Counting error correction

One important case deserves special mention. In some spectrographs, notably the Philips Autrometer (9.7), the comparison of standard with unknown is done as follows. The time At required for a preset number of counts to be given by the standard is established. The unknown is then counted for the same interval. Time is measured with such high precision that this measurement does not contribute to the over-all error. But At for the standard is subject to the fluctuation defined by Equation 10-4. The result of the comparison is therefore subject to the counting error of Equation 10-14 if no background correction is made, or to a similar counting error that is modified to allow for the background correction. 

When counting data with their associated uncertainty values are added, subtracted, multiplied, or divided with other counting data, or constants, the propagation of the error may be estimated in the final answer. Since both numbers will have associated uncertainties, it is necessary to use the correct relationships to establish the final error. The final error from that manipulation (when two data with their errors are used) will always have a final error larger than either of the errors of the two initial data. For more detailed treatment of counting errors, see Radioanalytical Chemistry, Chapter 10. 

The data generated by counting systems is likely to need correction for background signals and counter efficiency, and the instrument may require calibration before the sample activity can be computed. These procedures are carried out either automatically within the instrument or externally, possibly with the aid of a computer (C7). A useful discussion of counting errors is given by Skoog and West (S15). The complex data produced from mixtures of isotopes measured by y-ray spectrometry have been analyzed by a Fourier transform technique (12). 

Indeterminate errors really originate in the limited ability of the analyst to control or make corrections for external conditions, or the inability to recognize the appearance of factors that will result in errors. Some random errors stem from the more statistical nature of things, for example, nuclear counting errors. Sometimes, by changing conditions, some unknown error will disappear. Of course, it will be impossible to eliminate all possible random errors in an experiment, and the analyst must be content to minimize them to a tolerable or insignificant level. 

As noted in Section 3.2.1, multiplier gain can depend not merely on ionic mass for a fixed ion energybut also on ionic identity correction factors as large as 1.8 have been reported for this effect. Except in the case of pulse counting, such correction factors must be measured and applied and it is often not clear in the literature if this has been done. It must be stated. It would be useful, too, if the quantitative values for the correction factors were reported. Ryan and Futrell report, for example, an uncorrected rate constant of 0.96 x 10 cm molecule" sec" for the reaction CH4" (CH4,CH3)CHj , a value which was raised to 1.70 x 10" cm molecule sec" when the measured multiplier correction was applied. The currently accepted value for this rate constant is 1.2 x 10 cm molecule sec". Was the correction factor in error for that particular experiment or did the method yield an anomalously high rate constant Values in the literature for these correction factors would help to answer such questions.f... 

Table 3 Activities (Bq/kg) of corrected Ra, and in the sediment core. Uncertainties are la based on counting errors which were generally the dominant contributor.

Such significant increase of accuracy may be explained on the base of analysis of the numerical values of the theoretical correction coefficients and calculated for 1, , and for analytical pai ameter lQ.j,yipj.j,jj- Changing from lines intensities for the ratios of analytical element line intensity to the intensity of the line most effecting the result of analytical element (chromium in this case) measurement enables the decreases of the error 5 or even 10 times practically to the level of statistics of the count rate. In case of chromium the influencing elements will be titanium, tungsten or molybdenum. 

For both failure modes, terminations caused by conditions other than the DG and its immediate support systems were not counted. Conditions that invalidated tests or demands for this study Include any operating errors that would not have prevented the DG from being restarted and brought to load in a few minutes without corrective maintenance incorrect trip signals that would not have been operative in the emergency mode and minor water or oil lea)cs that would not have precluded operation of the DG in an emergency. 

To more easily determine the effective tube lengths for U-tubes, the correction chart shown in Figure 10-27B is convenient. The chart is based on many actual U-tube bundle layouts. Values read from the chart are not more than 1 % lower than those obtained by calculations, except where the curve is extrapolated to lower tube counts. Such extrapolations result in errors of 3%, 4%, and higher, giving larger values than those calculated. This does not apply to higher tube count extrapolations. The chart is limited to -in. and... 

People are the principal source of contamination in clean room operations. All personnel involved throughout the development and production of a parenteral product must be aware of the factors that influence the overall quality of a product as well as the factors on which they directly impinge. It is of particular importance that production personnel be properly trained so that human error is minimized. They should be made aware of the use of the products with which they are involved and the importance of following all procedures, especially proper aseptic techniques. Procedures must be set up to verify that the product is being manufactured as intended. After manufacture of a batch, production tickets must be carefully checked, sterilization charts examined, and labels verified for correctness and count. 

Whether you choose to submit by mail or not, remember that the appearance of your application makes a statement about you. In other words, neatness counts. The biggest drawback of the paper application is the potential for a sloppy presentation errors that are crossed out, smudges, typos corrected with globs of Wite-Out . You won t get points for neatness, but you can lose out if your essay, and application as a whole, are messy. 

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