Simplified expressions of uncertainty for single number quantities in ISO 3382-3 (2022)

The ISO 3382-3 (2022) standard defines single number quantities (SNQs) characterizing the spatial decay of speech (D2S, LpAS4m, rC) and of its intelligibility (rD). The standard assesses the accuracy of the measurement using a unique uncertainty value for each SNQ, relying on a round-robin test performed in a single office. To make this assessment more accurate, analytical expressions have been established by applying the law of propagation of uncertainty. These expressions, although precise, are too complex to be included in the standard. This work consists of their simplification, relying on 95 measurements conducted in 36 companies in France and Germany. First, the terms associated with distance measurement uncertainties were found to be negligible. Second, the estimation of the uncertainties of A-weighted speech levels and Speech Transmission Index, based on the measurements made at the workstations constituting the 95 paths, enabled further simplifications. Finally, simplified expressions turn out to be as accurate as the original expressions, and the estimated uncertainties are comparable to those reported by Yadav et al. (2019). If a unique value of uncertainty is to be retained for each SNQ, this study suggests 0.6 dB for D2S and LpAS4m, 7% for rC, and 10% for rD.