‎In this paper, under adaptive hybrid progressive censoring samples, Bayes estimation of the multi-component reliability, with the non-identical-component strengths, in unit generalized Gompertz distribution is considered. This problem is solved in three cases. In the first case, strengths and stress variables are assumed to have unknown, uncommon parameters. In the second case,  it is assumed that strengths and stress variables have two common and one uncommon parameter, so all of these parameters are unknown. In the third case, it is assumed that strengths and stress variables have two known common parameters and one unknown uncommon parameter. In each of these cases, Bayes estimation of the multi-component reliability, with the non-identical-component strengths, is obtained with different methods. Finally, different estimations are compared using the Monte Carlo simulation, and the results are implemented on one real data set.