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Year : 2012  |  Volume : 14  |  Issue : 59  |  Page : 210--214

A proposal for a more refined single number rating system for hearing protector attenuation specification

Warwick Williams 
 Senior Research Engineer, National Acoustic Laboratories, Chatswood, NSW 2067, Australia

Correspondence Address:
Warwick Williams
National Acoustic Laboratories, 126 Greville Street, Chatswood, NSW 2070


From a study of recent hearing protector attenuation test data, this work presents a proposal to reconsider how data, gathered by recognized standard subjective test procedures, is used to calculate the single number performance rating of hearing protectors. Current practice is to embed the expected performance (mean) and the variation in performance (standard deviation) in a single rating figure. A proposal is made for clearly separating expected performance from the variation while retaining the use of the current subjective test procedures. This proposal is applicable to all current single number rating systems including SNR, NRR, SLC 80, and the newer ANSI NRS Ax.

How to cite this article:
Williams W. A proposal for a more refined single number rating system for hearing protector attenuation specification.Noise Health 2012;14:210-214

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Williams W. A proposal for a more refined single number rating system for hearing protector attenuation specification. Noise Health [serial online] 2012 [cited 2023 Dec 5 ];14:210-214
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Hearing protectors are currently widely used in noisy situations in order to reduce an exposure to excessive noise. The specification of the attenuation performance and the selection method of appropriate hearing protectors in general falls under 3 broad methodologies; single number; multiple number; and octave band. [1]

The single number systems tend to be the simplest to use. They supply a single number that is a representative indication of the attenuation of sound immission for the individual using the particular hearing protectors. They are commonly implemented by estimating the amount, by which the offending noise needs to be attenuated for a 'safe' exposure and by relating this difference to the single number rating. A single number tends to be the easiest system to use, in practice; however, the main fault single numbers suffer arises from attempting to encapsulate a lot of information in a single figure such as attenuation data for multiple octave bands.

A multiple number system tries to surmount the difficulties of different attenuation(s) over multiple octave bands by specifying expected attenuations for 'high,' 'medium,' and 'low' frequency ranges. In a general sense, they are an advance on a single number rating in that they act so as to reduce the inexactness of a single number encompassing multiple frequencies but have the disadvantage of increased complexity of application. They are usually implemented by either a graphical or numerical method.

The octave band methods increase the complexity of specifying appropriate hearing protectors but have the significant advantage of directly addressing the necessary attenuation at each octave band. Thus, the attenuation characteristic required from a hearing protector can be precisely specified. The difficulty then comes from trying to find a commercially available hearing protector that fits that attenuation characteristic.

It should be noted that introducing more complex hearing protector specification does not necessarily produce better hearing protector outcomes in the field. A controlled study [2] found that while more complex hearing protector specification procedures had the potential to produce better exposure reduction for the wearer, the increased complexity of the necessary calculations tended to be offset by an increased number of calculation and application errors. This trade-off of increased complexity of specification versus increased error in end user application was the prime impetus for the introduction of the Classification System for hearing protector use in Australia and New Zealand. [3]

 Current Test and Specification Methodology

Hearing protector attenuation performance is assessed in the laboratory by using volunteer human test subjects with good hearing. These test subjects are exposed to low levels of noise when wearing (occluded) and when not wearing (unoccluded) the hearing protectors under test. The noise is presented over different frequency ranges so that, by using the combined subjective responses, the mean attenuation (M) at the different octave bands can be determined. The standard deviation (SD) of the mean attenuation at each octave band is also determined.

To calculate the single number rating of a hearing protector, the current practice is to use the mean attenuation (M j) at each octave band (j) and subtract from that a specified proportion (α, typically 0 ≤ a ≤ 2) of the standard deviation (αSD j) to estimate the proportion of population who could expect to receive that attenuation (A′j) or greater. For example, if the mean attenuation for the octave band centered on 2k Hz was 25 dB and the standard deviation was 5 dB, then according to statistical theory, 84% of the user population could expect to receive an attenuation of 20 dB or greater (i.e. M 2k - SD 2k , where a = 1).

These resultant values of mean attenuation and standard deviation, A i (M i, σi) are then combined in a predetermined relationship or function, A(M i - αSD i). This function is defined by the particular standard that the test laboratory is working to. This process is illustrated in [Table 1].{Table 1}

The most common single number rating systems are the SNR, SLC 80 , the 'old' NRR, or the more recent NRS AX . The rating criterion used will primarily depend on the jurisdiction the workplace where the hearing protectors are to be used.

The single number rating (SNR) is primarily used in Europe and is defined by ISO 4869 - 2 (1994). SNR is calculated using the mean calculated octave band attenuation and a = 0.84 of the standard deviation (M j - 0.84 SD j). This attenuation provides the expected minimum attenuation for 80% of the users at the j th octave band. Using the equation provided by ISO 4869 - 2, the SNR of the device can then be calculated.

The NRR and newer NRS AX are rating systems used in the USA. [4],[5] The calculation of NRR uses a factor of twice the standard deviation (a = 2) [6] while the NRS AX , like the SNR, uses 0.84 SD. [5] The Australian and New Zealand SLC 80 [7] tends to be more conservative and uses one standard deviation. Information on all of these parameters may commonly be found on packaging and performance data for the enclosed hearing protectors.

In New Zealand and Australia, it is common now-a-days to utilize the Class of a hearing protector to specify where its use is appropriate. [7] This classification of hearing protectors, designed to be a simple field based system, is based on the SLC 80 rating. [3]

At this stage, it should be noted that the standard deviation is a measure of the 'dispersion' of the data used to calculate the mean of the parameter under consideration. Thus, a difficulty arises when using any of these single number performance ratings in that the measure of dispersion or spread of the attenuation achieved by the hearing protector users is included and effectively hidden in the single number performance rating. Logically, it could be argued that it would be better if users could know the mean performance of the device and, separately, the amount of variation that could be expected in this performance. This is a similar requirement when purchasing any device. Reasonable purchasers expect some degree of variation to exist between different devices but also expect that variation not to be so great such that wide differences in performance can be expected.

Research at the National Acoustic Laboratories (NAL) examining the performance of 115 different models of hearing protectors, tested in accordance with the requirements of AS/NZS 1270: 2002, found that there was a statistically significant tendency for the standard deviation of hearing protectors to increase with decreasing attenuation - an inverse relationship. [8],[9],[10] For example, a hearing protector with a mean attenuation of around 30 dB could be expected to have a standard deviation of about 2 dB, while one with a mean attenuation of 20 dB would have a standard deviation in the order of 10 dB.

The overall result of including the standard deviation in the single number rating calculation is not only to obscure the likely variation in performance but also to provide a false indication of the actual attenuation likely to be achieved by users. This situation not only provides potentially false information but also penalizes those manufacturers who exercise better quality control over their products.

 Proposed New Methodology

A variation in the method for calculating the single number rating proposes separating the performance parameter from the variation in performance. This is in practice a simple procedure and maintains the same general process and formula use as is current. It is a relatively minor modification.

Rather than calculate the overall performance of a hearing protector using the formula as a function of the mean octave-band attenuations and their associated proportion of standard deviation, A(M j - αSD j), as discussed previously, the method would be to calculate the attenuation performance of the device for each individual subject iA 1 (a j1), where a j1 is the attenuation the individual test subject number 1 receives at octave-band j. To estimate the performance of the device, the mean attenuation is calculated for all test subjects, miA, along with its corresponding standard deviation iSD. If desired, a new parameter that includes a different percentage of individuals receiving a declared minimum attenuation would be denoted miA* (= miA - aiSD). This process is outlined in [Table 2].{Table 2}

The calculation of each individual's attenuation can use the same equation as used for SNR, NRR, SLC 80 , or NRSAx with the mean minus standard deviations, simply replaced by the individual's attenuations at each octave band.


Comparisons have been carried out using this proposed method for both the SLC80 [8] and NRR [10] parameters and are presented elsewhere. The results for 115 hearing protectors tested at the National Acoustic Laboratories are presented below in [Figure 1] [8] For SLC 80 , the results show that there is very close correlation between the original, SLC 80 , and modified miSLC 80 parameters.{Figure 1}

While this close correlation may raise the question 'why introduce to a new parameter?' it must be remembered that the old parameter (here SLC 80) includes information on the means and standard deviations of 7 octave bands, while the new parameter (miSLC 80) is calculated only from the overall attenuation mean and standard deviation. Hence, there is potentially greater variability involved with the SLC 80 as compared to the miSCL 80 . This becomes particularly important if an experimenter-fit procedure is used during testing compared to the user-fit as the user-fit procedure introduces greater variability. [11]

On average, the standard deviation of the resulting single parameter (iSD = 3.6 dB) is 1.1 dB less than the average of the standard deviations of the octave-band attenuations (SD = 4.7 dB). One reason for this is that a tacit assumption is made that the respective octave band attenuations for a tested hearing protector are assumed to be independent. This may not be the case, particularly for adjacent octave-bands, which may be reasonably expected to be correlated. This difference between the average of the standard deviations of the octave band attenuations and the average the standard deviation of the resulting single parameter of 1.1 dB is reflected in the negative dc off-set of the line-of-best-fit of the curve in [Figure 1]of -1.18 dB. Thus, by including multiple octave-band attenuations in the calculation of the single number rating for a device, the level of uncertainty is further increased.

[Figure 2] below shows tendency of the standard deviation to increase with respect to decreasing attenuation, again for the 115 devices as presented in [Figure 1].{Figure 2}

Except for the outlier at (2.1, 7.1), which was a very poorly performing device with particular design flaws, the illustrated data also demonstrated the difficulty of finding devices with attenuation less than around 18 dB. It should be noted that in respect to [Figure 2] and the parameter miSLC, there is no 'variation figure' included in the calculation and the range of values lies between 18.0 and 40.0 dB, while the range of miSLC 80 in [Figure 1] where the variability component is included is between 9.1 dB and 36.1 dB.

If for the time being we ignore the outlying point with the miSLC of 2.1 dB, then the next lowest point has an miSLC of 18.0 dB and a standard deviation of 9.5 dB. This means that while the mean attenuation for users is 18.0 dB, around 16% of users achieve an attenuation less than 8.5 dB (mean - SD) while around 16% experience 27.5 dB or greater (mean + SD). This is a huge variation, 19 dB, which is normally hidden in the single number rating. To separate this variability from the actual hearing protector, performance would be a distinct advantage to the end user. This could be expressed, for example, as {mean, SD} dB or in this case as the ordered pair {18, 9.5} dB.

The original concept of including the standard deviation flowed through the evolution of single number rating systems. Botsford (1973) [12] proposed the use of the Sound Level Conversion (SLC) system, which was the difference between the measured C-weighted free field (C) and the equivalent A-weighted, equivalent free field sound level (A′), experienced by the wearer under the hearing protector. Thus, the SLC represented the attenuation or protection provided by the device or "A′ = C - SLC" (p 33). The driver for use of the SLC was based in consideration of the protected ears perception of the sound in relation to the difference between the C-weighted and A-weighted (C - A) sound spectrum or the C - A difference of the offending sound. This was also supported from work by Waugh (1973). [13]

Johnson and Nixon (1974) [14] recommended "that the Botsford [SLC] method with a 6 dB safety factor be promoted as the best simplified method for evaluating hearing protector performance in noise" (p 27). However, their method of calculating the SLC also included using the mean octave band attenuation minus two standard deviations (M - 2SD) as the attenuation(s) to be used "to insure under-protection of only 1% of the cases" (p27) before the addition of the 6 dB 'safety factor.' The isolation factor resulting from over-protection appears to have been disregarded in favor of ensuring protection (and over-protection) for the majority. The NRR still uses the (M - 2SD) but with only a 3 dB safety factor. [6] Thus, the NRR attempts to err significantly on the side of caution or over-protection.

The use of the mean minus one standard deviation appears to have been initially recommended in around 1972 [15] with later support from Waugh (1976). [16] The aim of using (M - SD) was to ensure adequate protection of at least 80% of wearers while simultaneously reducing the risk of over-protection. In Australia, this resulted in the SLC80 [17] while later, it was adopted into the SNR. [18] An extensive comparison of single number ratings was discussed by Waugh (1984) [19] with consideration of the use of (M - SD), (M - 2SD), and 'safety factors.' Waugh's conclusion, after detailed consideration of the variability of attenuation experienced by users and possible variations in the acoustic spectra to which users may be exposed, including the (C - A) difference, was that "the M - SD distribution strikes a balance between under- and over-protection" (p 303) and that the "M - 2SD correction causes considerable increase in over-protection" (p 303).

The work discussed above was conducted at a time when there were not as many models of hearing protectors on the market as is currently the case. As can be seen from the data presented in [Figure 2], from a selection of 115 hearing protectors then available in Australia, there is a wide range of attenuation and, sometimes, a disturbingly wide range of variation in performance. In the current world market, there are many more hearing protectors available as new manufacturer enter the market, and existing manufacturers regularly change models through new designs and improvement to older models.

By including the variability of SD in performance in the single number rating for a device, there is a definite penalty imposed on those manufacturers and suppliers of devices who exercise good quality control. Should these manufacturers and suppliers be so penalized? Should the consumer be able to make a clear judgment as to which device better fits their purpose by a more open presentation of the performance data, mean, and standard deviation of the product they select?

The method suggested is applicable by simple substitution to any of the current single number hearing protector rating systems utilizing data collected using the available, standard, subject test protocols. Rather than a complex calculation that includes the subject group's mean and standard deviation, a simple determination of the mean individual attenuation and associated standard deviation would provide a clear indication of expected performance and variability. The provision of the standard deviation of attenuation performance provides the HP purchaser and indication of the quality of the device.


It is desirable that any performance rating of hearing protectors clearly indicates the performance to be expected by the end user. The current complex calculations combining means and standard deviations to produce a single figure do not satisfactorily do this. However, the aim can be accomplished by a separate presentation of the average individual attenuation and standard deviation as the performance figures.


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