Recent auditorium acoustics practice has included coupled-volume systems in several performing arts venues. This has stimulated research activities on acoustics in the coupled-volume systems. Based on experimentally measured room impulse responses acquired from existing auditoria, and several historically significant worship spaces, this paper addresses the challenges of analysing single-slope and multiple-slope sound energy decays often encountered in the experimentally measured room impulse responses in these venues. The analysis engages a parametric model of Schroeder decay functions, that decomposes the Schroeder decay data into single or multiple exponential decays along with a noise term. The model has been well validated using many experimental data. Several advanced analysis methods based on the decay model, such as nonlinear regressions, Bayesian probabilistic inference, and artificial neural networks have emerged to cope with analysis challenges raised in auditorium acoustics practice. This paper discusses conditions of implementing Schroeder integration for a higher efficiency of the numerical analysis and clarifies some unreasonable expectations/interpretations of Schroeder decay data. © 2023 Institute of Acoustics. All rights reserved.