Uncertainty budgeting example

The relative uncertainties of the difference or ratio between two values, for example, are often far smaller than the relative uncertainty of either value which would not appear in the uncertainty budget... 

Determination of amount of substance often requires measurements of different properties, for example sample mass, on a balance compared to a mass reference analyte identity by comparison to a reference, perhaps using a spectrometer and a database of known compounds and analyte quantitation by comparison to a different reference, perhaps a reference material. Each property of the result should be traceable, and each may contribute uncertainty to the reported result. Thus, claims of traceability of a result must include not only a description of the references and uncertainty budgets for comparison to them, but also a description of the scope of traceability. 

The following example of a high-accuracy INAA determination of Cr in SRM 1152a Stainless Steel illustrates the use of an uncertainty budget and the resulting observation of a satisfactory measurement outcome (Zeisler et al. 2005). The experiment had been designed to... 

Table 5.7 shows a notional uncertainty budget based on Equation (5.74). The data in the table are quoted by way of examples they should not be taken too seriously. Indeed, even the choice of items may not be relevant to other detector and analysis systems. The procedure one should follow is as follows ... 

Table 5.7 An example of an uncertainty budget based on Equation (5.74) ... 

The example shown is incomplete in that it does not take into account the degrees of freedom of each of the uncertainty items. Unless the overall number of degrees of freedom is infinite, calcnlation of the expanded uncertainty by multiplying by the factors derived from Table 5.1 would not be valid. It would not be appropriate to go into such matters here and for a fuller explanation of uncertainty budgets other sources should be consulted (e.g. Bell, 2001 and UKAS, 1997). It should be said that, for the majority of uncertainty items in a gamma spectrometry budget, infinite degrees of freedom can be assumed. 

Table 6.1 Example of an uncertainty budget for uncorrelated input quantities (Kacker, Sommer, and Kessel, 2007).

Reporting of the results of the analysis, the uncertainty budget, giving all necessary information to recapitulate it, for example, in the form of a table (Table 6.1). 

Example of Uncertainty Budget Estimation When Using Isotope Dilution... 

The subject of imcertainty of measiuement in spectrophotometric measiuements of the color of plastics is reviewed. Definitions of the components of imcertainty are offered, and methods of assessment and calculation of the components of uncertainty are revealed so that the user might prepare an uncertainty budget for one s own measurement system. The practical apphcations of total measurement system uncertainty in industrial apphcations are addressed. Finally, example data sets are presented from measurements of several colored plastic materials... 

This simple two component model for the Fe isotope composition of seawater does not consider the effects of the Fe isotope composition of dissolved Fe from rivers or from rain. Although the dissolved Fe fluxes are small (Fig. 19) the dissolved fluxes may have an important control on the overall Fe isotope composition of the oceans if they represent an Fe source that is preferentially added to the hydrogenous Fe budget that is ultimately sequestered into Fe-Mn nodules. In particular riverine components may be very important in the Pacific Ocean where a significant amount of Fe to the oceans can be delivered from rivers that drain oceanic islands (Sholkovitz et al. 1999). An additional uncertainty lies in how Fe from particulate matter is utilized in seawater. For example, does the solubilization of Fe from aerosol particles result in a significant Fe isotope fractionation, and does Fe speciation lead to Fe isotope fractionation ... 

Dr. Mitchell adds, You could give a rather amusing example of that and that would be discussions of the 1986 budget deficit, which, of course, is the difference between two very large numbers each of which have a considerable amount of uncertainty on it. 

There are three main parameters that influence the inflation correction mismatch. Firstly, the uncertainty in the maintenance planning. For example, the resurfacing of pavement, it covers the largest part of the maintenance budget in motorway projects. It is planned in a specific year in the exploitation period but there is no accurate information on deterioration over time and therefore it has a wide bandwidth in the maintenance planning. The index formula lacks the ability to cope with this uncertainty, which is one of the reasons for the index-gap. 

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