Uncertainty relative

TRANSITION-STATE THEORY ABSOLUTE TEMPERATURE ABSOLUTE UNCERTAINTY RELATIVE UNCERTAINTY ABSOLUTE ZERO ABSORBANCE... 

For addition and subtraction, use absolute uncertainty. Relative uncertainty can be found at the end of the calculation. 

Figure 8. Model-derived elevation uncertainty relative to the weighted mean elevation as a function of A(S180 ) resulting from uncertainty in the starting T and RH of orographically forced ascent of airmasses. Curves are lc (light gray), 2c (medium gray). The difference between the median (dark gray) and weighted mean is also shown.

By contrast, satisfactory practical mechanical, electrical, optical, and thermal measurements are often made adequately for the purpose at hand, even if less accurate than corresponds to the optimum achievable uncertainty relative to true value expressed under SI. Routine measurements in these fields can thus be expressed conveniently in terms of the relevant SI unit to an uncertainty determined principally by the uncertainty of the practical measurement in the field. 1 Harmony among most physical and engineering measurements can be achieved to the uncertainty of the measurement in the field by traceability of all measures to the SI unit without invoking an intermediate standard 2 or RM. 

In physical science there are occasionally instances where measurements need to be more reproducible than the lowest achievable uncertainty relative to the true value in SI units. Chemists, not just occasionally but as a rule, must achieve traceability of measurements by use of some standard, a reference material, a reference instrument, or a reference method [18], The spread of these measurements made in different laboratories is often required to be smaller than the uncertainty with respect to true value. Nevertheless, one should state any such measurement in moles along with an assessment of the quality of its reproducibility. Such a statement will be different depending on its applicability within a laboratory, between laboratories, for a given method and environment, or in relation to an RM. When an RM is used, one must also include its often larger uncertainty of traceability to the SI unit. This uncertainty of the value of the RM must be included in the total uncertainty of the unknown. 

Let us begin with the ISO definition [9] A calibration is a set of operations that establish, under specified conditions, the relationship between values of quantities indicated by a measuring instrument or measuring system, or values represented by a material measure or reference material, and the corresponding values realized by standards. Applied to amount measurements, the standards would then be the values assigned to the RMs (of defined composition) at the stated uncertainty relative to the true value of the property, expressed in SI units, or relative to an internationally recognized, certified standard RM for the relevant property, range, and matrix composition. 

Uncertainty components Evaluation of the uncertainty component Uncertainty (rel) ... 

Precision %RSD< 15 % at>3 levels n>5 at each level %RSD<20 % at LLOQ %RSD<20% n=4-7 CV<2.2 % Uncertainty evaluation Coefficient of variation (CV) 1 % Uncertainty of volumetric error 0.3 % Uncertainty of reference standard 0.1 % Uncertainty of weighing 0.5 % Uncertainty of other systematic errors Combined standard uncertainty Coverage factor Expanded uncertainty Relative expanded uncertainty (%) Intraassay CV=2-9 % Interassay CV=4-12%... 

The subjectivity of the qualitative assessment (see section 5.1.2.2) also opens the possibility of conscious or unconscious bias by the assessor. For this reason, it is desirable to report the steps from (1) to (5) in a transparent way so that others can review and evaluate the judgements that have been made. This has the advantage that it is always possible to do and that it is sufficient if the result is clearly conservative (protective) overall. However, it has disadvantages with regard to subjectivity when the outcome is not clearly conservative and when using separate uncertainty factors for many parameters that can lead to compounding conservatism. If an exposure/risk assessment contains a number of conservative assumptions, then the above table is likely to end up with an overall assessment that the true risk is probably lower than the quantitative estimate. However, if the assessment attempts to use realistic estimates/distributions for most inputs, then a table of unquantified uncertainties is the likely result. This undoubtedly is a difficulty for decision-makers unless the assessor can evaluate the combined uncertainty relative to the decision-makers decision threshold. 

Japan imports coking coals from the United States, Canada, Australia and many other foreign countries. Future supplies of coking coals involves some uncertainty relative to procurement of good-quality coals in sufficient quantities. Various measures have been examined to solve this problem in Japan, One such measure is the expansion of the scope of raw materials used for coke-making. 

The actual quantity of O2 predicted on the basis of model calculations appears to vary wildly depending on the assumed gas phase chemistry, the role of O2 reactions with Fe in the early oceans, and the transport mechanism. Oxygen levels reported as the result of recent theoretical calculations (Levine, 1982) range between lO " and 10" of the present atmospheric level (PAL). Enhanced levels of solar activity would have significantly increased the prebiological O2 levels. At the current level of uncertainty, relatively little can be deduced about the actual chemical mechanism responsible for fixing the O2 density prior to the establishment of photosynthetic sources of oxygen. 

Tactical decisions are primarily supply chain planning decisions and are made in a time horizon of moderate length, generally as monthly or quarterly decisions, covering a planning horizon of one or two years. Thus, these decisions are typically made in an environment characterized by less uncertainty relative to strategic decisions, but where the effects of uncertainty still are not inconsequential. Examples of tactical decisions include the following ... 

By definition, the last significant digit obtained from an instrument or a calculation has an associated uncertainty. Rounding leads to a nominal value, but it does not allow for expression of the inherent uncertainty. To do this, the uncertainties of each contributing factor, device, or instrument must be known and accounted for. For measuring devices such as analytical balances, Eppen-dorf pipets, and flasks, that value is either displayed on the device, supplied by the manufacturer, or determined empirically. Because these values are known, it is also possible to estimate the uncertainty (i.e., potential error) in any combined calculation. The only caveat is that the units must be the same. On an analytical balance, the imcertainty would be listed as 0.0001 g, whereas the rmcertainty on a volumetric flask would be reported as 0.12 mL. These are absolute uncertainties that cannot be combined as is, because the units do not match. To combine uncertainties, relative uncertainties must be used. These can be expressed as "1 part per. .." or as a percentage. That way, the units cancel and a relative imcertainty results, which may then be combined with other uncertainties expressed the same way (i.e., as unitless value). 

Think About It A common error is expressing the mass of the particle in grams instead of kilograms, but you should discover this inconsistency if you check your unit cancellation carefully. Remember that if one uncertainty is smaU. the other must be large. The uncertainty principle applies in a practical way only to submicroscopic particles. In the case of a macroscopic object, where the mass is much larger than that of an electron, small uncertainties, relative to the size of the object, are possible for both position and velocity. 

The coefficient of variation measures the size of the uncertainty relative to demand. It captures the fact that a product with a mean demand of 100 and a standard deviation of 100 has greater demand uncertainty than a product with a mean demand of 1,000 and a standard deviation of 100. Considering the standard deviation alone cannot capture this difference. 

Nominal frequency Ideal frequency, with zero uncertainty relative to its definition. 

---