Complicaciones que ocurren principalmente en el curso del trabajo o el parto

Most of the relevant literature on measurement uncertainty in sound insulation centres on inter-laboratory studies. Quality management standards [4] require laboratories to assess measurement uncertainty and attempt to: identify all significant components;

36 make a reasonable estimate of the size of the total uncertainty and its variability; ensure that the reported results do not give a false estimate of uncertainty. The main reason for assessing the measurement uncertainty in laboratories is to ensure that there is no competitive advantage, favouring one laboratory over another. The normal method of assessing measurement uncertainty is by carrying out inter-laboratory studies which follow an empirical method detailed in BS5725 [5, 7, 24-26].

There are several inter-laboratory and round robin studies, which identify the repeatability and reproducibility components [27-35]. They use the BS5725 assessment process to determine the repeatability (r) and reproducibility (R) compare the measurements obtained by each participant laboratory and with the reference values in ISO 140-2 [8]. It is important to note that the ISO r & R reference values are the product of several inter-laboratory studies, where a chosen element was reconstructed or remounted in each laboratory, measured, and the r and R values pooled. These uncertainty reference levels are being updated and in some additional cases redefined in the draft standard ISO/CD 12999-1 [9].

Most of the participants in inter-laboratory studies are national or commercial testing laboratories; each with their own in-house test facilities. The samples selected vary from lightweight partitions, for example see Farina et al [27], to heavyweight walls e.g. Luxemburg et al [35]. The samples are ideally reconstructed from readily available homogeneous materials or transported between and re-mounted in each laboratory. There are studies on field testing of sound insulation. These focus on existing buildings [31, 36, 37]. The studies are informative, but only comparable if they follow the BS5725 methodology. Closer inspection reveals deviations and inconsistencies in the test procedure, which can lead to discrepancies in the results. An example is the Delta study by Hoffmeyer et al [31], which undertook field measurements of separating walls between a pair of terraced houses. The reproducibility obtained showed good agreement with the reference values in ISO140-2. Further scrutiny shows that, to reduce the uncertainty caused by differences in test equipment, the 5 participating test laboratories in some instances used the same test kit. More importantly, due to time constraint, it was not possible to repeat all measurements. This meant that repeatability is not included in the reproducibility value as required by BS5725. It will therefore underestimate the value of “R” and is probably the reason the reproducibility was lower than the reference values. It is also noted that the reproducibility is calculated for each

37 room measured. The single test specimens are therefore identical, not only of similar construction. The reproducibility therefore does not incorporate the variability due to the reconstruction or remounting of the part. It therefore will underestimate the true reproducibility. Comparison with the reference values in ISO140-2 is erroneous. See Lang and also Hall [36, 38] where this also occurs.

Similar situations, where the test specimen is identical also occur in other research studies [39]. Their impact on the reproducibility may be acknowledged but often it is ignored, either because it is thought to be insignificant but also perhaps because it is not understood. It demonstrates that care is needed when attempting to draw direct comparisons between research on uncertainty.

1.4.3.2

Guide to the expression of uncertainty in measurement (GUM)

An alternative to the empirical method described in BS5725 is described in the guide to the expression of uncertainty in measurement (GUM) [6].

The method is based on modelling the uncertainties by constructing a combined budget which contains all input variables likely to contribute to the uncertainty in the measurement process. This method is considered in detail and leads to the development of a comprehensive list of factors likely to contribute to the total uncertainty in measuring airborne sound insulation in the field. These factors are often referred to as “input variables”.

1.4.3.3

Input variables

Informative research is cited if it describes variability in sound insulation performance of a construction, or if it estimates the variability in any measured component.

Where the research undertaken follows BS5725, the information obtained is limited to the terms defined in the standard. Repeatability is associated only with the instrumentation. What remains, referred to as the “between laboratory” variability, accounts for the rest of the variability in the measurement process.

The variables which contribute to this are many and may be difficult to quantify individually. An example of how the effects of one of these variables relating to the

38 mounting conditions of the test specimen is explored is by Schmitz et al [28]. In addition to calculating the r & R in an inter-laboratory study the mounting conditions of the specimen under test were investigated. The input variable related to the damping effect makes up the total reproducibility and its importance, though measurable, is based on its magnitude and its predictability. In this example Schmitz et al conclude that the influence of the total loss factor may be limited and will likely vary due to the specimen undergoing measurement. Wittstock et al [40] recommends the use of data without correcting for total loss factor. Flanking transmission is also considered by Cocchi et al [41] and Mahn [42], though it is also realised that when accounting for uncertainty in measurement, the variability due to this can be minimised by selecting a common construction across the test sample. This is not considered further in this thesis.

Other input variables can be identified, although only a few have been the focus of research and for some, their contribution to uncertainty is demonstrably small or can be minimised. An example is metrological conditions on site. The influence of temperature on measurement was highlighted by Scholes [43] and together with barometric pressure was the subject of recent research by Wittstock et al [44]. Humidity effects are provided in manufacturers information for the microphone, for example see the B&K handbook [45]. It is noted that the sound insulation value obtained may be affected by metrological conditions but their effects in this study can be minimised by ensuring the measurements are over a short time period, while the conditions are stable.

Others relate to the acoustics of the space and include room effects e.g. spatial variation in sound pressure level and discrete versus continuous sampling in the space; see Schroeder[46], Waterhouse [47-51], Lubman [49, 52-54] and Craik [55]. The uncertainty due to these influences is relatively large though predictable. Predicting the expected variability of sound pressure level is useful in assessing the consistency and reliability of the data obtained on site. It also helps indicate where site test conditions affect the measurement process.

The surface area of the test element and the room volume also contribute to the measured sound insulation. Theoretical formulae are provided in the International Standards ISO 140-4 [22] that can be used to determine the expected difference due to these factors. It is also possible to constrain the variability of these factors by testing similar room sizes. Other examples of how construction on site can affect the sound insulation performance of a test construction are detailed by Sewell [56] who

39 investigated the effects of a step or stagger on the performance of a construction. Though this does not apply to the survey samples in this thesis it indicates the limit of variability that can be expected from this construction feature. As previously stated the construction of the part being measured is also variable and, given a suitable test sample, can be calculated. This variability was referred to as “workmanship” and was calculated for a simple concrete floor by Craik et al [57, 58] the results of which inform this study.

Goydke et al in 2003 [59] assembled a number of input variables using the GUM approach and carried out a Monte-Carlo simulation, to calculate the uncertainty in sound insulation measurement. Wittstock also produced a model using GUM in 2005 [60] to predict measurement uncertainty but concluded that additional work was required to investigate the correlation effects between adjacent third octave bands. This additional work was completed by Wittstock in 2007 [61]. To apply an accurate estimate of uncertainty to any measurement an assumption about the independence of that measurement must be made. In the case of sound insulation measurement, it is known that the adjacent third octave bands are not independent and they have an unknown degree of correlation. It may be possible to estimate an upper limit for the correlation effects by assuming no correlation and apply a simulation process to determine the uncertainty and a correlation of 1 between third octave bands and apply the calculation techniques developed by Wittstock [60,8]. The correlation effects examined by Wittstock raise questions over the usefulness of GUM because correlation effects between third octave bands were found to dominate the measurement uncertainty of the single figure ratings. This evidence, together with its apparent tendency to significantly overestimate the measurement uncertainty shown by Lyn et al [62], suggests that GUM does not provide a suitable framework to assess uncertainty in sound insulation testing in the field.

1.4.3.4

Analysis of variance (ANOVA)

Available research has not identified or addressed the major components that make up reproducibility. BS5725 does not provide a solution for this and recent evidence shows the modelling method used in GUM appears unsuitable.

An alternative approach used in this thesis uses an empirical approach that incorporates analysis of variance (ANOVA) to identify the components of variance. ANOVA has

40 previously been used to good effect in acoustical research, two good examples of which are a laboratory sound insulation study by Taibo et al [63] and a round robin study on the measurement of absorption coefficients by Davern et al [64, 65]. The results demonstrate the strengths of the technique and offer insights into the contributions to variance which allows informed decisions to be made on improvements to the measurement process.

The main advantages of ANOVA are listed by Deldossi et al [66] and include the ability to determine the contribution of the operator and part and operator. Measurement system analysis has been developed as a specialist area of statistics by the Automobile Industries Action Group (AIAG) and is used in industry as a quality control tool. The ANOVA method used is called a Gauge Repeatability and Reproducibility study (GRR) and the appropriate one, for the purpose of this thesis study, is described by Burdick et al [67] as a Balanced Two Factor Crossed random model with interaction. It is this model and additional information provided by Montgomery[68-70] , Borror [71] and Burdick[72, 73] which forms the analytical framework, to separate out and quantify the components of variance in sound insulation measurement and their confidence intervals for timber and concrete floors.