Data interpretation measurement uncertainty

The next fonr chapters are devoted to various aspects of data interpretation, data presentation, and quahty assurance. Chapter 9 considers interpretation of data for radionuchde identification by decay scheme. Chapter 10 reviews the important topics of data calculation, measurement uncertainty, data evaluation, and reporting the results. Chapter 11 describes the quality assurance plan that must govern all laboratory operations. Chapter 12 discusses methods diagnostics to correct the analytical and measurement problems that can be expected to plague every laboratory. 

This chapter deals with handling the data generated by analytical methods. The first section describes the key statistical parameters used to summarize and describe data sets. These parameters are important, as they are essential for many of the quality assurance activities described in this book. It is impossible to carry out effective method validation, evaluate measurement uncertainty, construct and interpret control charts or evaluate the data from proficiency testing schemes without some knowledge of basic statistics. This chapter also describes the use of control charts in monitoring the performance of measurements over a period of time. Finally, the concept of measurement uncertainty is introduced. The importance of evaluating uncertainty is explained and a systematic approach to evaluating uncertainty is described. 

Measurement uncertainty is increasingly gaining attention, in particular in the framework of accreditation. The new accreditation standard ISO/IEC 17025 [17], which has been in force from December 2002 on, contains clear requirements on the estimation of MU and when and how it should be stated in test reports. ISO/IEC 17025 requires MU to be reported when required by the client and when relevant to the application and interpretation of the measurement results in the framework of certain specifications or decision limits. The MU should be readily available and reported together with the result as X U, where U is the expanded uncertainty [17, 47, 51, 54]. Also Eurachem and CCMAS within the Codex Alimentarius deal with MU as a separate issue [14,18-20]. Some even claim that MU will become the main unifying principle of analytical data quality [37]. 

Second, there is no unique scheme of data interpretation. The process of inference always remains arbitrary to some extent. In fact, all the existing DDT data combined still allow for an infinite number of models that could reproduce these data, even if we were to disregard the measurement uncertainties and take the data as absolute numbers. Although this may sound strange, it is less so if we think in terms of degrees of freedom. Let us assume that there are one million measurements of DDT concentration in the environment. Then a model which contains one million adjustable parameters can, in principle, exactly (that is, without residual error) reproduce these data. If we included models with more adjustable parameters than observa-... 

In presentation and interpretation of results, NARL aims for objectivity, clear presentation, and statistical data treatment that is transparent to participants, internationally accepted and metrologically sound. Sources of chemical standards, statements concerning traceability and estimates of measurement uncertainty are included in the study report. 

The ISO 5725 standard was used to interpret the data. Even if the main purpose of this standard is related to the validation of a method, it can be used to evaluate some components of the measurement uncertainty. The homogeneity of the population of results, in terms of mean and standard deviation was determined using statistical tests (Cochran and Grubbs). A few laboratories were rejected after the tests. Tables 3 and 4 present the comparison of overall performance of laboratories when working with usual and metrological calibrations solutions. 

Unfortunately the theory, when used for data interpretation, is based on many simplifications that are not always valid. The success of the method depends on the significance of the axial dispersion and the interfacial mass transfer and on the accuracy of the description of these effects. A comparative study of different measuring technique by [25] has shown, for the chromatographic method, that experimental uncertainties may lead to significantly broader confidence limits for the diffusion coefficients than for measurements in single pellets in a diffusion cell. 

The estimation of uncertainty replaces a full validation of the analytical method. It generates the necessary information at the right time. The statistical information received from the analysis can be used for the interpretation of the data and finally the analysis is designed to the customers needs. In this case measurement uncertainty is a good alternative to validation. 

The need for data analysis in any measurement science is a consequence of measurement uncertainty. Having made our measurement, and before we try to interpret the result, an immediate question is, or should be, How reliable is the result The nonscientific public is used to accepting measurements at face value. We rarely question... 

FIGURE 4.24 (a) Calculated profiles for HNO, NO2, and NO (solid lines) and N2O5 (dashed line) for the ATMOS simulation at 47° S, sunrise, assuming gas-phase chemistry only (McElroy et al., 1992). ATMOS data are indicated by the circles, which have been connected by dotted lines for convenience of interpretation. Error bars represent the lo- estimate of the measurement uncertainty, (b) Same as for part (a) except the simulation includes the heterogeneous hydrolysis of N2O, proceeding with an efficiency of y = 0.06. Reprinted from McElroy et al. (1992) with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB. UK. 

Nowadays we are able to obtain results for measurands 1-6, we might end up with a value for measurands 7-9, but a realistic measurement uncertainty will be far too large to identify any significant difference in the tungsten isotopic composition between parts of the solar system. However, values for measurands 1-8 or even 9 can be found in the literature, but the validity of the interpretations based on uncertain data needs to be questioned. 

An example adapted from Verneuil, et al. (Verneuil, V.S., P. Yan, and F. Madron, Banish Bad Plant Data, Chemical Engineeiing Progress, October 1992, 45-51) shows the impact of flow measurement error on misinterpretation of the unit operation. The success in interpreting and ultimately improving unit performance depends upon the uncertainty in the measurements. In Fig. 30-14, the materi balance constraint would indicate that S3 = —7, which is unrealistic. However, accounting for the uncertainties in both Si and S9 shows that the value for S3 is —7 28. Without considering uncertainties in the measurements, analysts might conclude that the flows or model contain bias (systematic) error. 

While over the past ten years, our ability to measure U-series disequilibria and interpret this data has improved significantly it is important to note that many questions still remain. In particular, because of uncertainties in the partition coefficients, fully quantitative constraints can only be obtained when more experimental data, as a function of P and T as well as source composition, become available. Furthermore, the robustness of the various melting models that are used to interpret the data needs to be established and 2D and 3D models need to be developed. However, full testing of these models will only be possible when more comprehensive data sets including all the geochemical parameters are available for more locations and settings. 

Several significant challenges exist in applying data analysis and interpretation techniques to industrial situations. These challenges include (1) the scale (amount of input data) and scope (number of interpretations) of the problem, (2) the scarcity of abnormal situation exemplars, (3) uncertainty in process measurements, (4) uncertainty in process discriminants, and (5) the dynamic nature of process conditions. 

Unless the coverage of adsorbate is monitored simultaneously using spectroscopic methods with the electrochemical kinetics, the results will always be subject to uncertainties of interpretation. A second difficulty is that oxidation of methanol generates not just C02 but small quantities of other products. The measured current will show contributions from all these reactions but they are likely to go by different pathways and the primary interest is that pathway that leads only to C02. These difficulties were addressed in a recent paper by Christensen and co-workers (1993) who used in situ FT1R both to monitor CO coverage and simultaneously to measure the rate of C02 formation. Within the reflection mode of the IR technique used in this paper this is not a straightforward undertaking and the effects of diffusion had to be taken into account in order to help quantify the data obtained. 

To eliminate the above uncertainties in the interpretation of the transport data, Hall-effect measurements were combined with layer removal on homogeneously doped n-type layers (Johnson and Herring, 1988a). The... 

All fire smoke is toxic. In the past two decades, a sizable research effort has resulted in the development of over twenty methods to measure the toxic potency of those fire smokes (6). Some methods have been based on determinations of specific chemical species alone. Values for the effect (e.g., lethality) of these chemicals on humans are obtained from (a) extrapolation from preexisting, lower concentration human exposure data or from (b) interpretation of autopsy data from accident and suicide victims. The uncertainty in these methods is large since ... 

Figure 10. Comparison of isotopic fractionations determined between Fe(II)aq and Fe carbonates relative to mole fraction of Fe from predictions based on spectroscopic data (Polyakov and Mineev 2000 Schauble et al. 2001), natural samples (Johnson et al. 2003), DIR (Johnson et al. 2004a), and abiotic formation of siderite under equilibrium conditions (Wiesli et al. 2004). Fe(II)aq exists as the hexaquo complex in the study of Wiesli et al. (2004) hexaquo Fe(II) is assumed for the other studies. Total cations normalized to unity, so that end-member siderite is plotted at Xpe = 1.0. Error bars shown reflect reported uncertainties analytical errors for data reported by Johnson et al. (2004a) and Wiesli et al. (2004) are smaller than the size of the symbol. Fractionations measured on bulk carbonate produced by DIR are interpreted to reflect kinetic isotope fractionations, whereas those estimated from partial dissolutions are interpreted to lie closer to those of equilibrium values because they reflect the outer layers of the crystals. Also shown are data for a Ca-bearing DIR experiment, where the bulk solid has a composition of q)proximately Cao.i5Feo.85C03, high-Ca and low-Ca refer to the range measured during partial dissolution studies (Johnson et al. 2004a). Adapted from Johnson et al. (2004a).

However, for Re < 10 the experimental values of Nu fall sharply with decreasing Reynolds number, well below the theoretical minimum of Nu = 2. This is attributable in part to experimental difficulties, for example fhe problem of measuring particle temperature, and in part to the theoretical interpretation of the data. Botterill (1975) posed the question of what exactly is measured by a bare wire thermocouple inserted in a fluidized bed. Despite the uncertainties in the experimental evidence, Botterill concluded that it probably does indeed measure the particle temperature. This was the assumption of Smith and Nienow (1982) who used bare wire thermocouples to measure bed particle temperatures during fluidized bed granulation. In the region Re < 10, as Kunii and Levenspiel (1991) indicate, the data can be represented by an expression due to Kothari... 

Statistically, Cv is a measure of reliability, or evaluated from the opposite but equivalent perspective, it is also indicative of the degree of uncertainty. It is alternatively interpreted as the inverse ratio of data to noise in the data in signalprocessing-related applications. Thus, it is apparent that a small value of Cv is desirable as it signifies a small degree of noise or variability (e.g., in a data set) and, hence, reflects low uncertainty. 

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