This paper addresses the problem of the estimation of the long-term (yearly) mean of the Community Noise Equivalent Level (CNEL) or day/night average sound level (LDN). Recent environmental noise standards have emphasized the significance of this problem. While it is possible to continually monitor the noise level, it is not necessarily desirable or practical. It is desirable to sample the level over a relatively short period of time and use this information to draw reliable inferences about the long term mean level. Examination of daily average noise levels (either in mean square pressure or in decibel units) shows that while the data may be stationary with respect to mean level over a several month period, they exhibit a strong pattern of autocorrelation in which positive correlation predominates. As a result, the sample sizes required to achieve a desired level of precision in the sample mean estimate are much larger than they would otherwise be if the data were uncorrelated serially in time. To assess the level of autocorrelation in the data, autoregressive-moving average (ARMA) models are developed for the noise data via the Dynamic Data System (DDS) approach to time series analysis. These models are then used to derive estimates of the sample mean variance and therefore to establish sampling strategies. For the data examined, to obtain an estimate of the mean level within a 5-dB range (±50% of the mean in mean square pressure units), sample sizes in the range of 20–50 consecutive daily averages would be required. If the daily averages were uncorrelated in time, only 5–15 consecutive daily averages would be required. The data used in this study were obtain from continuous monitoring at a number of sites in the vicinity of a busy Naval Air Station. Some data obtained from a large commercial airport were also analyzed and found to have even stronger positive autocorrelation, and therefore requiring even larger sample sizes for mean value estimation. © 1979, American Association of Physics Teachers. All rights reserved.
