The performance of surface damping treatments may vary once the surface is exposed to a wide range of temperatures, because the performance of viscoelastic damping material is highly dependent on operational temperature. In addition, experimental data for dynamic responses of viscoelastic material are inherently random, which makes it difficult to design a robust damping layout. In this paper a statistical modeling procedure with a statistical calibration method is suggested for the variability characterization of viscoelastic damping material in constrained-layer damping structures. First, the viscoelastic material property is decomposed into two sources: (i) a random complex modulus due to operational temperature variability, and (ii) experimental/model errors in the complex modulus. Next, the variability in the damping material property is obtained using the statistical calibration method by solving an unconstrained optimization problem with a likelihood function metric. Two case studies are considered to show the influence of the material variability on the acoustic performances in the structural-acoustic systems. It is shown that the variability of the damping material is propagated to that of the acoustic performances in the systems. Finally, robust and reliable damping layout designs of the two case studies are obtained through the reliability-based design optimization (RBDO) amidst severe variability in operational temperature and the damping material.