In practical survival investigations, researchers frequently encounter failure observations attributable to diverse causes of failure, which substantially influence the statistical estimation of both survival and failure rate functions. The failure data collected in such scenarios are formally known in the literature as competing risk data. This framework complicates statistical inference, as traditional methods must account for latent failure times. This study investigates the independent competing risks model with two distinct failure causes when time-to-event data are modeled using the Xgamma distribution under an improved adaptive progressive Type-II censoring scheme. The focus is on estimating the distribution parameters, as well as the survival and failure rate functions. Both frequentist and Bayesian inferential frameworks are applied to derive point estimates and construct confidence or credible intervals for the parameters and the two survival metrics. The Bayesian estimates are obtained using the squared error loss function and the computational technique of Markov Chain Monte Carlo sampling. The statistical performance of the proposed methods is assessed via simulation experiments. To empirically validate the competing risks model with the Xgamma distribution, two real-world datasets with competing failure modes are analyzed, demonstrating its applicability for survival estimation.