ECMA-425 1st Edition / December 2024
Statistical background correction for information technology and telecommunications equipment noise measurements
Reference number ECMA-123:2009
© Ecma International 2009
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Contents
Page
1
Scope ...................................................................................................................................................... 1
2
Normative references ............................................................................................................................ 1
3
Terms and definitions ........................................................................................................................... 1
4
Background corrected source level .................................................................................................... 3
5
Statistical background noise correction ............................................................................................. 4
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Background noise steadiness ............................................................................................................. 5
7
Background noise sampling ................................................................................................................ 5
Annex A (informative) Statistical and legacy background noise corrections compared ............................ 7 Annex B (informative) Background noise steadiness examples ................................................................... 9 Annex C (informative) Measurement uncertainty .......................................................................................... 11
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Introduction This standard describes a statistical background correction (SBC) for removing background noise contributions from measured noise levels. Measured source levels include a background contribution because background noise is present during source measurement. Since the source is of interest, there is motivation to remove the background contribution. The background must be estimated from background samples obtained when the source is not operating. Background estimation and measured source level correction become increasingly difficult as background fluctuation increases and confidence in the background contribution decreases. The formulation of the SBC addresses this situation with an explicit description of time-varying background noise. The statistics of the background noise are assumed to be time-invariant (stationary) and are estimated from samples of the background noise. Application of the SBC to a measured source level produces a background corrected source level that upper bounds the true source level with known confidence. The magnitude of the SBC increases with background steadiness and with background proximity to the measured source level, as confidence in the measured background increases. The background variation description distinguishes the SBC from the legacy background correction (LBC) 𝐾1 , which has no such description. Use of the SBC is permissible only for adequately steady backgrounds, but the legacy correction may be used for any background, regardless its fluctuation. The nature and values of SBC and LBC maxima also contrast. The SBC maximum is determined by considerations of background fluctuation and sampling, while heuristic caps limit the legacy correction according to the standard—ISO 3741, ISO 3744, ISO 3745, and ISO 11201—and measurement grade being followed. The various legacy caps produce different corrections that obscure source comparisons and introduce a 0.8 dB “grade penalty” such that backgroundcorrected source levels for engineering grade are lower than for precision grade, thereby discouraging precision grade measurements. The SBC avoids the grade penalty by uniformly addressing background noise. The SBC depends not only on measured source-background level difference, like the LBC, but also on background steadiness, unlike the LBC, regardless of standard or measurement grade being followed. For steady backgrounds close in level to the measured source the SBC is larger than the LBC and provides lower background corrected source levels. Minimized background corrected source levels are often desired for precision grade 1 and engineering grade 2 measurements. For grade 1 the legacy correction is capped at 0.46 dB for source-background level differences Δ𝐿 below 10 dB; for grade 2 it is capped at 1.26 dB for Δ𝐿 below 6 dB. For steady backgrounds within 6 dB of the measured source (Δ𝐿 < 6 dB) the SBC is as much as 3 dB greater than the grade 1 LBC, and up to 2 dB greater than the grade 2 LBC, and provides correspondingly lower background corrected source levels. Since the statistical and legacy background noise corrections produce different source corrections, it is envisioned that future noise emission standards allow test directors to choose between the two corrections. SBC implementation involves a modest increase in processing of background samples, to figure not only the measured mean but also the measured variance of background noise. The additional effort is justified when accuracy is needed, and the measured source level is within 6 dB of a steady background. It should be noted that, while the SBC described in this standard applies to acoustic decibel levels like sound pressure level and sound power level obtained with one or more sensors and spanning narrow or broad frequency bands, the SBC framework may also be applied to other dynamic signals like acceleration, velocity, and displacement.
This Ecma Standard was developed by Technical Committee 26 and was adopted by the General Assembly of December 2024
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Statistical background noise correction for information technology and telecommunications equipment noise measurements
1
Scope
This standard describes a statistical background noise correction by which background noise contributions may be removed from measured noise levels. The statistical background noise is an alternative to the legacy background noise correction found in ECMA-74 and ISO 7779, ISO 3741, ISO 3744, ISO 3745, and ISO 11201. Background noise corrections are used to obtain the background corrected source level, which is an estimate of the level radiated by the source or device under test. The background corrected source level is obtained by subtracting the background noise correction from the measured noise emission or source level, which contains both source and background contributions. Measurement of noise emissions generated by Information Technology and Telecommunications Equipment (ITT) is described in ECMA-74 and ISO 7779.
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Normative references
The following referenced documents are indispensable for the application of this Standard. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ECMA-108, Determination of High-frequency Sound Power Levels Emitted by Information Technology and Telecommunications Equipment NOTE ISO 9295[3] is ISO counterpart of ECMA-108. It is noted that, after the revision in 2015, the scope of ISO 9295 covers machinery and equipment in general, not limited to information technology and telecommunications equipment.
ISO 3741, Acoustics — Determination of sound power levels and sound energy levels of noise sources using sound pressure — Precision methods for reverberation test rooms ISO 3744, Acoustics — Determination of sound power levels and sound energy levels of noise sources using sound pressure — Engineering methods for an essentially free field over a reflecting plane ISO 3745, Acoustics — Determination of sound power levels and sound energy levels of noise sources using sound pressure — Precision methods for anechoic test rooms and hemi-anechoic test rooms ISO 11201, Acoustics — Noise emitted by machinery and equipment — Determination of emission sound pressure levels at a work station and at other specified positions in an essentially free field over a reflecting plane with negligible environmental corrections
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Terms and definitions
For the purposes of this document, the following terms and definitions apply. 3.1 background noise level, 𝑳𝑩 the measured level of background noise in decibels (dB)
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3.2 background corrected source level, 𝑳̂ an estimate of the true source level obtained by subtracting a background correction from the measured source level, in decibels (dB) 3.3 measured source level, 𝑳 a sound level in decibels (dB) measured for operating equipment containing source and background noise contributions 3.4 background correction 𝑲 an adjustment that removes the background contribution in a measured source level 3.5 legacy background correction 𝑲𝟏 LBC a background correction involving the measured source-background level difference 3.6 legacy background correction cap 𝑲𝑪 the maximum allowable legacy background correction 3.7 measured source-background level difference 𝚫𝑳 the difference in decibels (dB) between the measured source level and the measured background level 3.8 statistical background correction 𝑲𝑺 SBC a background correction involving not only the measured source-background level difference but also the steadiness of the background noise 3.9 minimum measured source-background level difference 𝚫𝑳min the smallest measured source-background level difference at which the statistical background correction may be applied 3.10 background steadiness 𝑴 a statistic describing the consistency and repeatability of the background taken over samples of the background 3.11 measured background standard mean 𝒎𝒃𝟐 the average of background noise (not background noise level) over several samples of the background 3.12 measured background standard deviation 𝒔𝒃𝟐 a statistic describing the consistency and repeatability of background noise (not background noise level) over several samples of the background 3.13 background noise 𝒃𝟐 the time-average of the square of sound pressure generated by all sources other than the noise source under test 3.14 background noise sample 𝒃𝟐𝒊 a sample of background noise with sample index 𝑖
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3.15 background sample count 𝑵 the number of background samples used to form the mean, standard deviation, and steadiness of the background 3.16 enveloping percentile 𝒛𝒆 the standard normal percentile in the statistical background correction that serves to upper bound the true source with specified confidence 3.17 physical source percentile 𝒛𝒑 the standard normal percentile in the minimum measured source-background level difference that assures with specified confidence a source description due to the equipment noise source under test, as opposed to a fictitious source arising from background fluctuation 3.18 relative percentile error 𝜽 the error in the realized (actual) enveloping percentile relative to the enveloping percentile arising from the formulation of the statistical background correction due to a non-stationary background or departure from the theoretical statistical distribution of the background sample difference 3.19 background correction error 𝜹𝑲 the maximum allowable decibel (dB) error in the statistical background correction 3.20 nondimensional ratio 𝒙 a unitless quotient of a power or energy quantity relative to a reference quantity used to form a decibel (dB) level 3.21 mean square sound pressure 𝒑𝟐 the time average of squared sound pressure 3.22 sound pressure reference 𝒑𝟎 the reference quantity used to form a sound pressure level 3.23 sound power 𝑾 the time rate of sound energy radiation by a sound source 3.24 sound power reference 𝑾𝟎 the reference quantity used to form a sound power level
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Background corrected source level
The background corrected source level 𝐿̂ is an estimate of the true source level and is given by: 𝐿̂ = 𝐿 − 𝐾
(1)
where 𝐿 is the measured source level which contains a background noise contribution, and K is a background noise correction. The measured source level is obtained by measuring the sound level of an operating device under test and contains source and background noise contributions. The source contribution is due to the sound radiated by the device. The background noise contribution is due to ambient and instrumentation noise. The
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source levels 𝐿 and 𝐿̂ may be sound pressure levels, sound power levels, sound energy levels, or any power or energy quantity that can be expressed in decibels, gathered by one or more microphones or other sensors, and may span a narrow, one-third octave, or broad (e.g. overall) band of frequency. NOTE Because the scope and focus of this Standard is background noise correction, corrections for other systematic errors producing bias in measured source levels are omitted in Equation (1). Other systematic error sources include sound reflections, associated with the environmental correction 𝐾2 of ISO 3744 and ISO 3745, as well as sound absorption, sound incidence angle, and instrumentation.
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Statistical background noise correction
The statistical background correction is given by: 𝐾𝑆 = −10 log10 [1 − 10−Δ𝐿/10 (1 −
2.33 √𝑀
)]
for
𝛥𝐿 ≥ 𝛥𝐿min = 10 log10 [1 +
39 √𝑀
]
(2)
in which M is the steadiness of the background noise given in Equation 4 in Clause 6, 𝛥𝐿 is the measured source-background level difference, and 𝛥𝐿min is the minimum allowable source-background level difference. A background corrected source level obtained using Equations (1) and (2) produces a background corrected source level that upper bounds the true source level with 95% confidence. The measured source-background level difference 𝛥𝐿 is the amount by which the measured source level 𝐿 exceeds the measured background level 𝐿𝐵 : 𝛥𝐿 = 𝐿 − 𝐿𝐵
(3)
The measured background level 𝐿𝐵 is obtained by measuring the background noise while the source under test is not generating sound. The measured source and background levels 𝐿 and 𝐿𝐵 are averages over time of a power or energy quantity, expressed in decibels, and pertain to identical frequency bands, sensors, sensor locations, and spatial averaging schemes over sensors when spatial averaging is employed. As Equation (2) implies, the statistical background noise correction is permitted only when the measured sourcebackground level difference 𝛥𝐿 is greater than or equal to 𝛥𝐿min . The SBC shall not be used to adjust a measured source level when the measured source-background level difference is less than 𝛥𝐿min . The statistical and legacy background corrections are compared in Annex A. A spreadsheet implementing the SBC is available at https://ecma-international.org/publications-andstandards/technical-reports/ecma-tr-107/. NOTE 1 The general form of the statistical background correction is 𝐾𝑆 = −10 log10 [1 − 10−Δ𝐿/10 (1 − 𝑧𝑒 √2/𝑀)] for 𝛥𝐿 ≥ 𝛥𝐿min = 10 log10 [1 + 𝑧𝑝 √2/𝑀(1 + 4.34|𝜃|/𝛿𝐾)] [1,2,3]. The standard normal percentile 𝑧𝑒 specifies the confidence of the upper envelope applied by the background corrected source level on the true source. The standard normal percentile 𝑧𝑝 specifies the confidence of obtaining a description of the source under test, not background fluctuation, from the background corrected source level at the minimum measured source-background level difference 𝛥𝐿min . Parameter 𝛿𝐾 is allowable background noise correction error. Parameter 𝜃 is the relative error of the upper envelope percentile 𝑧𝑒 that arises when the realized background distribution departs from the background distribution underlying the 𝐾𝑆 formulation. NOTE 2 In Equation 2 the SBC is obtained with 𝑧𝑒 = 95%, and the minimum measured source-background level difference is obtained with 𝑧𝑝 = 99%, |𝜃| = 25%, and 𝛿𝐾 = 0.1 dB [4,5]. The latter three parameter values impose a more restrictive limit on the magnitude of 𝐾𝑆 for backgrounds near the measured source than the 𝑧𝑝 = 95%, |𝜃| = 5%, and 𝛿𝐾 = 0.2 dB used in [1]. NOTE 3 The legacy background noise correction, when not capped, is equally likely to understate or overstate the true source level. This is seen from the equality of uncapped legacy background noise correction (upper right-hand side of Equation A-1) and the general form of the 𝐾𝑆 correction in NOTE 1 when evaluated for 50% confidence at which 𝑧𝑒 = 0. NOTE 4 The requirement 𝛥𝐿 ≥ 𝛥𝐿min statistically assures a physical source description by minimizing the difference of background noise sampled during source and background measurements for specified maximum errors 𝛿𝐾 in the statistical
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background noise correction and 𝜃 in the background noise difference percentile [1,2,3]. The measured source-background level difference 𝛥𝐿 contains background sample difference, since the measured source level and the measured background level each contain a background sample. It is possible for the background sample difference to be large enough that the time-varying background masquerades as a source, particularly when an unsteady background approaches the measured source level. In this case the background fluctuates high during source measurement and low during background measurement. To assure a physical source description of the equipment under test with high probability, the background sample difference is minimized to the 1 st percentile of its statistical distribution, below the mean background sample difference. The percentile 𝑧𝑝 = 99% is allowed by the symmetry of the distribution of the background sample difference and assures a physical source description 99 out of 100 times on average.
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Background noise steadiness
To determine background steadiness at least three (3) samples of background noise shall be used. The following calculations are to be performed without numerical rounding. Background noise steadiness 𝑀 describes the consistency of the background noise and is given by 𝑚𝑏 2 2 ) (4) 𝑠𝑏 2 in which 𝑚𝑏2 and 𝑠𝑏2 are the measured mean and measured standard deviation of the background noise 𝑏 2 , which is the time-average of the square of background sound pressure. The measured mean and measured standard deviation of the background noise are obtained by: 𝑀=(
𝑁
1 𝑚𝑏2 = ∑ 𝑏𝑖2 𝑁
(5)
𝑖=1
𝑁
1/2
1 𝑠𝑏 2 = [ ∑(𝑏𝑖2 − 𝑚𝑏2 )2 ] 𝑁−1
(6)
𝑖=1
where 𝑖 = 1 … 𝑁 is sample index, and the 𝑏𝑖2 are background noise samples and are related to samples of background noise level 𝐿𝐵𝑖 : 𝑏𝑖2 = 𝑝𝑜2 10𝐿𝐵𝑖/10
(7)
The 20 micro-Pa reference pressure 𝑝𝑜 has no effect on steadiness because of cancellation in the numerator and denominator of Equation 4. An example of the calculation of background steadiness is given in Annex B. Uncertainty for background corrections and background corrected source levels are described in Annex C. NOTE 1
Rounding is prohibited because it introduces numerical noise and reduces background steadiness.
NOTE 2 The SBC may be applied to any decibel level 𝐿 = 10 lg10 (𝑥) in which the nondimensional ratio 𝑥 follows the type of level. For sound pressure level, 𝑥 = 𝑝2 /𝑝02 in which 𝑝2 is the time average of squared pressure in Pascals and the reference quantity 𝑝0 = 20 micro-Pa. For sound power level, 𝑥 = 𝑊/𝑊0 is the ratio of sound power 𝑊 in Watts to the reference quantity 𝑊0 = 1 pico-Watt. The reference quantity cancels in the numerator and denominator of Equation 4 and therefore does not affect the SBC.
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Background noise sampling
Background noise shall be measured while the equipment under test is configured not to generate noise.
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Background noise shall be measured with the same microphone(s), at the same fixed or traversing position(s), and data acquisition system as for the equipment under test. At least three (3) background samples, each measured within 36 hours, before or after the equipment noise measurement of interest, shall be used to form the SBC. The background samples are candidate background noise samples for forming the SBC according to Clauses 5 and 6. The candidate background noise samples selected for SBC formation must be confirmed as statistically stationary relative to previously measured background data before using them to form the SBC. NOTE 1 There are many ways to satisfy the background sampling requirement. A workflow involving one (1) background sample measured at the start and end of a work period, for example 8am and 5pm, satisfies the background sampling requirement, even on non-successive days like the first day of the workweek, since the background samples measured on the first day and the following day are within 36 hours of any equipment noise measurement on the first day. NOTE 2 Ambient phenomena producing background noise include but are not limited to foot and vehicle traffic, HVAC and machinery operations, and instrumentation noise due to electromagnetic radiation from these operations. Listening to recordings can confirm that ambient events in outlier noise samples are absent from non-outlier background and equipment noise measurements. NOTE 3 Visual inspection of background data may be used to confirm stationarity of background samples relative to previously measured background data. Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests may also be used [8,9]. NOTE 4 Outlier removal can restore stationarity of candidate background samples relative to previously measured background data. Outlier removal can also introduce competing effects on the SBC. Outlier removal increases background steadiness, thereby increasing the SBC. When a high background outlier is removed, the measured background level decreases, increasing the measured source-background level difference 𝛥𝐿 and decreasing the SBC. See Equation 3 and Figure B.1. NOTE 5 Visual inspection and control charts may be used to identify outliers. The interquartile range (IQR) test and Carling’s modified IQR test may also be used.The normal and Chi-square outlier tests are not recommended because the outlier effect on the measured mean and variance used in these tests tends to mask the outliers themselves [6,7]. NOTE 6 Statistical outliers among the candidate samples may be removed if and only if the ambient phenomena causing the outliers do not affect non-outlier samples and do not affect the equipment noise measurement of interest. Listening to recordings can confirm that ambient events in outlier noise samples are absent from non-outlier background and equipment noise measurements. Outliers generally indicate a change in the phenomena responsible for background noise. NOTE 7 Instead of removing outliers, it is always preferable to repeat background and equipment noise measurements under controlled conditions. NOTE 8 A library or baseline of background noise samples is needed to confirm that the background samples used to form the SBC are stationary relative to the previously measured background data. The background data library is also needed to identify outliers.
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Annex A (informative) Statistical and legacy background noise corrections compared
The legacy background noise correction (LBC) 𝐾1 is given by: −10 lg10 (1 − 10−𝛥𝐿/10 ) 𝛥𝐿 > 𝛥𝐿𝑐 (A.1) 𝐾1 = { 𝐾𝑐 𝛥𝐿 ≤ 𝛥𝐿𝑐 in which 𝛥𝐿 is the measured source-background level difference, and the cap 𝐾𝑐 limits the background noise correction to its value at a critical source-background level difference 𝛥𝐿𝑐 . Several measurement grade and frequency dependent caps are given in ISO 3741, ISO 3744, ISO 3745, and ISO 11201; apart from rounding there are two cap values: 𝐾𝑐 = 1.26 dB corresponding to 𝛥𝐿𝑐 = 6 dB and 𝐾𝑐 = 0.46 dB corresponding to 𝛥𝐿𝑐 = 10 dB. The two caps cause the “grade penalty” that produces background corrected source levels 0.8 dB lower for engineering grade than for precision grade methods [1,2,3]. Figure A-1 also shows the statistical background correction (SBC) 𝐾𝑆 for background steadiness values of 30, 300, and 3000. The SBC increases with background steadiness and with decreasing measured sourcebackground level difference. Some features of the SBC: •
With sufficient background steadiness, the SBC can be 2 to 3 dB larger than the LBC at measured source-background level differences below 6 dB where caps limit the magnitude of the legacy correction.
•
In the regime 𝛥𝐿 < 6 dB where steady backgrounds approach the measured source level, steady backgrounds are rewarded with larger corrections, thereby incentivizing precision measurements and low noise chambers.
•
When the LBC is capped, the SBC remains within 0.2 dB and below the uncapped legacy correction, approaching the LBC as background steadiness increases. This behaviour occurs because the SBC is sensitive to background steadiness, but the LBC is built on the assumption of a constant background.
•
Unsteady backgrounds may be disqualified depending on the background steadiness variation and the measured source-background level difference parameters. The legacy background noise correction has no such restriction and may be applied for all backgrounds.
•
The SBC produces background corrected source levels free of the grade penalty, which obscures source comparisons by 0.8 dB and perversely incentivizes measurement grade over precision grade.
•
The SBC produces background corrected source levels that upper bound the true source with 95% confidence. When uncapped, the LBC bounds the true source with 50% confidence.
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Figure B.1 – Statistical 𝑲𝑺 and legacy 𝑲𝟏 background noise corrections
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Annex B (informative) Background noise steadiness examples
Examples of background noise steadiness are given in Table B.1 using background noise data in acoustic rooms provided by three manufacturers, whose identity is withheld by request. Table B.1 – Background noise for three chambers Background Noise Level (dB) Chamber
Nondimensional Background Noise
Statistics Steadiness M
S1
S2
S3
S4
S1
S2
S3
S4
Mean
Std. dev.
Chamber A
6,9
7,0
7,5
7,3
4,9
5,0
5,6
5,4
5,2
0,33
250
Chamber B
16,56
16,75
16,56
16,57
45,0
47,0
45,0
45,0
45,8
0,975
2210
Chamber C
21,74
21,78
21,76
21,91
149
151
150
155
151
2,61
3360
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Annex C (informative) Measurement uncertainty
The effect of background corrections on measurement uncertainty may be understood by recalling that background corrections remove the background contribution in measured source levels. During source measurement the background contribution combines with the source, upwardly biasing the measured source level relative to the true source. In the nomenclature of ISO/IEC Guide 98-3 [10] the measured source level contains “systematic error”. Removal of the systematic error by the legacy or statistical background correction is imperfect because the measured source-background level difference Δ𝐿 and background steadiness 𝑀 parameters on which background corrections depend are estimates derived from background samples. It has been shown that background corrected source levels formed by the SBC and LBC are comparable in terms of overstating the true source level [5]. The uncertainty of a background corrected source level may be expressed using the methods of ISO/IEC Guide 98-3 [10]. The measured source level and measured background noise level have standard uncertainties given by the standard deviations 𝑠𝐿 and 𝑠𝐿𝐵 of the measured source and background noise levels, respectively. The sensitivity coefficient 𝑐𝐿̂ of a background corrected source level 𝐿̂ is given by : 1+ 𝑐𝐿̂ =
1 10Δ𝐿/10 − 1 + 2.33/√𝑀 1+
1
for 𝐾𝑆 (C.1) for 𝐾1
{ 10Δ𝐿/10 − 1 in which 𝐾𝑆 is the statistical background correction and 𝐾1 is the legacy background correction. The sensitivity coefficient 𝑐𝐿̂ describes the random error in the background corrected source level due to the random error in the measured source level 𝐿 and measured background level 𝐿𝐵 . See Equations (1) and (3). NOTE 1 Source overstatement may occur because of the stochastic nature of background samples used to form background corrections. The source overstatement is defined as the excess of the background corrected source level above the true source. In reference [5] Monte Carlo methods are used to determine the envelopes that upper bound 95% and 99% of source overstatements for three background samples at the measured source-background level difference Δ𝐿 giving the largest overstatements, namely Δ𝐿min for the SBC and Δ𝐿𝐶 for the LBC. The 95% envelope is 0.2 dB and constant over background steadiness for the SBC; for the LBC with Δ𝐿𝐶 = 6 dB it increases to 1 dB with decreasing steadiness below the background steadiness of 250 where the 95% source overstatement envelopes for the SBC and LBC are equal and cross one another. NOTE 2
Standard uncertainty is defined as the measured standard deviation in ISO/IEC Guide 98-3 [10].
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