The occurrence of asymmetric probability distributions is quite common. Phenomena such as salary, number of failures, sound level values, etc. have skewed distributions. In such cases, estimating the mean using the interval method can be inaccurate as it ignores the distribution’s asymmetry. Another method of constructing confidence intervals, which does not require symmetry of distributions, is the method based on Chebyshev’s theorem. However, the intervals thus obtained are symmetrical. The approach proposed in this article uses the concept of Chebyshev’s theorem and semivariances to construct new confidence and uncertainty intervals. The article examines the properties of semivariance-based confidence intervals for long-term noise indicators from acoustic monitoring of the city of Gdansk and compares them with classical confidence intervals. The new uncertainty assessment tool proposed in this article in the form of a semivariance-based uncertainty interval can therefore be the basis for new uncertainty assessment methodology and more effective uncertainty.

Assessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random results L1; L2; : : : ; Ln of the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

The authors focus their attention on the analysis of the probability density function of the equivalent noise level, in the context of a determination of the uncertainty of the obtained results in regard to the control of environmental acoustic hazards. In so doing, they discuss problems of correctness in the applicability of the classical normal distribution for the estimation of the expected interval value of the equivalent sound level. The authors also provide a set of procedures with respect to its derivation, based upon an assumption of the determined distribution of the measurement results. The obtained results then create the plane for the correct uncertainty calculation of the results of the determined controlled environmental acoustic hazard coefficient.

The paper formulates some objections to the methods of evaluation of uncertainty in noise measurement which are presented in two standards: ISO 9612 (2009) and DIN 45641 (1990). In particular, it focuses on approximation of an equivalent sound level by a function which depends on the arithmetic average of sound levels. Depending on the nature of a random sample the exact value of the equivalent sound level may be significantly different from an approximate one, which might lead to erroneous estimation of the uncertainty of noise indicators. The article presents an analysis of this problem and the adequacy of the solution depending on the type of a random sample.