Uncertainty calculation for hearing protector noise attenuation measurements by REAT method

Abstract

Introduction1 Metrology is the science of measurement and it encompasses all theoretical and practical aspects related to it. For this reason, the Metrology plays an important role in quality assurance and quality measurements. High quality measurements should be based on a well-developed procedure and supported by a standardised method to assure quality control of products. The errors of measurement can be expressed by the measurement uncertainty value. This value can be used to quantify the confidence limits of the measured results and allows comparison of measurements carried out by different laboratories and for different products (INMETRO et al., 1997). Brinkmann (1988) showed that, in spite of the different methods available for noise attenuation measurements for hearing protectors (see Fig. 1), the values for the sources of errors are still not well understood and the working groups are encountering difficulties in quantifying this measurement uncertainty. This study was developed REAT MeasurementsThe latest standard REAT method for the measurement of the noise attenuation of hearing protectors is ANSI S12.6-1997 (ANSI, 1997) (methods A and B). The measurements are carried out in each 1/1-octave band frequency from 125 to 8000 Hz (seven bands) and the results are given in the form of an average attenuation value and a standard deviation for each frequency band. These parameters are obtained from ten attenuation measurements in case of earmuffs (ten test subjects) or twenty for earplugs (twenty test subjects). The test is repeated twice for each subject and a subject average value for these trials is calculated. Each test is composed of open and closed threshold measurements (see Fig. 2). After the calculation of this mean value for each subject, these results are used to determine the overall average and its standard deviation. As can be observed, the determination of the HPD attenuation is not a direct measurement. Instead, it is calculated from the thresholds measured for all the subjects. As will be demonstrated here, this is responsible for most of the measurement uncertainty. Uncertainty CalculationThe general equation presented below is recommended by the "Guide to expression of uncertainty in measurements" (INMETRO et al., 1997) and shows the relation between the measurement uncertainty and the input parameters of the HPD attenuation. It can be written as:where u(x 1 ), u(x 2 ), …, u(x n ) are the standard uncertainties of the input parameters for the attenuation measurement, u(G) represents the combined uncertainty of measurements and G is the mensurand. It should be clear that Eq.(1) has to be applied to the attenuation and standard deviation equations presented in Fig. 2. AttenuationConsidering "n" test subjects, the overall average attenuation (A f ) can be written as: where CT 1A is the closed threshold value for the first trial A and the first subject; OT 1A is the open threshold value for the first trial A and the first subject; CT 1B is the closed threshold value for the second trial ...