Radioactivity statistical analysis

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 ... 

In general, proper statistical analysis of long-term stability data collected, as recommended in Section VII.E, should support at least a 1-year expiration dating period. Exceptions do exist, for example, with short half-life radioactive drug products. 

Spectrophotometric devices, called microplate readers, collect raw data resulting from colorimetric or fluorescent screens. Similarly, scintillation devices measure the amount of radioactivity in samples from drug screens. The computer format of the data will then allow it to be exported into a spreadsheet or statistical analysis computer program for analysis. 

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 ... 

The NAA method for the determination of firearm discharge residue has been generally accepted, but applications have been limited to just a few laboratories. In the process of establishing NAA capability for the State of Illinois crime laboratories we re-examined the standard techniques (10). In the course of our work it became clear that post-irradiation is the cause of several constraints which have discouraged a more widespread use of NAA. The inherent time limitation due to the 87 min. half-life of 139Ba necessitates fast manipulations of radioactive solutions which in turn requires an experienced radiochemist. In addition to an ever present danger of overexposure and contamination, typically only a dozen samples can be irradiated per batch, which makes the method quite expensive. The developed statistical bivariate-normal analysis (11) is convenient for routine applications. With this in mind, a method was developed which a) eliminates post-irradiation radiochemistry and thus maximizes time for analysis b) accommodates over 130 samples per irradiation capsule (rabbit) c) does not require a collection of occupational handblanks and d) utilizes a simplified statistical concept based on natural antimony and barium levels on hands for the interpretation of data. The detailed procedure will be published elsewhere (15). 

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. 

To insure that a statistical average behavior is observed in the chemical experiments with No and Lr, it has been necessary to make repeated measurements for each data point. Indeed, the determination of the distribution coefficients for Lr in a solvent extraction experiment required over 200 experiments to define the behavior of about 150 atoms of Lr (JL). Experiments of this kind are exceptionally difficult and computer-controlled equipment has been devised to perform either a portion or all of operations needed for the chemical tests and the analysis of samples. Computer automation, although requiring a larger effort to implement, permits an experiment to be repeated many times in rapid sequence with the added advantage of doing each quickly before the complete decay of the radioactive atoms of a shortlived isotope. 

The difference between the activity of the matrix spike and that of the unspiked matrix should be approximately equal to the activity of the added radioactive tracer. The recommended test statistic for a matrix spike analysis is computed as in Eq. 

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) ... 

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. 

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