter estimates with independent gamma priors under both the squared error loss and LINEX loss functions. As closed-form solutions for Bayes estimates are unavailable, we employ the Metropolis-Hastings algorithm to compute the estimates, along with their highest posterior density credible intervals. To assess the efficiency of these methods, Monte Carlo simulations are performed. Finally, we analyze a real dataset of breast cancer survival times to demonstrate the practical application of these techniques.