Uncertainties or Errors of Measurements

Uncertainties of Gibbs excess masses (3.52) as represented by their mean square deviations (MSD) (a ) can be calculated by applying the Gauss Law of propagation of uncertainty of error to eqs. (3.51) and (3.52) respectively  

To provide an overview of all parameters to be measured and uncertainties to be considered we list them in a table  

As can be recognized from eqs. (3.55a, b, 3.56a, b) accurate measurements of gas concentrations (y, yf) or, equivalently (w, wf) are very important in order to get small dispersions of adsorbate s mass mfgg. Due to experience it also can be said that accurate measurements of the system s pressure (p) and temperature (T) are essential, whereas the influence of the real gas factor (Z) and its uncertainly often is rather small. Given MSDs of gas concentrations =ayjf 10, of microbalance measurement (on/f2) 10 and of all the 

As a supplement we add pure and binary mixture data taken for adsorption equilibria in a liquid-solid system. This is to be understood as an example demonstrating that microbalances can also provide information on liquid adsorption processes, a field which in view of protein adsorption phenomena for separation certainly has potential for future development. 

Data show that the AC has a good selectivity for CO2 although its gas concentration is only yco2 = 8 %, its concentration in the adsorbate is about xco2 = 25 %. Hence this AC can be considered as a sorbent for purification of low energy gas consisting of(CH4, CO2, N2) from CO2. 

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As has been outlined in Chap. 2 uncertainties or errors of measured data constitute an important part of any kind of experimental work and hence always should be considered [2.18], However, for sake of brevity we here provide the reader only with the formulae allowing one to calculate uncertainties or mean square deviations (MSD) (cj ge) of th Gibbs excess mass (m g) of an adsorbate which has been measured gravimetrically by using a two beam balance. This mass can be calculated from eq. (3.14) combined with eqs. (3.10) and (3.13). By using Gauss law ofpropagation of uncertainties we have... 

MSBs should be cleaned from time to time as small particles, for example activated carbon or zeolite powders may be transferred from the sorbent basket to the permanent magnet. Here they can change the magnetic field permanently and by this cause systematic uncertainties or errors of measurement. Once these are detected, they may be corrected by recalibrating the zero load position of the balance, cp. Fig. 4.12. 

As already outlined in Chap. 2, Sects. 2.3 and 4.3 uncertainties or errors of measurements are important quantities for any kind of experimental work and should be provided for any quantity measured. Consequently we here denote the dispersions or mean square deviations (MSD), i = 1, 2 of the... 

The outer layer of samples (gloves, coveralls, socks, face wash, hand wash, and hat) allowed measurement of the complete dose encountered on the outside of the protective clothing without any subsampling. This eliminated any uncertainty or error due to the highly variable deposition of residues across the body surface. This is the upper limit of the potential dose that could be encountered by the operator, and it is used to assess the effectiveness of the protective clothing and other preventive measures. 

Every measured number, however, no matter how carefully measured, has some degree of uncertainty. This uncertainty (or margin of error) in a measurement can be illustrated by the two... 

Uncertainty. Synonym error. A measure of the the inherent variability of repeated measurements of a quantity. A prediction of the probable variability of a result, based on the inherent uncertainties in the data, found from a mathematical calculation of how the data uncertainties would, in combination, lead to uncertainty in the result. This calculation or process by which one predicts the size of the uncertainty in results from the uncertainties in data and procedure is called error analysis. 

Regardless of the care taken in measuring a variable, the measurement is subject to uncertainty or errors. The reliability of an instrument is a critical factor in its selection and in the interpretation of collected data. There are few quantities that are known or can be measured precisely. One exception is the speed of light in a vacuum that is exactly 299 792 458 ms . For other quantities, the uncertainty in the value is expressed in two ways the first is to define the value with a limited number of digits (or figures) and the second is to include a second number indicating the probability that the measured value lies within a defined interval—its uncertainty, which is discussed in detail later in this chapter. It represents an interval in which the true value of a measurement lies. If the uncertainty of the measured volume in a graduated cylinder equals 1 ml. 

Uncertainty expresses the range of possible values that a measurement or result might reasonably be expected to have. Note that this definition of uncertainty is not the same as that for precision. The precision of an analysis, whether reported as a range or a standard deviation, is calculated from experimental data and provides an estimation of indeterminate error affecting measurements. Uncertainty accounts for all errors, both determinate and indeterminate, that might affect our result. Although we always try to correct determinate errors, the correction itself is subject to random effects or indeterminate errors. 

Every measured quantity or component in the main equations, Eqs. (12.30) and (12.31), influence the accuracy of the final flow rate. Usually a brief description of the estimation of the confidence limits is included in each standard. The principles more or less follow those presented earlier in Treatment of Measurement Uncertainties. There are also more comprehensive error estimation procedures available.These usually include, beyond the estimation procedure itself, some basics and worked examples. 

The records required are only for formal calibrations and verification and not for instances of self-calibration or zeroing using null adjustment mechanisms. While calibration usually involves some adjustment to the device, non-adjustable devices are often verified rather than calibrated. However, as was discussed previously, it is not strictly correct to regard all calibration as involving some adjustment. Slip gages and surface tables are calibrated but not adjusted. An error record is produced to enable users to determine the uncertainty of measurement in a particular range or location and compensate for the inaccuracies when recording the results. 

The precision stated in Table 10 is given by the standard deviations obtained from a statistical analysis of the experimental data of one run and of a number of runs. These parameters give an indication of the internal consistency of the data of one run of measurements and of the reproducibility between runs. The systematic error is far more difficult to discern and to evaluate, which causes an uncertainty in the resulting values. Such an estimate of systematic errors or uncertainties can be obtained if the measuring method can also be applied under circumstances where a more exact or a true value of the property to be determined is known from other sources. 

First of all, we should make a clear distinction between accuracy and precision. Accuracy is a measure of how close a given value is to the true value, whereas precision is a measure of the uncertainty in the value or how reproducible the value is. For example, if we were to measure the width of a standard piece of paper using a ruler, we might find that it is 21.5 cm, give or take 0.1 cm. The give or take (i.e., the uncertainty) value of 0.1 cm is the precision of the measurement, which is determined by how close we are able to reproduce the measurement with the ruler. However, it is possible that when the ruler is compared with a standard unit of measure it is found to be in error by, say, 0.2 cm. Thus the accuracy of the ruler is limited, which contributes to the uncertainty of the measurement, although we may not know what this limitation is unless we can compare our instrument to one we know to be true. 

The more sophisticated treatment of Ingle and Crouch [7] comes very close but also misses the mark for an unexplained reason they insert the condition ... it is assumed there is no uncertainty in measuring Ert and Eot... . Now in fact this could happen (or at least there could be no variation in AEr) for example, if one reference spectrum was used in conjunction with multiple sample spectra using an FTIR spectrometer. However, that would not be a true indication of the total error of the measurement, since the effect of the noise in the reference reading would have been removed from the calculated SD, whereas the true total error of the reading would in... 

Accuracy is often used to describe the overall doubt about a measurement result. It is made up of contributions from both bias and precision. There are a number of definitions in the Standards dealing with quality of measurements [3-5]. They are only different in the detail. The definition of accuracy in ISO 5725-1 1994, is The closeness of agreement between a test result and the accepted reference value . This means it is only appropriate to use this term when discussing a single result. The term accuracy , when applied to a set of observed values, describes the consequence of a combination of random variations and a common systematic error or bias component. It is preferable to express the quality of a result as its uncertainty, which is an estimate of the range of values within which, with a specified degree of confidence, the true value is estimated to lie. For example, the concentration of cadmium in river water is quoted as 83.2 2.2 nmol l-1 this indicates the interval bracketing the best estimate of the true value. Measurement uncertainty is discussed in detail in Chapter 6. 

In contrast, a systematic error remains constant or varies in a predictable way over a series of measurements. This type of error differs from random error in that it cannot be reduced by making multiple measurements. Systematic error can be corrected for if it is detected, but the correction would not be exact since there would inevitably be some uncertainty about the exact value of the systematic error. As an example, in analytical chemistry we very often run a blank determination to assess the contribution of the reagents to the measured response, in the known absence of the analyte. The value of this blank measurement is subtracted from the values of the sample and standard measurements before the final result is calculated. If we did not subtract the blank reading (assuming it to be non-zero) from our measurements, then this would introduce a systematic error into our final result. 

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