Statistical analysis of uncertainties of gamma-peak identification and area calculation in particulate air-filter environment radionuclide measurements using the results of a Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) organized intercomparison, Part I: Assessment of reliability and uncertainties of isotope detection and energy precision using artificial spiked test spectra, Part II: Assessment of the true type I error rate and the quality of peak area estimators in relation to type II errors using large numbers of natural spectra

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Abstract

In this paper, the uncertainties of gamma-ray small peak analysis have been examined. As the intensity of a gamma-ray peak approaches its detection decision limit, derived parameters such as centroid channel energy, peak area, peak area uncertainty, baseline determination, and peak significance are statistically sensitive. The intercomparison exercise organized by the CTBTO provided an excellent opportunity for this to be studied. Near background levels, the false-positive and false-negative peak identification frequencies in artificial test spectra have been compared to statistically predictable limiting values. In addition, naturally occurring radon progeny were used to compare observed variance against nominal uncertainties. The results infer that the applied fit algorithms do not always represent the best estimator. Understanding the statistically predicted peak-finding limit is important for data evaluation and analysis assessment. Furthermore, these results are useful to optimize analytical procedures to achieve the best results.

Introduction

Atmospheric particulate radionuclide monitoring and measurement are typically performed using high-volume air samplers and high-resolution gamma spectrometry. Anthropogenic and natural gamma-emitting radionuclides can be detected by their gamma-ray peaks. If measurements take place near the detection limit, an increasing variety of effects become significant, such as: the statistical fluctuations inherent in radioactivity counting, the interference of other naturally occurring radionuclides and other effects of a complex spectrum baseline.

In the process of identifying gamma-ray peaks near background levels, identifying uncertainties present in the analysis is a crucial issue. There is a risk of a false-positive peak and subsequent nuclide identification (type I error) or conversely of a nonidentification of a true gamma-ray peak (false-negative or type II error). Due to the statistical nature of the measurement process, these risks cannot be avoided, but they should be under control and consistent with the settings of the parameters that control the spectrum analysis.

A radionuclide analysis intercomparison exercise organized by the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) provided an excellent opportunity for this statistical analysis study. The exercise consisted of two phases and aimed to evaluate the data processing capabilities of the CTBTO's International Data Center (IDC) and related National Data Centers (NDC). In the first phase, the IDC and participating NDCs processed real-world spectra from daily measurements at radionuclide stations in the International Monitoring System (IMS). In the second phase, using Monte Carlo generated artificial peaks, a total of 430 anthropogenic nuclides were artificially spiked into 100 background spectra representing five different measurement systems, at different but known concentrations. The numerical spiking simulated the statistical nature of the measurement. The added counts x in the peak region were sampled from a known normal distribution with mean a and variance σ2 (Toivonen and Pelikan, 2005). These spectra were delivered to the participants for performance assessment of their radionuclide analysis software and procedures. They were also designed to challenge the capability of the participants to identify peak signals near the background level. In combination, the two phases of the intercomparison allowed a comprehensive evaluation of peak detectability across the energy spectrum for different measurement systems. The results for the analysis of the artificial peaks are corroborated by detailed studies of real spectra from a common measurement system by using natural peaks, which confirms and extends the essential conclusions obtained with the spiked spectra.

In the first part of this paper, a Monte Carlo simulation of the decay of eight radionuclides, each of which decays with the release of a monoenergy gamma ray, has been made (cf. Table 1). The radionuclides were selected on the basis that they provide a range of gamma-ray energies at locations judged relatively free of background peaks or unusual background features, for example neutron edges (Siiskonen and Toivonen, 2005). The selected nuclides have gamma-ray energies from 100 to 800 keV. The test spectra represented these isotopes with principal peak areas ranging from 0.5 to 10 times reference peak decision level with both high and low continuum backgrounds and were ideal to test peak finding capability in a range of spectrum environments.

Analysis routines should be able to find small and well-defined single peaks with empirically quantifiable false-positive and false-negative detection frequencies consistent with the preselected risk criterion based upon Currie's concept of critical level, LC (Currie, 1968).

Four participants using different software packages and analytical procedures were examined in this intercomparison. The total number of known spiking events investigated was 195, which is an appropriate population for statistically significant false-negative nuclide detection frequency studies.

In the second part of this paper, analysis results from different NDCs and from the IDC using routine spectra collected during a system-wide test operation period are compared. A typical routine spectrum obtained from the CTBT-IMS is dominated by the natural radionuclides 212Pb, 212Bi, 208Tl and 7Be. These and other isotopes of the natural decay scheme, detector background and cosmic-induced radioactivity render a complex spectrum with 20–70 identifiable peaks in the energy range between 60 and 2700 keV.

The analysis of a total of 80 spectra per day covering an energy range of more than 2.5 MeV implies a high number of hypothesis tests on the presence of treaty relevant radionuclides and subsequently a significant number of false fission product identifications, i.e. statistical type I errors.

Strong 220Rn progeny peaks in real IMS spectra allowed the prediction of true areas of particular small 220Rn peaks at or near baseline levels. Comparison of these predicted values with areas determined by participant's analysis routines was used to determine the quality of the employed peak area estimators. The quality of this peak area estimator was directly related to the expected type II error rate.

Section snippets

Peak significance and small peak identification near background level

Typically, the peak detection procedure in standard spectrum software is a two-step process. The Mariscotti peak search algorithm (Mariscotti, 1967), which is not discussed further here, is widely used for peak-finding. Its threshold for detection is kept relatively low in order to ensure a maximum sensitivity of the system as a whole. Upon identification of a potential peak, specific procedures decide on the validity of the peak. They first calculate the area A of a potential peak and compare

Peak identification uncertainty

Four participants had set the critical limit at k1−α=1.645. Only these participants were used for this study in order to ensure comparability of the results. In theory, maximum false-positive (type I error) identification probability should be 5%. The empirical false-positive rates are listed in Table 1. These were calculated based upon the number of times the nuclide was observed in spectra that were not spiked. They provide only an indicative rate, as the number of instances was relatively

Conclusions

The use of a high number of artificially “spiked” spectra with small contributions from man-made radionuclides has proven to be a valuable material for intercomparisons of spectrum analysis and the specific capability to detect traces of man-made radioactivity in air filter samples.

Compared against statistical theory, the results show that the real peak detection rate is less than theoretically expected. Several reasons are proposed: tight energy tolerances employed in the association of peaks

References (8)

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