Total precision

A complete monitoring program, as mentioned previously, must include periodic replication for total precision assessment, plus reference sample measurement to assure accuracy. It was this... 

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. 

Azen 1979 Massart et al. 1990 Gardiner 1997). This random effects model is often used in analytical chemistry to breakdown a total precision into its components such as between-days and within-days, or between-laboratories and within-laboratories in collaborative trials, to validate an analytical method using reference material. 

For each mass on the Product W curve, the data will be analyzed by variance components analysis (VGA) to estimate the precision components due to InterOperator, InterDay, InterAssay, and Repeatability. For each expected mass, the precision components will be recorded as a variance, standard deviation, and percent of total precision. Nonzero components will be reported with a two-sided 95% confidence interval for the standard deviation. Within each mass, total variance is defined as the sum of the variance components. Total precision will be expressed as a variance, standard deviation, and coefficient of variation (%CV) also called the percent relative standard deviation or %RSD. 

Total precision is defined as the sum of the precision components. This summation takes place on the variance scale (variance = standard deviation squared). In theory, variances from independent terms in a model add up to total variance. See the precision analysis in the validation analysis example of the next section. 

The precision data is shown in Table 1. Three serum samples were assayed in replicates of 2, two separate times per day, for 20 testing days. Within-run precision and Total precision were calculated according to the NCCLS EP5-A protocol. 

There are many possible sources of errors in a protein structure determination. None of the intensities measured are totally precise, but contain the experimental errors normally encountered for the methods used. In addition, the heavy-atom positions and relative phase angles derived from them may contain errors due to disturbances to atomic positions caused by introduction of the heavy atom. 

Ca analyses were made using atomic absorption spectrometry. A K-La buffer was used. Total precision is about 3%. 

All these uncertainties translate into uncertainties about fuzzy sets membership functions [28]. Type-1 fuzzy Logic caruiot fully handle these uncertainties because type-1 fuzzy logic membership functions are totally precise which means that all kinds of uncertainties will disappear as soon as type-1 fuzzy set membership functions are used [11]. The existence of uncertainties in the majority of... 

Fig. 7.33 Approximate equivalent circuit for cell E2, taking into account double-layers and the stoichiometry effect of the ion blockage. Ap-proximation b) results for low frequencies and corresponds to the treatment above (Section 7.3.4). Approximation c) is a useful approximation for ion conductors (Randles circuit [609, 610]). The factor occurring in (a) is not totally precise. In the case of impedance spectroscopy the factor 12, which is also not precise, is given instead (see Section 7.3.6). According to Ref. [610j.

One particularly important property of the relationships for multipass exchangers is illustrated by the two streams shown in Fig. E.l. The problem overall is predicted to require 3.889 shells (4 shells in practice). If the problem is divided arbitrarily into two parts S and T as shown in Fig. El, then part S requires 2.899 and Part T requires 0.990, giving a total of precisely 3.889. It does not matter how many vertical sections the problem is divided into or how big the sections are, the same identical result is obtained, provided fractional (noninteger) numbers of shells are used. When the problem is divided into four arbitrary parts A, B, C, and D (Fig. E.l), adding up the individual shell requirements gives precisely 3.889 again. 

If the total surface area is small (say, a few hundred square centimeters), the amount adsorbed becomes so little that measurements are difficult by normal procedures. Thus the change in pressure-volume product on admitting gas to the adsorbent becomes so small that precision is impaired. 

Hydrolysis of />-Tolunitrile. As in the case of benzonitrile, alkaline h> drolysis is preferable to hydrolysis by 70% sulphuric acid. Boil a mixture of 5 g. of p-tolunitrile, 75 ml. of 10% aqueous sodium hydroxide solution and 15 ml. of ethanol under a reflux water-condenser. The ethanol is added partly to increase the speed of the hydrolysis, but in particular to prevent the nitrile (which volatilises in the steam) from actually crystallising in the condenser. The solution becomes clear after about i hour s heating, but the boiling should be continued for a total period of 1-5 hours to ensure complete hydrolysis. Then precipitate and isolate the p-toluic acid, CH3CgH4COOH, in precisely the same way as the benzoic acid in the above hydrolysis of benzonitrile. Yield 5 5 g. (almost theoretical). The p-toluic acid has m.p. 178°, and may be recrystallised from a mixture of equal volumes of water and rectified spirit. 

Convergence limit and Iteration limit specify the precision of the SCF calculation. Con vergen ce lim it refers to th e difference in total electronic energy (in kcal/mol) between two successive SCF iterations yielding a converged result. Iteration limit specifies the maximum number of iterations allowed to reach that goal. 

In the two-sample collaborative test, each analyst performs a single determination on two separate samples. The resulting data are reduced to a set of differences, D, and a set of totals, T, each characterized by a mean value and a standard deviation. Extracting values for random errors affecting precision and systematic differences between analysts is relatively straightforward for this experimental design. 

The previous discussion has centered on how to obtain as much molecular mass and chemical structure information as possible from a given sample. However, there are many uses of mass spectrometry where precise isotope ratios are needed and total molecular mass information is unimportant. For accurate measurement of isotope ratio, the sample can be vaporized and then directed into a plasma torch. The sample can be a gas or a solution that is vaporized to form an aerosol, or it can be a solid that is vaporized to an aerosol by laser ablation. Whatever method is used to vaporize the sample, it is then swept into the flame of a plasma torch. Operating at temperatures of about 5000 K and containing large numbers of gas ions and electrons, the plasma completely fragments all substances into ionized atoms within a few milliseconds. The ionized atoms are then passed into a mass analyzer for measurement of their atomic mass and abundance of isotopes. Even intractable substances such as glass, ceramics, rock, and bone can be examined directly by this technique. 

Sandstone. Sandstone wheels were once quarried extensively for farm and industrial use, and special grades of stone for precision honing, sharpening, and lapping are a small but important portion of today s abrasive industry. Production of honing and sharpening stones from deposits of dense, fine grain sandstone in Arkansas account for 76% of the value (about 2 million in 1987) and 88% of the total quantity of such stones in the United States (4). 

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