Measurement uncertainty associated with

Combined Standard Uncertainty is the standard uncertainty that is obtained by combining (root of the sum of squares) individual standard measurement uncertainties associated with the input quantities in a measurement model. 

To apply this method, the scientist measures the Siv Sr and 8,Rb/8 Sr ratios in several samples and plots the results on a 87Rb-87Sr evolution diagram. Each data point has a measurement uncertainty associated with it, so the points will not fell exactly on a straight line even in the... 

The estimates obtained by applying Eqs. 8-10 are intended to give a first estimate of the measurement uncertainty associated with a particular parameter. If such estimates of the uncertainty are found to be a significant contribution to the overall uncertainty for the method, further study of the effect of the parameters is advised, to establish the true relationship between changes in the parameter and the result of the method. However, if the uncertainties are found to be small compared to other uncertainty components (i.e. the uncertainties associated with precision and trueness) then no further study is required. 

Finally, it should be stressed that at present only the measurement uncertainty associated with the analytical work is required in the common reporting template, but research regarding the influence of the sampling process is progressing and in the future the uncertainty associated with sampling will also have to be taken into account. 

Analytical results for the determination of antibiotic residues in food, in common with results generated in other laboratories or branches of analytical chemistry, must be reliable and comparable. It is a requirement for laboratories accredited under the ISO/IEC 17025 quality system that the measurement uncertainty associated with a result should be made available and reported if it is required by the client, is relevant to the validity of the test results, or may affect compliance with a specification, for example, compliance with a maximum residue limit (MRL) for antibiotics. The Codex Alimentarius Commission also recommends that laboratories provide their customers on request with information on the measurement uncertainty or a statement of confidence associated with quantitative results for veterinary drug residues. The relevant sections in ISO 17025 are quoted below ... 

Measurement uncertainty is defined by the International Standards Organization (ISO) as a parameter associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand. The uncertainty is expressed as a range within which the tme value of the measurand is believed to lie. In a practical sense, measurement uncertainty can be considered as a measure of the quality of measurement results. It gives an answer to the question How well does the result represent the value of the quantity being measured Therefore, the measurement uncertainty associated with a result is an essential part of quantitative results, and along with traceability, it can allow users to assess the reliability of the result and compare results among different sources or with reference values. 

Description Uncertainty sets the limits within which a result is regarded as accurate, that is, precise and true [27]. The combined measurement uncertainty is obtained using the individual (standard) measurement uncertainties associated with the input quantities. This means specifically that all calibrations or corrections have intrinsic uncertainty components, which have to be considered in the combined measurement uncertainty of a measurement result. 

Each of the input parameters has an uncertainty associated with it. This uncertainty arises from the inaccuracy in the measured data, plus the uncertainty as to what the values are for the parts of the field for which there are no measurements. Take for example a field with five appraisal wells, with the following values of average porosity for a particular sand ... 

When providing input for the STOMP calculation a range of values of porosity (and all of the other input parameters) should be provided, based on the measured data and estimates of how the parameters may vary away from the control points. The uncertainty associated with each parameter may be expressed in terms of a probability density function, and these may be combined to create a probability density function for STOMP. 

Starting with the quantum-mechanical postulate regarding a one-to-one correspondence between system properties and Hemiitian operators, and the mathematical result that only operators which conmuite have a connnon set of eigenfiinctions, a rather remarkable property of nature can be demonstrated. Suppose that one desires to detennine the values of the two quantities A and B, and that tire corresponding quantum-mechanical operators do not commute. In addition, the properties are to be measured simultaneously so that both reflect the same quantum-mechanical state of the system. If the wavefiinction is neither an eigenfiinction of dnor W, then there is necessarily some uncertainty associated with the measurement. To see this, simply expand the wavefiinction i in temis of the eigenfiinctions of the relevant operators... 

Uncertainty on tlie other hand, represents lack of knowledge about factors such as adverse effects or contaminant levels which may be reduced with additional study. Generally, risk assessments carry several categories of uncertainly, and each merits consideration. Measurement micertainty refers to tlie usual eiTor tliat accompanies scientific measurements—standard statistical teclmiques can often be used to express measurement micertainty. A substantial aniomit of uncertainty is often inlierent in enviromiiental sampling, and assessments should address tliese micertainties. There are likewise uncertainties associated with tlie use of scientific models, e.g., dose-response models, and models of environmental fate and transport. Evaluation of model uncertainty would consider tlie scientific basis for the model and available empirical validation. 

Our concepts of petroleum reserves and resources and their measurements are changing to reflect the uncertainty associated with these terms. Petroleum reseiwes have been largely calculated deterministically (i.e. single point estimates with the assumption of certainty). In the past decade, reseiwe and resource calculations have incorporated uncertainty into their estimates using probabilistic methodologies. One of the questions now being addressed are such as how certain arc you that the rcsciwcs you estimate arc the actual reseiwes and what is the range of uncertainty associated with that estimate New techniques arc required to address the critical question of how much petroleum we have and under what conditions it can be developed. 

Anyone making a measurement has a responsibility to indicate the uncertainty associated with it. Such information is vital to someone who wants to repeat the experiment or judge its precision. The three volume measurements referred to earlier could be reported as... 

Strategy Assume each student reported the mass in such a way as to indicate the uncertainty associated with the measurement Then follow a common sense approach. 

Each measuring device has limitations that fix its accuracy. Hence every individual observation has some uncertainty associated with it. Since every regularity of nature is discovered through observations, every regularity (law, rule, theory) has uncertainty attached to it. 

The ITS-90 scale is designed to give temperatures T90 that do not differ from the Kelvin Thermodynamic Scale by more than the uncertainties associated with the measurement of the fixed points on the date of adoption of ITS-90 (January 1, 1990), to extend the low-temperature range previously covered by EPT-76, and to replace the high-temperature thermocouple measurements of IPTS-68 with platinum resistance thermometry. The result is a scale that has better agreement with thermodynamic temperatures, and much better continuity, reproducibility, and accuracy than all previous international scales. 

The data in each column of experimental matrix D, are scaled by dividing that column by the uncertainty associated with that measurement resulting in the matrix D ... 

In Figs. 24 and 25 we show the measured double differential cross sections for electron emission at zero degrees in collisions of 100-keV protons with He and H2 [39] compared to CDW-EIS predictions [39]. Uncertainties associated with the experimental results vary from 1% near the electron capture to the continuum peak to about 15% near the extreme wings of the distribution. These results have been scaled to provide a best fit with CDW-EIS calculations. In both cases there is satisfactory agreement between the CDW-EIS calculations and experiment, particularly with excellent agreement for electrons with velocities greater than v, where v is the velocity of the projectile. For lower-energy electrons the eikonal description of the initial state may have its limitations, especially for lower-impact parameters. 

As mentioned in Section 4.3.3, bias is the difference between the mean value (x) of a number of test results and an accepted reference value (xo) for the test material. As with all aspects of measurement, there will be an uncertainty associated with any estimate of bias, which will depend on the uncertainty associated with the test results Uj and the uncertainty of the reference value urm> as illustrated in Figure 4.7. Increasing the number of measurements can reduce random effects... 

As we have seen in previous sections, the result of a measurement is not complete unless an estimate of the uncertainty associated with the result is available. In any measurement procedure, there will be a number of aspects of the procedure that will contribute to the uncertainty. Uncertainty arises due to the presence of both random and systematic errors. To obtain an estimate of the uncertainty in a result, we need to identify the possible sources of uncertainty, obtain an estimate of their magnitude and combine them to obtain a single value which encompasses the effect of all the significant sources of error. This section introduces a systematic approach to evaluating uncertainty. 

To allow the uncertainty to be evaluated effectively, a model equation describing the method of analysis is required. The starting point is the equation used to calculate the final result. Intially, we will need to consider the uncertainties associated with the parameters that appear in this equation. It may be necessary to add terms to this equation (i.e. expand the model) to include other parameters that may influence the final result and therefore contribute to the measurement uncertainty. 

One common characteristic of many advanced scientific techniques, as indicated in Table 2, is that they are applied at the measurement frontier, where the net signal (S) is comparable to the residual background or blank (B) effect. The problem is compounded because (a) one or a few measurements are generally relied upon to estimate the blank—especially when samples are costly or difficult to obtain, and (b) the uncertainty associated with the observed blank is assumed normal and random and calculated either from counting statistics or replication with just a few degrees of freedom. (The disastrous consequences which may follow such naive faith in the stability of the blank are nowhere better illustrated than in trace chemical analysis, where S B is often the rule [10].) For radioactivity (or mass spectrometric) counting techniques it can be shown that the smallest detectable non-Poisson random error component is approximately 6, where ... 

We will be dealing with two types of numbers in chemistry—exact and measured ones. Exact values have no uncertainty associated with them. They are... 

We deal with two types of numbers in chemistry—exact and measured. Exact values are just that—exact, by definition. There is no uncertainty associated with them. There are exactly 12 items in a dozen and 144 in a gross. Measured values, like the ones you deal with in the lab, have uncertainty associated with them because of the limitations of our measuring instruments. When those measured values are used in calculations, the answer must reflect that combined uncertainty by the number of significant figures that are reported in the final answer. The more significant figures reported, the greater the certainty in the answer. 

K. K. Irikura, R. D. Johnson III, R. Kacker. Uncertainty Associated with Virtual Measurements from Computational Quantum Chemistry Models. Metrologia 2004, 41, 369-375. 

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