Now what do we do with these good numbers? John R. Franks William J. Murphy NIOSH, MS C-27, 4676 Columbia Pkwy. Cincinnati OH 45226-1998
Present Protector Standards • ANSI 3.19-1974 Method for Measurement of Real-Ear Protection of Hearing Protectors and and Physical Attenuation of Earmuffs • ANSI S12.6-1997 Methods for Measuring the Real-Ear Attenuation of Hearing Protectors • ISO 4869 Estimation of Effective A-Weighted Sound Pressure Levels When Hearing Protectors are Worn.
Present Protector Standards • Applications • ANSI S3.19 – U.S. EPA Noise Reduction Rating • ANSI S 12.6 – National Hearing Conservation Association NRR(SF) • ISO 4869 – SNR and the HML
Present Protector Standards • Calculation Methods – Single Number NRR = 107.9 dBC − 10 log
8000
∑10
0.1(
L Af − APV f 9 8) −3 dB
f =125
NRR ( sf ) = 108.5 dBC − 10 log
8000
∑10
0.1(
L Af − APV f 8 4) − 5 dB
f =63
SNR = 100. dBC − 10 log
8000
∑10
0.1(
L Af − APV fx )
f =63
• Where LAf= A-weighted octave-band level at frequency f and APVfx = Assumed Protection Value for each frequency for for Protection Performance Value x (0.98 for NRR, 0.84 for NRR(sf), typically 0.84 for SNR)
Present Protector Standards High, Middle, Low (HML) Calculation Method 4
4
i =1
i =1
8
8
i =5
i =5
8
8
i =5
i =5
H x = 0.25∑ PNR xi − 0.48∑ d i ⋅ PNR xi M x = 0.25∑ PNR xi − 0.16∑ d i ⋅ PNR xi L x = 0.25∑ PNR xi + 0.23∑ d i ⋅ PNR xi where PNR xi = 100 dBA − 10 log
8000
∑10
f = 63
0.1(L Afi −APV fx )
Present Protector Standards • APV – Assumed Protection Value • Mean REAT less protection performance value: x (%) x (standard deviations) 50 0.50 75 0.67 84 1.00 95 1.64 98 2.00
Present Protector Standards • Key to all rating systems is the A-weighted noise level for test frequency band – LAf minus an Assumed Protection Value. • The Assumed Protective Value is calculated as the mean REAT minus a multiple of the standard deviation of the REATs.
Issues – What does Mean mean? – How do you calculate a standard deviation for REATs? – Is the goal to protect only those below a given level? – Is over protection addressed?
Issues • What does Mean mean? – ANSI S3.19: Mean is average for 30 REATs from ten subjects. – ANSI S12.6: Mean is the grand mean of the mean subject REATs for 10 subjects (muffs) or 20 subjects (plugs and semi-inserts). – ISO 4869: Mean is the average REAT for 16 subjects with one REAT each (no withinsubject repeated measures).
Issues • How do you calculate a standard deviation for REATs? N =30
– ANSI S3.19:
σ=
∑ (x − x) i =1
2
i
(N − 1)
Where xi are the individual observations, µ is the mean and N is the number of observations (ten subjects with three measures each, N= 30)
Issues • How do you calculate a standard deviation for REATs? N
– ANSI S12.6:
σ=
∑ (x − x) i =1
2
i
(N − 1)
Where xi is the individual’s average of two REAT trials and µ is the mean of the individual averages, and N is the number of subjects (10 for muffs, 20 for plugs and semi-inserts)
Issues • How do you calculate a standard deviation for REATs? N
– ISO 4869
σ=
∑ (x − x) i =1
2
i
(N − 1)
– Where xi is the REAT of each individual subject’s (i) one trial and µ is the mean attenuation of all subjects, and N is the number of subjects (16 for all protectors)
Issues
Attenuation Distribution
• Use of means and standard deviations appropriate for normally distributed data 10 8
Well-Fit Protectors
6 4 2 0 -20 -10 0 10 20 30 40 50 60
Attenuation (dB)
1 − d(x) = e 2πσ
( x − µ )2 2σ
2
• Use of means and standard deviations is not appropriate for non-normal and multimodal data distributions
φ d(x) = e 2πσ1
( x − µ 1 )2 − 2σ 12
Attenuation Distribution
Issues 10 8
Well-Fit Protectors
6 4
Poorly-Fit Protectors
2 0 -20 -10 0 10 20 30 40 50 60
Attenuation (dB)
1− φ + e 2πσ 2
( x − µ 2 )2 − 2σ 22
Solutions
10
100
8
80
6
60
4
40
2
20
0 -20 -10
0
10
20
30
40
Attenuation (dB)
50
0 60
Cumulative Distribution (%)
Attenuation Distribution
• Use a cumulative distribution model that makes no assumptions about normality or modality.
Solutions Cumulative Distributions and Fits Bilsom UF-1 Subject-Fit Data 100 80 60
125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz
40 20 0 -20
0
20
40
60
Real Ear Attenuation at Threshold (dB)
Poorly-Behaved Earplug Cumulative Distribution (%)
Cumulative Distribution (%)
Well-Behaved Earmuff
Cumulative Distributions and Fits EP100 Subject-Fit Data 100 80 60
125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz
40 20 0 -20
0
20
40
60
Real Ear Attenuation at Threshold (dB)
Solutions • For a poorly behaved device, differences can be appreciative between Gaussian and cumulative models Cumulative Distribution (%)
Comparison of Fitting Models 50 Express 1000 Hz Gaussian Fit Cumulative Fit
40 30
CDA 16% = 6.0 dB 20 10
µ−σ = 10.6 dB
0 0
5
10
15
Attenuation (dB)
20
25
Solutions • Calculate the Assumed Protection Value, APVfx, any single-or multiple-number rating by using the values off the cumulative distributions at the desired confidence level: x = 2% for the NRR, x = 16% for the NRR(sf), SNR, HML.
Solutions • Create a new rating system that uses values from cumulative distributions at a lower (16%) and upper (84%) limits. • For the NRR(sf), two numbers would be generated:
APV f 16
APV f 84
Solutions • The new label would read, for example • Noise Reduction Range = 16 to 22 dB, best suited for noise levels less than 91 dBA Laeq • Notice: The smaller the range, the more likely the protector will provide you the same noise reduction as it did for the rating test panel.
FIN • Relevant NIOSH publications: • Revised Noise Criteria Document: 98-126 – hardcopy, HTML, and PDF • Practical Guide: 96-110 – hardcopy, HTML, and PDF • Hearing Protector Compendium: 94-105 – hardcopy and PDF • Contact:
[email protected] 