A reliability-based topology optimization method is proposed to optimally design mufflers under noise frequency and temperature uncertainties. The optimal mufflers designed with deterministic noise frequency and temperature frequently fail to reduce duct noise effectively when the noise frequency or temperature varies. To resolve this problem, a reliability-based acoustical topology optimization problem is formulated for a two-dimensional expansion chamber muffler. The partition volume inside the muffler is selected as the objective function, and its acoustical reliability and transmission loss are used as constraints so as to design a simple but highly reliable muffler. To expedite finding an optimal solution, a gradient-based optimizer is used; further, to calculate the acoustical reliability and its sensitivity, the first-order reliability method and the weighted uniform sampling method are selectively employed. The formulated design problem is solved for various design conditions, and the acoustical reliabilities of optimal mufflers designed according to the proposed method and the deterministic muffler method are compared. Finally, the noise attenuation performance of the optimally designed muffler is experimentally validated. (C) 2021 Elsevier Ltd. All rights reserved.