This study takes into account the estimation concerns of the model parameter, reliability, and hazard rate functions of the Muth distribution when a sample is produced using generalized progressive hybrid censoring. The generalized progressive hybrid censoring scheme is suggested to get around the progressive hybrid censoring scheme's potential drawback of having extremely few failures. The maximum likelihood estimates of the model parameter and some life indices are obtained. The approximate confidence intervals for various parameters are calculated using the asymptotic distribution of the maximum likelihood estimates across the observed Fisher information matrix. Furthermore, the beta prior and squared error loss function are used to offer Bayes point estimates and the highest posterior density credible intervals of the unknown parameters, and the Markov Chain Monte Carlo technique is used to acquire the necessary estimates. We provide thorough simulation results to demonstrate the utility of the suggested methodologies. Finally, one genuine data set is analyzed as an example.