Precision measurement errors

For precise measurements, diere is a slight correction for the effect of the slightly different pressure on the chemical potentials of the solid or of the components of the solution. More important, corrections must be made for the non-ideality of the pure gas and of the gaseous mixture. With these corrections, equation (A2.1.60) can be verified within experimental error. 

There are two contradictory requirements here. The first is to keep the difference between Ci and C as small as possible so that it can be neglected. The second is to analyze these two only very slightly different concentrations with such precision that the difference will be significantly greater than the measurement error. This second need is for calculation of the rate of reaction, as shown in the first equation of this section. 

The means and habit of making highly precise measurements, with careful attention to the identification of sources of random and systematic error, were well established by the period I am discussing. According to a recent historical essay by... 

MMA polymerization is one of the most studied systems and was thought to be explicable, within experimental error, in terms of Bemoullian statistics. Moad et ai.jb have made precise measurements of the configurational sequence distribution for PMMA prepared from 13C-labeled monomer. It is clear that... 

Since we do not have the precise model function Gp embedded in the feedforward controller function in Eq. (10-8), we cannot expect perfect rejection of disturbances. In fact, feedforward control is never used by itself it is implemented in conjunction with a feedback loop to provide the so-called feedback trim (Fig. 10.4a). The feedback loop handles (1) measurement errors, (2) errors in the feedforward function, (3) changes in unmeasured load variables, such as the inlet process stream temperature in the furnace that one single feedforward loop cannot handle, and of course, (4) set point changes. 

Precision is defined as the closeness of agreement between independent test results obtained under stipulated conditions (Fleming et al. [1996b] Prichard et al. [2001]). Precision characterizes the random component of the measurement error and, therefore, it does not relate to the true value. 

We will address aspects of reproducibility, which has previously been defined as, the precision between laboratories . It has also been defined as total between-laboratory precision . This is a measure of the ability of different laboratories to evaluate each other. Reproducibility includes all the measurement errors or variances, including the within-laboratory error. Other terms include precision, defined as the closeness of agreement between independent test results obtained under stipulated conditions [3] and repeatability, or the precision for the same analyst within the same laboratory, or within-laboratory precision . Note that for none of these definitions do we require the true value for an analytical sample . In practice we do not know the true analyte value unless we have created the sample, and then it is only known to a given certainty (i.e., within a determined uncertainty). 

Several factors need to be considered to reduce the pH measurement error. First, an electrode with a high response slope should be used. Second, it is important to use a meter that is capable of measuring the millivolts or microvolts accurately and precisely. With modem meter technology, this is not normally a limiting factor. The... 

The error in this estimate compared to the equatorial value of GM/Rc2 is always less than 4% for a spin frequency v < 600 Hz (Bhattacharyya et al. 2003). Bhattacharyya et al. (2003) also find that future high-precision measurements could detect a signature of frame-dragging if there are two horns in the line profile. The ratio of the depth of the low energy (red) horn to the depth of the high energy (blue) horn increases quickly with the increase of a/M, but it either decreases or slowly increases with the increase of other parameters. Hence a precise measurement of a line profile could demonstrate the existence of frame-dragging. 

IV accuracy profiles are based on total measurement error that is a combination of the systematic error (measured by method biases) and random error (measured by method precision, i.e. RSDIP) (Rozet et... 

While competitive methods to determine KIE s are free from errors due to differences in reaction conditions (impurities, temperature, pH, etc.) they do require access to equipment that allows high precision measurements of isotope ratios. The selection of an appropriate analytical technique depends on the type of the isotope and its location in the molecule. For studies with stable isotopes the most commonly used technique (and usually the most appropriate) is isotope ratio mass spectrometry (IRMS). 

Measurement of precision. Measurement of data quality is valuable for both the analyst and the data user. Least-squares curve-of-best-fit statistical programs usually provide some information on precision (correlation coefficient, standard error of estimate). However, these are not sufficiently quantitative and often overstate the quality parameters of the data. 

P/T-value (precision to tolerance ratio), addresses what portion of the specification is taken up by the measurement error. The % P/T-value is an important metric for the method capability towards application in release testing against specifications. 

If the measuring error caused by temperature fluctuations is not to exceed an acceptable level, the temperature should be held constant within about 0.5 °C in measurements where a high precision is required (for example the determination of equilibrium constants), the solutions must be thermostatted at least within 0.1 °C. It is recommended [158] that the measurement generally be... 

Cd, K and Zn are not precisely determined. Previously reported (13) results for Identical split samples Indicates that most of this experimental error was due to analytical Imprecision rather than collection and handling. Many of the samples were near the detection limit for the five trace metals (As, Cd, Cu, Pb, Zn), To determine the effect of these measurement errors the PCA was repeated with uncertainty scaled data. (The data standard deviation used In autoscaling was replaced with the measurement absolute error.)... 

Precision is a measure of the reproducibility of a given result. The role of precision in demonstrating a method s accuracy has not been addressed. However, a clear understanding of the Q.C. method being presented here requires that we briefly examine a few basic features of measurement errors. 

Random error is the divergence, due to chance alone, of an observation on a sample from the true population value, leading to lack of precision in the measurement of an association. There are three major sources of random error individual/biological variation, sampling error, and measurement error. Random error can be minimized but can never be completely eliminated since only a sample of the population can be studied, individual variation always occurs, and no measurement is perfectly accurate. 

Designed Experiments Produce More Precise Models. In the context of linear regression, this is demonstrated by examining the statistical uncertainties of the regression coefficients. Equation 2.1 is the regression model where the response for the th sample (r ) of an instrument is shown as a linear function of the sample concentration (c.) with measurement error... 

The best precision is obtained for isotope ratios near unity (unless the element to be determined is near the detection limit, when the ratio of spike isotope to natural isotope should be between 3 and 10) so that noise contributes only to the uncertainty of natural isotope measurement. Errors also become large when the isotope ratio in the spiked sample approaches the ratio of the isotopes in the spike (overspiking), or the ratio of the isotopes in the sample (underspiking), the two situations being illustrated in Fig. 5.11. The accuracy and precision of the isotope dilution analysis ultimately depend on the accuracy and precision of the isotope ratio measurement, so all the precautions that apply to isotope ratio analysis also apply in this case. 

Application of Eq. (1) requires, however, determination of c and eeofthe substrate with high precision. Small errors in the measurement of ee and c can lead to major apparent changes of S with conversion, particularly in the case of high S values, a problem which is often underestimated in the measurement of S [6]. However, the overall error can be reduced by analysis of a series of ee versus c values [12]. 

This example shows how low-precision measurements can yield highly accurate results through averaging of repeated measurements. In the case of Jeweler A, the error in the official measurement was 0.864 g-0.856 g=0.008 g. The corresponding percent error was (0.008 g/0.856 g)xl00=0.9%. In the case of Jeweler B, the error in the official measurement was 0.856 g-0.856 g=0.000 g. Accordingly, the percent error was 0%. 

The purpose of the statistical analysis is to estimate the bias and the precision (measured by the CVp of the total precision error of a subject method) and resolve the latter error into components CVg due to the sampling method (less pump error), due to the analytical method (including error in the desorption efficiency factor), and CVp (an assumed level of pump error). Appendix II gives the definitions and computational formulae for the statistical analysis. 

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