PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Components of Variation in Reverberation Time Measurement – Part
2: Field Testing Rooms of Heavyweight Construction
Bill WHITFIELD1;
1noise.co.uk Ltd, England

ABSTRACTThis paper uses analysis of variance (ANOVA) and a specific design of experiment (DOE) and construction
choice to isolate the component of variance associated with the part (or room) being measured along withindividual contributions of measurement uncertainty from the measurement system and the person making
the measurement.
It demonstrates how the gauge repeatability and reproducibility (GRR) technique can be used to identify thevariability in reverberation time measurement over the frequency range 100-3150Hz and as individualcomponent parts of the testing process associated with field sound insulation testing in the UK.
The experiment uses the measurement of reverberation time associated with the ‘interrupted source method’
from EN ISO 354: 2003.
Keywords: Measurement Uncertainty, Reverberation Time, ANOVA, GRR, Gauge, Repeatability,
Reproducibility

1. INTRODUCTION
This paper is Part 2 of 2 papers looking at the measurement uncertainty associated with themeasurement of reverberation time in the field and concentrates on residential rooms formed ofheavyweight (concrete/masonry) floor construction.
The design of any scientific experiment must not only document and include details of the designof the experiment and the measurement procedure but must also attempt to attach a measurement error
to the empirical results. Indeed some emphasise that an experiment is not complete until an analysis of
the final result has been conducted ([1]). This is good practice as it allows the informed reader tounderstand, at a basic level, the likely variability in the measurement process and appreciate theprecision which can be attached to the experimental procedure.
This paper looks at the uncertainty associated with the field measurement of reverberation time andfocuses on this as a component of the pre-completion sound insulation testing requirements of the
Building Regulations for England and Wales. Field tests are the ubiquitous method of demonstratingcompliance with the sound insulation performance standards and the definitive method of
demonstrating conformity with the minimum sound insulation values should compliance be contested.
Annex B of Approved Document E [(2)] Part of the field test procedure requires the measurement of
the reverberation time in the room in order to correct for the receiver room’s effect on the soundinsulation performance of the surface being measured. The sound insulation value calculated in each
1/3rd octave band is ‘standardized’ (DnT) to a 0.5 second reverberation time using the met hods as
detailed in the international standards [(3, 4)] for determining the airborne and impact performance ofthe surface.
This correction for reverberation time effect is detailed in equation (1):ࡰ࢔ࢀ ൌ ࡰ ൅  ૚૙ ‫܏ܔ‬ࢀࢊ࡮࢏ 
ࢀ૙Where:
D is the level difference,
T is the reverberation time measured in the receiving room;T 0 is the reference reverberation time; for dwellings, T0 = 0,5 s
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bill@noise.co.uk(1)

In this paper we are interested in the measurement uncertainty in measuring ‘T’.
It is worthwhile noting the following from the standards: ‘NOTE 1: The standardizing of the level
difference to a reverberation time of 0,5 s takes into account that in dwellings with furniture th ereverberation time has been found to be reasonably independent of the volume and of frequency and tobe approximately equal to 0,5 s. With this standardizing, DnT is dependent on the direction of thesound transmission if the two rooms have different volumes.’ See Burgess & Utley et al and Diaz et al[(5, 6)].
This paper analyses the data from a special design of experiment (DoE) called a Gauge
Repeatability and Reproducibility (GRR) experiment that was carried out on a residential block offlats of heavy-weight concrete/masonry construction where measurement of reverberation times weremade in unfurnished bedrooms. In this GRR the room is the part being measured and its size andshape was ‘blocked’ in this instance by choosing rooms of identical dimensions to determine the rooms’
effect on reverberation time from apparently identical parts. It was, however, noted that not all therooms were completely clear of building materials and some had stacked plasterboard and paint tinsevident on the floor which were not removed by the test engineers.
The measurement uncertainty is split into components of variance to identify the uncertainty
contribution of the instrumentation, test engineer (operator) and the part (or in this case receiver room)
being measured using advanced analysis of variance (ANOVA) which is described in more detailbelow.

2. SITE SURVEY – ROOM AND CONSTRUCTION DETAILS
2.1 Site
The airborne sound insulation tests were carried out on a residential scheme which was nearing
completion. The floor elements were between matched room pairs and five individual operators wereused, each with their own test systems. An aim of this approach was to minimise systematic deviationsin the measurement and thus the variability in measurement test data. Each “test system” wasemployed to test 5 notionally identical room pairs, or ‘parts’, to determine the performance of theseparating floor. In all, the 5 room pairs were tested by each tester (reproducibility) on two separate
occasions (repeatability) over the space of one day. This resulted in 10 test results for each system.
The measurement procedure was designed to represent the noise.co.uk Ltd UKAS Accredited
method statement using a static sampling approach during a normal operational day. The test method
for measurement of reverberation time used the ‘interrupted source’ method from the standard [(7)].
Each test operator complied with the following procedure: Position the Loudspeaker in the receive
room taking care to ensure that the speaker is more than 0.5m from any of the room boundaries, ensurethat the microphone positions used to measure the reverberation time are set up to be greater than 2mfrom the source, 1.5m from each other and 1m from any room boundary where practicable , take areverberation time (RT) measurement, Repeat the RT measurement step for a further minimum 5 runs,
making 6 readings in total. Measurements should be made using at least one speaker position, with
two readings at three selected microphone positions.
The tests were carried out in a small bedroom (Bed 2) that measured approximately 3.1m long x
2.975m wide x 2.375m high with an approximate room volume of 21.3m3. Five identical room pairs
were selected across the development. See Figure 1 below.
The rooms were of bare concrete floor, plasterboard wall and ceilings and were unfurnished. The
floor element being measured on the test was a concrete construction and was Robust Detail E-FC-4,
which from the top down consisted of: 65mm sand/cement screed; 6mm Isorubber resilient layercomplete with 6/260 flanking edge strip to perimeter of floor layer; Proprietary 200mm PCC plank
floor system (min. 300kg/m2 ); plasterboard ceiling consisting 15mm Knauf Wallboard (with 3mm
skim finish to Knauf's recommendations), on MF suspended ceiling grid, with min 150mm ceiling
void.

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Figure 1: 4 out of the 5 Matched room pairs, Bed 2 shown on site layout plan.

Figure 2: Light weight floor section whose sound insulation was being measured during the test.
Drawing on earlier research on identifying the components of variance in the field measurement ofsound insulation by Whitfield and Gibbs, [(8-10)] the experimental approach uses (ANOVA) and a(GRR) test method. The usefulness of these methods is mentioned by Mandel [(11)] and Tsai [(12)] andthe previous use of ANOVA in acoustic research is not without precedent, see Taibo and Glasserman deDayan [(13)] and it has also been used for measurement of reverberation time, all be it in the context ofmeasuring the absorption of an element in a laboratory environment ,see Davern and Dubout P [(14,15)].
The main advantages of ANOVA are listed by Deldossi and Zappa [(16)] and include the ability todetermine the contribution of the operator and part and operator by part inte raction. A key contribution
to the development of GRR was written by Montgomery and Runger [(17, 18)] and culminated in amonograph on the subject, including its special applications by Burdick et al [(19)], in which the
ANOVA design, for the purpose of this research, is described as a Balanced Two Factor Crossed

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random model with interaction. It informs this research on achieving an accurate and reliable estimateof the variability in the measurement process due to the part, the operator and the instrument. It is thismodel and additional information provided by Montgomery [(17, 18, 20)] and Burdick et al [(19)]which forms the analytical framework to separate out and quantify the components of variance inreverberation time measurement.

3. GRR
3.1 DOE
The GRR has a particular DoE which relies on a number of gauge “operators” to measure a numberof test specimens (parts) a repeated number of times. In this DoE due to the onerous test procedurerequired to capture one result (test) 5 UKAS accredited sound insulation test operators were used, eachwith their own test kit and tasked at measuring 5 floor specimens (parts) 2 times each. The model isdetailed in equation (2):
Y ijk= μ+ Oi+ P j+ ᇾ(OP)ᇿ ij + E (k(ij))
where:(2)

i = 1, 2,....., p : j = 1, 2, ......., o : k = 1, 2,…., r and;p = number of parts;o = number of operators;r = number of repetitions; and,Oi , Pj ,ᇾ(OP)ᇿij, and R (k(ij)) are random variables representing the effects of the operator, parts,
operator by part interaction and the replications on the measurement and μ is an overall mean. Clearly,
in the experiment described here p = 5, o = 5 and r = 2
The definition of reproducibility in the GRR is covered in Burdick et al [(19)] and incorporates theinteraction term and is shown in equation (3): The combined Gauge variance components are shown inequation (3) and the total variance shown in equation (4) which describes the total measurement
uncertainty associated with the field testing of this particular part.
ଶଶߪ௥௘௣௥௢ௗ௨௖௜௕௜௟௜௧௬ൌ  ߪைଶ ൅  ߪ௉ை

(3)

ଶ
ଶ
ଶ
ߪ௚௔௨௚௘ൌ  ߪ௥௘௣௘௔௧௔௕௜௟௜௧௬൅  ߪோ௘௣௥௢ௗ௨௖௜௕௜௟௜௧௬

(4)

ଶ
ଶ
ଶ
ߪ௧௢௧௔௟ൌ  ߪ௚௔௨௚௘൅  ߪ௣௔௥௧

(5)

It should be noted that in a GRR the reproducibility term does not contain the repeatability term bydefinition. This is different to the method of assessment in BS5725 [(21)] where repeatability isembedded in the reproducibility term resulting in reproducibility always being greater than
repeatability. In GRR, the reproducibility can be separated out into two components of variance,ଶଶ
defined as the operator variance ( ߪை )and the operator by part interaction ( ߪ௉ை ). This is an importantfeature of ANOVA because it detects any interaction the operator has with the part being measured. In
some cases the interaction term can be significant, and dominant as demonstrated by Whitfield andGibbs [(22)] and it would remain hidden if using the BS5725 method of calculating repeatability ‘ r’
and reproducibility ‘R’. Typical RT results for a typical single operator repeating measurements aredetailed in Figure 3 and across all operators sampling a single room in Figure 4:
The difference in the RT measured by operator ‘SP’ in Room 1 are not easily explained as measured
levels from their sound level meter were consistent over both repeat measurements made. It is possible
to now use the repeated measured values with the reproduced values of other operators to reduce thetotal uncertainty of measurement into its component parts.

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Figure 3 : Typical operator RT for Room 1 (Secs)

Figure 4: Average operator RTs for Room 1 (Secs)
The results of the ANOVA analysis are graphically illustrated in Figure 5 for individualcomponents of variance. The total variance of the RT measurement process ranges between 0.019 and0.33 seconds and shows a steadily rising level peaking at 500Hz and falling steadily to 2500Hz. This
characteristic is replicated in the components associated with the engineer (oper ator), operator by partinteraction term and the part to part variation across the same frequency range and these variances arebroken down in Figure 5 to show the components associated with Reproducibility ‘R’ the operator bypart interaction and part to part (Room) components of variance. It is noted that the ANOVA of the data
determined there was significant interaction between the operator and the part being m easured so thevariance associated by ‘reproducibility’ includes this term. It is likely that as the floors of some of therooms had stacked building materials the random measurement process was constrained, leading tointeraction of the operator and the part; for example: it was difficult to place the loudspeaker in certain
areas of the room due to stacked plasterboard.

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Figure 5: Total Variance with (r) (instrument), (R) (Operator), interaction and part (Room) variances

Figure 6: Variances associated with the instrument (r) and the Part (Room)
The ability to detect interaction is an important feature of ANOVA because it detects an yinteraction the operator has with the part being measured. In some cases the interaction term can besignificant in a measurement routine, at certain frequencies can also be dominant as demonstrated by
Whitfield and Gibbs [(23)] and it would remain hidden if using the BS5725 method of calculating
repeatability ‘r’ and reproducibility ‘R‘or assuming an approach using GUM [(24)].
What’s notable from the GRR data shown in Figure 6 is that the variance associated with the
instrument (r) is generally higher at the lower frequencies falling after peaking at 0.034 seconds at
100Hz to below 0.012 seconds above 200Hz which generally indicates high levels of repeatability inthe measurement process. The higher variance at lower frequencies is likely partly due to thelimitations of the sound level meter,RT response at lower frequencies and the less diffuse sound fieldin the relatively small rooms.

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This is in contrast to the variance attributable to the part being measured which shows the variancelevels are lower than the variance associated with the instrument between 100-125Hz and significantly
higher at 160Hz and above. The part to part variation in this case was likely due to abandoned building
materials in some of the receiver rooms which could not easily be moved by the on site test teams.
Even so the room dimensions are as far as practical equivalent and the varianc e due to the part in thiscase dominates over the variance associated with the instrument and the operator.
The dominant contributor to the total uncertainty associated with the measurement of reverberation
time in this experiment is, therefore, dependent on frequency and is due in the main to the part being
measured closely, followed by the operator’s contribution, with the instrument offering only a small
contribution at 125Hz and above.

4. CONCLUSION
4.1 ANOVA GRR
The calculation of measurement uncertainty in the measurement of reverberation time in the fieldtesting of sound insulation can be carried out using a specialist DoE based on ANOVA. This allows thecomponents of variance to be broken down into the uncertainty associated with the instrument , thatassociated with the operator , and that associated by the part being measured.
In order to identify how the part, in this case the room in which the reverberation time is measured,contributes to the overall uncertainty of measurement this factor can be ‘blocked’ by choosing
identical rooms of the same shape size and finish varying only by the workmanship used to create them.
It is noted that the GRR type experiment uses the same experimental effort as that required bytraditional means of identifying ‘r’ and ‘R’ e.g. BS5725, but allows the researcher to splice out
significantly more detail from the same data about the contributors to the overall uncertainty including
any interaction between the operators making the measurement and the part bein g measured. The
blocking of the room effect in this experiment was affected by the on site condition of the rooms assome had stored building materials in them which was not ideal. It did, however, show that in field test
situations there are additional contributory factors that add to the uncertainty of measurement andinitiate interactions, however unwanted, into the randomized measurement process. The GRR ANOVA
methods highlight these effects and add detail to the understanding of uncertainty that is bey ond thescope of the BS5725 or GUM methods for assessing measurement uncertainty in the survey process.

Table 1 : Components of variance table for RT measurement across the frequency range 100-3150Hz
The contributions from the instrument, operator and part together with the operator by partinteraction is summarised in Table 1 for ease of reference.
More data from GRR experiments is desirable to investigate further the uncertainties associatedwith the measurement of RT in field test situations and include other room types, constructions androom sizes. There is also the possibility to extend the frequency range of interest to include both higher

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and lower frequency bands e.g. 50 Hz – 5KHz providing the instrumentation used, room size and its
absorption areas allows these to be reliably measured.

ACKNOWLEDGEMENTS
The author acknowledges both Crest Nicholson for the free use of its site in Hitchin and thenoise.co.uk Ltd test team for diligently following instructions to test the sample in perhaps non ideal
conditions!

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