Measurement uncertainity

Typically we read the scale on measuring devices to 0.1 unit of the smallest scale division on the device. We estimate this final significant figure, which makes the final significant figure in the measurement uncertain. 

Uncertainty in measurement, uncertain (doubtful) digit, significant figures, exact numbers... 

Figure 1. Dynamic model of testing of the material as a black box , where IN - loads and actions OUT - response of the material as measuring characteristics N - noise (combination of uncertain factors) ...

One feature of this inequality warrants special attention. In the previous paragraph it was shown that the precise measurement of A made possible when v is an eigenfiinction of A necessarily results in some uncertainty in a simultaneous measurement of B when the operators /land fido not conmuite. However, the mathematical statement of the uncertainty principle tells us that measurement of B is in fact completely uncertain one can say nothing at all about B apart from the fact that any and all values of B are equally probable A specific example is provided by associating A and B with the position and momentum of a particle moving along the v-axis. It is rather easy to demonstrate that [p, x]=- ih, so that If... 

The digits in a measured quantity, including all digits known exactly and one digit (the last) whose quantity is uncertain. 

Phthalates in Air. Atmospheric levels of phthalates in general are very low. They vary, for DEHP, from nondetectable to 132 ng/m (50). The latter value, measured in 1977, is the concentration found in an urban area adsorbed on airborne particulate matter and hence the biological avaUabUity is uncertain. More recent measurements (52) in both industrial and remote areas of Sweden showed DEHP concentrations varying from 0.3 to 77 ng/m with a median value of 2 ng/m. ... 

The third difference is that many process details are relatively uncertain when a plant is designed. For example, iaert loading for vacuum jets is rarely known to within 50%. Although the first two differences are negative, the third provides a unique opportunity to measure the tme need and revise the system accordingly. 

Color. Many water samples have a yellow to brownish-yeUow color which is caused by natural substances, eg, leaves, bark, humus, and peat material. Turbidity in a sample can make the measurement of color uncertain and is usually removed by centrifiigation prior to analysis. The color is usually measured by comparison of the sample with known concentrations of colored solutions. A platinum—cobalt solution is used as the standard, and the unit of color is that produced by 1 mg/L platinum as chloroplatinate ion. The standard is prepared from potassium chloroplatinate (K PtCl ) and cobalt chloride (C0CI26H2O). The sample may also be compared to suitably caUbrated special glass color disks. 

Calcium has a face-centered cubic crystal stmcture (a = 0.5582 nm) at room temperature but transforms into a body-centered cubic (a = 0.4477 nm) form at 428 2° C (3). Some of the more important physical properties of calcium are given in Table 1. For additional physical properties, see references 7—12. Measurements of the physical properties of calcium are usually somewhat uncertain owing to the effects that small levels of impurities can exert. 

Analysts The above is a formidable barrier. Analysts must use limited and uncertain measurements to operate and control the plant and understand the internal process. Multiple interpretations can result from analyzing hmited, sparse, suboptimal data. Both intuitive and complex algorithmic analysis methods add bias. Expert and artificial iutefligence systems may ultimately be developed to recognize and handle all of these hmitations during the model development. However, the current state-of-the-art requires the intervention of skilled analysts to draw accurate conclusions about plant operation. 

Plant-performance analysis reqmres the proper analysis of limited, uncertain plant measurements to develop a model of plant operations for troubleshooting, design, and control. 

Thorinm-232 is the only non-radiogenic thorium isotope of the U/Th decay series. Thorinm-232 enters the ocean by continental weathering and is mostly in the particulate form. Early measurements of Th were by alpha-spectrometry and required large volume samples ca. 1000 T). Not only did this make sample collection difficult, but the signal-to-noise ratio was often low and uncertain. With the development of a neutron activation analysis " and amass spectrometry method " the quality of the data greatly improved, and the required volume for mass spectrometry was reduced to less than a liter. Surface ocean waters typically have elevated concentrations of dissolved and particulate 17,3 7,62... 

NO emissions did not exceed 2 ng Nm s and their measurement was only possible by chamber methods. The low NO emissions but high NjO emissions show that denitrification was the main source of NjO at this site. The discrepancies between the chamber and micrometeorological methods illustrated the need to define the flux-footprint of a micrometeorological measurement very carefully, and to use this information in the field to choose the locations in which chambers are placed. Without such an approach, the integration of results from chambers into estimates of field-scale emission remains an uncertain method. 

Here Iq is the thermal conductivity of the system, consisting of the porous solid and the reacting fluid inside the pores. This is the most uncertain value, while everything else is measurable. Two things must be remembered. First, data on thermal conductivity of catalysts are approximate. The solid fraction of the catalyst (1-0) always reduces the possibility for diflhision, while the solid can contribute to the thermal conductivity. Second, the outside temperature difference normal to the surface or Daiv, will become too high, much before the inside gradient can cause a problem. See Hutching and Carberry (19), Carberry (20). 

For saturated hydrocarbons, exchange is too slow and reference points are so uncertain that direct determination of pAT values by exchange measurements is not feasible. The most useful proach to obtain pK data for such hydrocarbons involves making a measurement of the electrochemical potential for the reaction... 

If a measurement is repeated only a few times, the estimate for the distribution variance calculated from this sample is uncertain and the tiornial distribution cannot be applied. In this case another distribution is used, f his distribution is Student s distribution or the /-distribution, and it has one more parameter the number of degrees of freedom, t>. The /-distribution takes into account, through the p parameter, the uncertainty of the variance. The values of the cumulative /-distribution function cannot be evaluated by elementary methods, and tabulated values or other calculation methods have to be used. 

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. 

Hazard, risk, failure, and reliability are interrelated concepts concerned witli uncertain events and tlierefore amenable to quantitative measurement via probability. "Hazard" is defined as a potentially dangerous event. For example, tlie release of toxic fumes, a power outage, or pump failure. Actualization of the potential danger represented by a hazard results in undesirable consequences associated with risk. 

Hazard, risk, failure, and reliability are interrelated concepts concerned with uncertain events and tlierefore amenable to quantitative measurement via probability. 

A method that has been the standard of choice for many years is the Lowry procedure. This method uses Cn ions along with Folin-Ciocalteau reagent, a combination of phosphomolybdic and phosphotnngstic acid complexes that react with Cn. Cn is generated from Cn by readily oxidizable protein components, such as cysteine or the phenols and indoles of tyrosine and tryptophan. Although the precise chemistry of the Lowry method remains uncertain, the Cn reaction with the Folin reagent gives intensely colored products measurable spectrophotometrically. 

The coordination chemistry of the large, electropositive Ln ions is complicated, especially in solution, by ill-defined stereochemistries and uncertain coordination numbers. This is well illustrated by the aquo ions themselves.These are known for all the lanthanides, providing the solutions are moderately acidic to prevent hydrolysis, with hydration numbers probably about 8 or 9 but with reported values depending on the methods used to measure them. It is likely that the primary hydration number decreases as the cationic radius falls across the series. However, confusion arises because the polarization of the H2O molecules attached directly to the cation facilitates hydrogen bonding to other H2O molecules. As this tendency will be the greater, the smaller the cation, it is quite reasonable that the secondary hydration number increases across the series. 

The amount of information required to specify the state of the system to within an accuracy e (or, equivalently, the information gain in making a measurement that is uncertain by an amount e ), is given by... 

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