The evaluation of the reliability function in the context of the competing risk model is the main objective of this study. Following this objective, this article analyzes different competing risk datasets: (1) thirty-six small electrical appliances subjected to independent testing based on eighteen different modes, and (2) seventy-seven male mice (aged 35–42 days) exposed to 300 X-ray radiation. Employing adaptive progressively Type-II censored data, various estimation problems are explored where the parent distribution is considered to be the XGamma distribution. In addition to the reliability function, point and interval estimates of the model parameters are assessed from both classical and Bayesian standpoints. The classical maximum likelihood approach is employed to get approximate confidence intervals in addition to the classical point estimates. The Bayesian estimates with the squared error loss function are discussed, and the highest posterior density intervals are acquired. The Markov Chain Monte Carlo method is utilized to obtain the Bayesian estimates and the corresponding interval ranges. Utilizing numerous experimental designs, extensive Monte Carlo simulation trials are conducted to figure out the effectiveness of the stated methodologies. The analysis demonstrated that the XGamma model is suitable for analyzing the specified data. Furthermore, it is noted that the Bayesian estimation method yields more accurate estimates, both point and interval, for reliability and model parameters.