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Year : 2020  |  Volume : 22  |  Issue : 105  |  Page : 35--45

The insertion loss distribution function of an ear plug, and its implications for the ear plug acceptability

Paolo Lenzuni, Diego Annesi, Pietro Nataletti 
 Italian National Workers’ Compensation Authority (INAIL), Italy

Correspondence Address:
Paolo Lenzuni
INAIL – Tuscany Regional Research Center, Via delle Porte Nuove 61, 50144 Firenze


Introduction: In order to establish the acceptability of a hearing protector device (HPD) used in a given noisy environment, two key elements must be known with the highest possible accuracy: the insertion loss of the HPD and the associated variability. Methods leading to objective field measurements of insertion loss have become widely available in the last decade and have started to replace the traditional subjective “Real-Ear Attenuation at Threshold” (REAT) laboratory measurements. The latter have long been known to provide a gross overestimate of the attenuation, thus leading to a strong underestimate of the worker’s exposure to noise. Methods: In this work we present objective measurements of the insertion loss of an ear plug, carried out using the E-A-Rfit procedure by 3M on a large sample of 36 female and 64 male subjects. This large number of independent measurements has been exploited to calculate the distribution function of effective noise levels, that is noise levels that take into account the use of the HPD. The knowledge of the distribution function has in its turn allowed the calculation of the uncertainty on the effective noise levels. Results: This new estimate of uncertainty (6 to 7 dB) is significantly larger than most previous estimates, which range between 4 and 5 dB when using objective data but with an improper uncertainty propagation, and around 3 dB when using REAT subjective data. We show that the revised new estimate of uncertainty is much more realistic as it includes contributions that are missed by the other methods. Conclusions: By plugging this revised estimate of uncertainty into the criterion for checking the acceptability of the HPD, a better assessment of the actual protection provided by the HPD itself is possible.

How to cite this article:
Lenzuni P, Annesi D, Nataletti P. The insertion loss distribution function of an ear plug, and its implications for the ear plug acceptability.Noise Health 2020;22:35-45

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Lenzuni P, Annesi D, Nataletti P. The insertion loss distribution function of an ear plug, and its implications for the ear plug acceptability. Noise Health [serial online] 2020 [cited 2022 Oct 2 ];22:35-45
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The attenuation to noise that ear plugs are able to provide is known to show a very large variability from subject to subject,[1] which dwarfs all other contributions to the uncertainty on attenuation.[2] A significant fraction of such variability is due to the training that the subject has received and his/her motivation to use the ear plug at or near its ideal performance. While some progress towards a lower variability can be achieved by adequately training and motivating employees,[3],[4] inevitable differences in individual approaches to self-protection will keep the distribution fairly wide no matter what.

An additional contribution to the observed variability can be attributed to biological (anthropometric) diversity. Custom-shaped ear plugs perform much better from this point of view, as they are built to fit the shape of the individual’s ear canal. However, very few companies provide customized ear plugs to their employees, whereas the vast majority of them rely on generic low-cost single-use ear plugs.

Not much is known on the shape of the distribution function of the insertion loss (IL) provided by an ear plug to a population of exposed workers. Common practice is based on the assumption that this distribution is approximately normal.

A widely used statistic that quantifies the insertion loss provided to a majority of subjects is the Assumed Protection Value (APV),[5] where APV = Mean − 1 sigma. Because in a normal distribution this corresponds to the 16th percentile of the distribution, about 16% of exposed workers are expected to receive a protection lower than the APV. It has become standard practice that the APV’s at individual octave band centre frequencies are used to quantify the “minimum” attenuation provided by an HPD in any noise exposure calculation.

This approach is unnecessarily crude for at least three different reasons:it is based on the assumption of insertion losses being normally distributed, which is unjustified and most likely wrong[6];it accepts that a sizeable fraction of the exposed population (16%) is under-protected;it makes use of data which are computed by means of the “trained subject-fit” procedure, originally codified in ISO 4869-1,[7] and now also known as ANSI/ASA S12-6[8] method A, which is widely known to result in gross overestimates of the insertion loss.[9],[10]

Individual and objective assessment of insertion loss provided by an ear plug has now been possible for about a decade using different approaches.[11],[12],[13],[14] The use of such methods in actual workplaces is however still limited and will hardly become widespread in the next years. Statistical methods are therefore still needed to derive a reliable estimate of the attenuation provided by a HPD to a worker.

In this work we adopt one objective method (E-A-Rfit) to measure individual insertion losses of a specific model of ear plug. The distribution functions of attenuation values at octave band frequencies are then used to derive information of the shape and the variance of the distribution of actual (effective) sound pressure levels that take into account the presence of the HPD. Finally, the uncertainty on this effective level is determined and a statistical test is performed to determine the acceptability of the HPD in a given acoustical context. This allows a more reliable and more realistic test of performance to be carried out.


Object of tests

The investigated ear plug is model 1100 of 3M. This is a typical general purpose ear plug with a conic shape near the bottom and a rounded shape near the head for better insertion.

Its low cost and good nominal performance see [Table 1] have made it a very popular choice by employers.{Table 1}


Tests were carried out on 64 male and 36 female university students and staff. Their age range was 20 to 30 years, with mean 25.3 years and standard deviation 2.7 years. None of them reported any previous occupational exposure to noise as well as any previous experience in the use of ear plugs. They were all in good health and no ear-related pathologies, either previous or current, were reported.

Given the extremely short signal duration (see the section on Experimental Design), exposure to noise in this work is well below any possible threshold for TTS. All tested subjects received adequate information about the exposure to noise implied by the test, and they all expressed a verbal informed consent.

The E-A-RFit method

The principles of the E-A-Rfit method are extensively described in the literature.[11],[12] In synthesis, the E-A-RFit system hardware consists of two microphones: an “external” microphone which measures sound pressure immediately outside the ear canal, and an “internal” microphone. This latter microphone is physically also located outside the ear canal, in order to minimize the invasiveness of the device. However, it is acoustically coupled to the region near the eardrum by means of a miniature probe which is inserted through the Hearing Protector Device (HPD) to be tested.

The straightforward difference between the two sound pressure levels measured by the external and the internal microphone corresponds to the transmission loss (TR) of the HPD as fitted. This is later converted into the difference between the sound pressure levels that would be measured at the eardrum with and without the HPD as fitted, called Insertion Loss (IL). This is achieved by introducing two correction factors that adequately take into account: 1) the length of the probe tube between the microphone and the eardrum; 2) bone-conduction pathways that are missed by the E-A-RFit method. A final compensation factor is introduced to calculate the actual sound pressure at the eardrum starting from the value measured by the “internal” microphone.

Experimental design

All subjects have initially been trained to the use of the ear plug just before being tested, by means of a 5-minute video clip showing the correct insertion procedure. Each subject has been invited to seat at a distance of 0.5 m from a loudspeaker, in such a way that the loudspeaker-to-subject vector was aligned with the subject’s line of sight [Figure 1]. Each test has been carried out using a 15-second pink noise signal appropriate for measuring attenuations at octave bands between 125 to 8000 Hz.{Figure 1}

For each tested subject, the sound pressure levels of the external and internal microphones have been recorded for each of the two ears. Two independent estimates of the insertion loss (IL) have accordingly been performed, one for each ear. All measurements have been carried out in May 2019.

Statistical analysis

Insertion loss data for the left and the right ear have been mutually compared using a t-test in order to detect any hypothetical statistically significant differences. As no difference emerged at the P = 0.05 level for any tested frequency, the value used in subsequent analysis has been taken as the average of the left and right IL.

Statistical calculations have mostly been carried out using Excel® spreadsheets with custom-built macros. A minor part has been performed using the data analysis software Kyplot.


Statistical distributions of insertion losses

[Figure 2] shows the distribution functions of the measured insertion losses at all octave bands between 125 and 8000 Hz. All distributions are very wide, with 5th and 95th quantiles often separated by more than 20 dB.{Figure 2}

As a general trend, the mode of the distribution increases as frequency increases. Distributions tend to be roughly symmetric at low frequency, and become more and more asymmetric as frequency increases. At 2000 Hz and above, all distributions show a very steep shoulder on the high side and a very pronounced tail on the low side.

Gender difference

No separate analysis of the distribution functions of insertion losses in the male-only (M) and female-only (F) sub-samples has been carried out, due to the limited size of both sub-samples. The mean values of the insertion losses in the M and F sub-samples[15] show that:the insertion loss in both sub-samples is almost identical (± 2 dB) at all frequencies f ≥ 500 Hz;there is some evidence that the insertion loss might be higher in the F sub-sample at 125 Hz and 250 Hz. However the difference of the two means found in our study (3–3.5 dB) is not statistically significant at the 95% level, due to the limited size of the two sub-samples.

Additional research focused in particular on female subjects has been scheduled, which could lead to more robust conclusions on this topic.

Compliance with normative limits

EC Directive 2003/10/CE[16] states in its article 6.1.c that “individual hearing protectors shall be so selected as to eliminate the risk to hearing or to reduce the risk to a minimum”.

The qualitative concept of reducing the risk to a minimum has later been quantified by EN 458[17] that shows in its Table A.4 (here replicated as [Table 2]) the range of acceptable noise equivalent levels.{Table 2}

In synthesis, the quantity L’p,A,eq must lie between the national reference (L’NR) and (L’NR − 15 dB). The lower limit is aimed at preventing overprotection and is of no relevance in this context. So the only significant compliance test is that L’p,A,eq is no larger than L’NR. The quantity


is improperly defined[17] as “the level effective to the ear”. Indeed, as shown by equation (1), it corresponds to the environmental sound pressure A-weighted level which would give the same tympanic pressure as the one that exists when the HPD is worn. In this paper the quantity L’p,A,eq shall be indicated as “effective equivalent A-weighted sound pressure level” or just “effective equivalent sound pressure level”. In equation (1) the sum is carried out over the N = 7 octave bands from 125 to 8000 Hz. Simple statistical methods[18] indicate that the compliance test has the form:


Here U(L’p,A,eq) is the extended uncertainty associated to L’p,A,eq, so that the quantity L’p,A,eq + U(L’p,A,eq) on the left hand side of equation (2) is the upper extreme of the one-sided confidence interval on L’p,A,eq. If the inequality (2) is fulfilled, there is a known probability (usually set at 95%) that L’p,A,eq is indeed lower than L’NR.

There are two methods to calculate U(L’p,A,eq): an analytical method (to be discussed in the next section Uncertainty - analytical method), and an empirical method (to be discussed in the ensuing section Uncertainty - empirical method).

Uncertainty-analytical method

Full method and simplified method

In the analytical method, the extended uncertainty U(L’p,A,eq) is calculated as a multiple of the uncertainty u(L’p,A,eq). The latter is in its turn calculated by appropriately combining all the uncertainties on the variables requested for the calculation of L’p,A,eq, that is the individual A-weighted octave band levels (Lp,Aeq,n), and the octave band insertion losses (ILn). Equation (16) of ISO/IEC Guide 98-3[19]:


provides the formal template for the calculation of the uncertainty on a dependent variable y.

In equation (3):cj are the sensitivity coefficients;xj are the variables;u(xj) are the uncertainties on xj;r(xj, xk) are the correlation coefficients between variables.

As shown in equation (1), L’p,A,eq depends on N environmental octave band levels Lp,Aeq,n and N octave band insertion losses ILn. Environmental levels and insertion losses can be assumed to be mutually independent. For the specific case under investigation, equation (3) can then be written as the sum of two contributions: the first one includes the variances of Lp,Aeq,n and the variances of ILn:


while the second one takes into account the mutual correlation among Lp,Aeq,n at different octave bands as well as the mutual correlation among ILn at different octave bands:


Correlation terms, whose calculation is somewhat cumbersome, are usually ignored in current practice, which is equivalent to assume that both individual A-weighted octave band levels (Lp,Aeq,n) and individual insertion losses (ILn) are independent of one another. In this paper, two values of u(L’p,A,eq) have been computed: one using only equation (4a), which will be referred to as “analytical simplified”; another one using both equations (4a) and (4b), which will be referred to as “analytical full”.

Finally, the extended uncertainty U(L’p,A,eq) has been calculated as a multiple of U(L’p,A,eq):


where the factor 1.645 assumes a mono-lateral interval with 95% confidence level.

Uncertainty on octave band levels of the environmental noise

As extensively discussed in the previous section, the calculation of u(L’p,A,eq) requires the knowledge of the uncertainties on octave band levels in the work environment u(Lp,Aeq,n) and of octave band insertion losses u(ILn). Values of u(Lp,Aeq,n) result from three contributions: random fluctuations of the noise itself; uncertainty due to instrumentation; uncertainty due to the microphone position.Random fluctuations: When measurements are taken in compliance with the task-based strategy of ISO 9612,[20] differences among A-weighted values due to random fluctuations of noise, must not exceed 3 dB. In principle, uncertainties in individual octave band levels could be substantially larger, if significant anti-correlation exists between values in different bands. However tests carried out in the Acoustic Laboratory of the INAIL Research center (Monteporzio Catone, Rome, Italy) show that for a variety of industrial sources, uncertainties in the most relevant octave bands (those with a significant fraction of the total energy) do not exceed 2 dB. Slightly larger than average values can occur in low-frequency noise, because A-weighting gives lower weight to low frequencies. As a general rule, larger than average values occur in broadband noise, that is when significant energy appears over many octave bands.Instrumentation: The uncertainty in individual octave bands due to instrumentation has been found to be below 0.5 dB in all octave bands of interest in this study.[21]Microphone position: A rough estimate of this contribution has been set at 1 dB for A-weighted values regardless of the acoustic field.[20] Uncertainties in individual octave bands due to the measurement position have been quantified by carrying out tests with different microphone positions in different acoustic fields. Such tests indicate that uncertainties in the most relevant octave bands do not exceed 1.5 dB. As indicated above for random fluctuations, larger than average values occur in broadband noise.

The overall uncertainties on individual octave band levels of workplace environmental noises are of order 2.5 dB or less, with significant contributions from both random noise fluctuations and microphone position.

Uncertainty on octave band insertion losses

Uncertainties on octave band insertion losses u(ILn) have been quantified using the standard deviations of the distributions found in this work.

Uncertainty on the effective equivalent sound pressure level

Because the two sensitivity coefficients [INSIDE:1] and [INSIDE:2] are identical, equation (4a) shows that contributions to u(L’p,A,eq) are proportional to the two uncertainties, on octave band insertion losses u(ILn), and on octave band environmental noise. Given the numerical values presented in [Figure 2] and the estimates provided in 3.4.3, the uncertainty on the effective noise equivalent level is dominated by uncertainties on octave band insertion losses u(ILn).

Simplified method using “trained subject-fit” data

An additional estimate of both L’p,A,eq and U(L’p,A,eq) has been found using again the simplified analytical method, this time setting ILn and u(ILn) equal to the mean values and standard deviations provided by the ear plug manufacturer. These values result from a procedure known as “trained subject-fit”.[7] It is well known that both mean values and standard deviations determined with this procedure are unrealistic. Mean values are gross overestimates, and probably trace the ideal performance much more than the average workplace performance. On the opposite, standard deviations are clear underestimates, since the extremely rigid experimental procedure removes much of the variability expected in the sample.

Uncertainty-empirical method

In the empirical method, no assumption is made about the mutual dependency of individual octave band levels and insertion losses. An input environmental noise Lp,eq with a given octave band spectrum is assumed. By combining Lp,eq with each of the 100 experimentally determined insertion loss octave band spectra, and applying A-weighting, 100 octave band spectra of L’p,Aeq,n:


are calculated, with n = 1 to 7 corresponding to octave band center frequencies from 125 to 8000 Hz. [Figure 3] shows the probability distributions of the effective equivalent sound pressure level L’p,Aeq,n, at one representative low (250 Hz, n = 2) and high (2000 Hz, n = 5) frequency, assuming a triangle-shaped environmental noise spectrum Lp,eq.{Figure 3}

In the empirical method, U(L’p,A,eq) has not been calculated as a multiple of u(L’p,A,eq), but directly as the difference between the mean and the upper 95th quantile of the distribution of L’p,A,eq, as shown in [Figure 4].{Figure 4}


[Table 3] compares the mean values of the effective equivalent sound pressure level L’p,A,eq and the associated extended uncertainties U(L’p,A,eq) calculated using the four different procedures previously outlined: the empirical (E) method, columns 2 and 3; the analytical full (AF) method applied to the experimental values found in this work, columns 4 and 5; the analytical simplified (AS) method applied to the experimental values found in this work, columns 6 and 7; the analytical simplified method applied to the manufacturer-declared values (ASI) found according to the “trained subject-fit”[7] procedure, columns 8 and 9.{Table 3}

This comparison is carried out for four different input environmental noises, characterized by different frequency spectra shown in [Figure 5].{Figure 5}

Such spectra have been selected to represent extreme cases, so that any workplace noise would give results within the range explored in this work. All workplace noises have the same A-weighted global level Lp,A,eq = 105 dB(A). The information shown in [Table 3] on the extended uncertainty has also been displayed in [Figure 6] for improved clarity of presentation.{Figure 6}

The following are the most remarkable points:The mean values are highest in the empirical method than in the analytical method. This is due to the non-linearity of the algorithm that calculates L’p,A,eq. In the analytical method, L’p,A,eq is found as the energetic sum over the seven relevant octave bands of the mean sound levels calculated by subtracting the MEAN insertion loss. In the empirical method, the sum over octave bands is carried out for each tested subject, and the mean over the 100 tested subjects is performed in the last stage of the calculation. Because some of the subjects display a very small attenuation, some of the effective levels L’p,A,eq are particularly high, which forces a higher final value of the mean L’p,A,eq.The mean values are lowest in the analytical simplified method using “trained subject-fit” data. This is simply due to the grossly overestimated values of insertion losses produced following the “trained subject-fit” procedure.Extended uncertainties U(L’p,A,eq) calculated using the analytical simplified method based on “trained subject-fit” data are much smaller than those based on this work’s data, because uncertainties on individual octave band insertion losses are much smaller themselves.Extended uncertainties are much smaller in the analytical simplified method than in the empirical method, when applied to the same dataset. This reflects, as previously noticed, the missing terms of covariance in the simplified analytical approach, which cannot be ignored given the substantial mutual correlation of individual insertion losses in different octave bands. This conclusion might have been anticipated from the shapes of the distributions shown in [Figure 3]. In the case of uncorrelated variables, the combination of many independent distributions would result in a normal (hence symmetrical) distribution, as dictated by the central limit theorem. On the opposite, the asymmetric shapes of the distributions shown in [Figure 3] point to significant correlation between the variables.Extended uncertainties calculated using the analytical full method are roughly comparable to those calculated using the empirical method. This was of course expected given that both methods take into account the actual mutual correlations between octave band insertion losses. The small differences are mostly attributable to the approximate empirical determination of the 95th quantile in a sample of 100 and the deviation of the distribution from a true normal distribution which is implicitly assumed by the use of the coverage factor 1.645 in equation (5).

Assuming a national reference level L’NR = 80 dB(A) (as indicated by the Italian national technical standard on occupational exposure to noise[22]), the compliance test for acceptability (equation 2) is passed if the methods “analytic simplified” and “analytic simplified ISO” are used. The test is failed if the methods “analytic full” and “empiric” are used [Figure 7].{Figure 7}

A calculation of the uncertainty using the analytical full method that includes correlation terms is probably too complex for the average user. A possible shortcut is to use the “Approximate Full” (AppF) value


found by multiplying the estimate uM(L’p,A,eq) obtained using a generic (simplified) method M, by a method-dependent correction factor KM. Based on values displayed in [Table 3], we estimate that actual uncertainties are 1.5 to 2 times larger than zero-correlation uncertainties (method AS), and 2 to 3 times larger than trained subject-fit uncertainties (method ASI). Recommended correction factors are:KAS-Method B = 1.75, to be adopted when “inexperienced subject-fit” data (ANSI/ASA S12-6[8] Method B) are used;KAS-Method A = 2.5, to be adopted when “trained subject-fit” data (ISO 4869-1[7] or ANSI/ASA S12-6[8] Method A) are used.


The traditional statistical method that quantifies the insertion loss of an ear plug using the laboratory “trained subject-fit” procedure[8] (Method A), has long been known to result in strong overestimates of the mean octave band values, as well as strong underestimates of the associated standard deviations. Individual methods are clearly much more reliable, but their popularity is still limited, so statistical approach will remain in use for quite some time.

Estimates based on objective estimates as well as on the laboratory “inexperienced subject-fit” procedure[8] (Method B) mark a significant improvement in both respects. However, predictions of the effective equivalent A-weighted sound pressure levels, often used to verify that the vast majority of workers are adequately protected, still fail to approach real workplace values unless the existing correlation between octave band insertion losses are taken into account. This study shows in fact that estimates of the effective sound pressure values derived from actual empirical distributions of insertion losses closely trace values calculated including correlation terms.

Because the full calculation is somewhat complex, we recommend that an approximate estimate of the uncertainty/expanded uncertainty is derived by multiplying uncertainties found using simplified methods by a factor KM that ranges between 1.75 and 2.5. By plugging this new estimate of uncertainty into the criterion for checking the acceptability of the hearing protector, a better assessment of the actual protection provided by the HPD is possible.


The authors gratefully acknowledge 3M Italia for providing the experimental equipment used in this project.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


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