Development of an Adaptive Hybrid ABC (AHABC) algorithm for q-Weibull distribution. AHABC combines local Nelder-Mead simplex method with ABC to enhance local search. AHABC efficiently finds the optimal solution for the q-Weibull ML problem. AHABC outperforms ABC and self-adaptive hybrid ABC in accuracy and convergence speed. Useful model for reliability data with non-monotonic hazard rate.