In parameter estimation techniques, the distribution parameters are usually independent, but theoretically, they are dependent because they are estimated from the same set of samples. The parameter dependence is unlike the statistical dependence between random variables. Thus, based on this dependence, the Runge-Kutta method can be applied to estimate the Burr-XII parameters and reliability and compare them with the Bayesian estimates based on the informative and kernel priors, via Monte Carlo simulations. The simulation results indicated that the Runge-Kutta method is highly favorable, which provides better estimates and outperforms the Bayesian method using different loss functions. Finally, real data analyses are presented to demonstrate the efficiency of the proposed methods based on the generalized progressive hybrid-censoring scheme.