Statistical analysis radioactivity counting

While radioactive decay is itself a random process, the Gaussian distribution function fails to account for probability relationships describing rates of radioactive decay Instead, appropriate statistical analysis of scintillation counting data relies on the use of the Poisson probability distribution function ... 

Measurement methods have limits of detection arising from the presence of naturally occurring radioactive materials, from statistical fluctuations in counting rates, and from factors related to sample preparation and analysis. Appendix II describes the concepts of minimum significant activity (MSA) and minimum detectable activity (MDA), which are used to characterize the limits of detection of any measurement method. 

ILL All measurement methods have limits of detection. These arise from a number of factors, such as natural radioactivity, statistical fluctuations in counting rates and factors related to sample preparation and analysis. Consequently, the detection of intakes is also limited. The dose resulting from an intake of less than the detection limit of the measmement method will be missed. 

One common characteristic of many advanced scientific techniques, as indicated in Table 2, is that they are applied at the measurement frontier, where the net signal (S) is comparable to the residual background or blank (B) effect. The problem is compounded because (a) one or a few measurements are generally relied upon to estimate the blank—especially when samples are costly or difficult to obtain, and (b) the uncertainty associated with the observed blank is assumed normal and random and calculated either from counting statistics or replication with just a few degrees of freedom. (The disastrous consequences which may follow such naive faith in the stability of the blank are nowhere better illustrated than in trace chemical analysis, where S B is often the rule [10].) For radioactivity (or mass spectrometric) counting techniques it can be shown that the smallest detectable non-Poisson random error component is approximately 6, where ... 

In NAA it is possible to study separately diflFerent sources of error and to come up with a good estimate of how they affect the accuracy of determination for each element. A basic source of error is introduced by the statistics of counting radioactive emissions and is called the counting error. The size of the error is calculated directly from all of the counts used in the analysis of each peak. These errors vary considerably from element to element, but for our purposes we are only interested in those peaks that have counting errors of a few percent or less. 

Since radioactive decay follows Poisson statistics, a lower limit to the precision of an analysis can be obtained by a single measurement. In practice, counting statistics generally is the limiting uncertainty, since chi-squared tests often show that the single-measurement precision is an excellent predictor of sample-to-sample repeatability. 

The applicability of radioanalytical chemistry methods is tested initially with radioactive tracers and realistic mock samples. A tracer that can be measured reliably and conveniently, such as a radionuclide that emits gamma rays, is preferred. If initial tracer tests are successful, tests are repeated with the media that will be analyzed. These tests must demonstrate that the radionuclide of interest is recovered consistently with good yield and that no interfering radionuclides or solids remain. The extent of reproducibility is determined by analyzing acmal samples in replicate for chemical and radionuclide yield. Replicate samples are identical samples from the same batch, processed and counted separately to assess the variability or uncertainty in the analysis. The recommended test statistic for a duplicate analysis is computed using Eq. (10.27) ... 

Standard deviation is one of the parameter to characterise image quality. It defines the presence of noise component in image. Which is due to many reasons, e.g., random nature of radioactive decay, scattered gamma photons, low counting statistics, as well as genertaed by image reconstruction, analysis, and also attenuation correction techniques. 

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