Results of Comparative Evaluation of Algorithms for Calculating Scaling Factors of Difficult-To-Measure Nuclides in CHNPP Wastes at 241Am Example

O. V. Mykhailov

Institute for Safety Problems of Nuclear Power Plants,
NAS of Ukraine, 36a, Kirova st., Chornobyl, 07270, Ukraine



The criteria for radwaste acceptance valid in the Exclusion Zone of SSE “Chornobyl NPP” require that each batch (package) of solid radioactive waste (SRW) sent for burial be certified. For the radionuclides that are difficult to measure (DTM) with using standard control systems directly in a package, the IAEA recommends using the Scaling Factors (SF). In the course of special studies to determine their quantitative values, some difficulties were encountered when analyzing laboratory data on the DTM nuclide in SRW, which largely consisted of so-called nondetectable (ND) results declared in the reports as <MDA (less than the minimum detectable activity). The work was aimed to evaluate the known algorithms for SF determination used in the world practice of radwaste management, in terms of acceptability of their application to laboratory data sampling with different proportions of ND results (<MDA) on the example of 241Am content in ChNPP historical waste. Three data sampling were formed with the share of ND results equaling to 18, 42 and 55 percent. This work addresses several methods for SF calculation, which are used in radwaste management systems of the countries with developed nuclear fuel cycle. Among the selected algorithms for data process testing, the most powerful one of methods for ND results censoring is included — the method of maximum likelihood estimation (MLE), which allows by restoring the normal law of distribution of random data to most accurately adjust the value of mean contaminant content according to the probability of appearance of each of measurement results, with taking into account the added ND results after their censoring by a numerical value multiple of MDA. The possibilities of selected algorithms, from the viewpoint of accuracy of statistical indicators’ reproduction in the initial arrays of experimental data sampling with SF application, were investigated on “problematic” data sampling related to 241Am content in ChNPP historical waste. The studied algorithms are ranked according to the quantitative scale of acceptability (reliability) assessment for each of them for the use in radwaste management system of ChNPP for certification of DTM activity contained in the SRW packages. The data obtained allowed drawing conclusions on the most acceptable algorithms that can be recommended for SF calculation, depending on the content of experimental data collected after laboratory control. The influence of data censoring on the accuracy of reproduction of the original spectrum of experimental data for different algorithms is estimated. The validity of use of Mean Activity Method recommended by the IAEA for data sampling, which contains a significant proportion of ND results, was confirmed.

Keywords: radioactive waste, Chornobyl NPP, specific activity, minimum detectable activity, difficult-to-measure nuclides, key nuclides, scaling factor.


1. Criteria for acceptance of waste for burial in specially equipped near-surface repository for solid radwaste (SESRSRW). First stage of SESRSRW operation. Acceptance of RAW from SSE “ChNPP” PTLRW and PTSRW for burial in two symmetrical compartments of SESRSRW. Revision 5. Endorsed by acting Director General of State Corporation “UkrSE ‘Radon’”. Chornobyl, 2009. 38 p. (in Ukr.)
2. ISO 21238:2007. Nuclear energy — Nuclear fuel technology — Scaling factor method to determine the radioactivity of low- and intermediate-level radioactive waste packages generated at nuclear power plants. Geneva: International Organization for Standardization, 2007.
3. IAEA (2009). Determination and use of scaling factors for waste characterization in NPP. IAEA Nuclear Energy Series NW-T-1.18. Vienna: IAEA, 142 р.
4. Taddei M. H. T., Macacini J. F., Vicente R., Marumo J. T., Terremoto L. A. A. (2015). Determination of scaling factors to estimate the radionuclide inventory of wastes from the IEA-R1 research reactor. J. Radioanal. Nucl. Chem., vol. 303, no. 3, рp. 2467–2481. doi: 10.1007/s10967–014–3789–3.
5. Zaffora B., Magistris M., Saporta G., La Torre F. P. (2016). Statistical sampling applied to the radiological characterization of historical waste. EPJ Nuclear Sci. Technol., vol. 2, art. 34. doi: 10.1051/epjn/2016031.
6. Albertone L., Altavilla M., Marga M., Porzio L., Tozzi G., Tura P. (2019). Control experiences regarding clearable materials from nuclear power plants and nuclear installations: Scaling factors determination and measurements’ acceptance criteria definition. Environments, vol. 11, no. 6, p. 120. doi:10.3390/environments6110120.
7. Mykhailov O. V., Bezmylov V. M. (2020). New methodological approaches in solving certification problem of historical solid radioactive waste sent for burial from Chornobyl Nuclear Power Plant. Nuclear Power and the Environment, vol. 19, no. 4, pp. 39–49.
8. Mikhailov A. V., Pavliuchenko N. I., Miasnikov A. V., Terzi A. K. (2019). [Results of radionuclide vectors determination to be used in characterization of SSE NPP’s solid radwaste]. Problemy Chornobyl’skoi zony vidchuzhennia [Problems of Chornobyl exclusion zone], vol. 20, pp. 13–26. (in Russ.)
9. Maksymenko А. М., Bondarkov M. D., Oskolkov B. Ya., Seida V. A., Dubas V. N. (2019). [Results for Studies of Hard-to-Measure Radionuclides in the Metal of Chornobyl Nuclear Power Plant Equipment being Dismanlted, and Estimation of Scaling Factor]. Yaderna Energetyka ta Dovkillia [Nuclear Power and the Environment], vol. 13, no. 1, pp. 67–75. (in Russ.)
10. Varlakov A. P., Sergeecheva Y. V., Ivliev M. V., Varlakova G. A., Gorbunov V. A., Karlin S. V. (2020). Application of the nuclide-vector methodology to determine the activity of difficult-to-measure radionuclides in radioactive waste streams. Radioactive Waste, vol. 10, no. 1, pp. 85–91. doi: 10.25283/2587–9707–2020–1–85–91. (in Russ.)
11. US EPA (2006). Data Quality Assessment: Statistical Methods for Practitioners. EPA QA/G-9S. Washington: United States Environmental Protection Agency. Office of Environmental Information, 198 р. Available at:–08/documents/g9s-final.pdf.
12. Ogden T. L. (2010). Handling results below the level of detection. The Annals of Occupational Hygiene, vol. 54, no. 3, pp. 255–256. Available at:
13. Croghan C. W., Egeghy P. P. (2003). Methods of dealing with values below the limit of detection using SAS. Las Vegas: United States Environmental Protection
Agency, 5 p. Available at: https://pdfs.semanticscholar. org/98ec/87a1208e06a9f4e08136d245a986c5ff5019.pdf.
14. Finkelstein M. M, Verma D. K. (2001). Exposure estimation in the presence of nondetectable values: another look. AIHA J., vol. 62, pp. 195–198. Available at:
15. Ross S. M. (2004). Introduction to probability and statistics for engineers and scientists. Third Edition. USA: Elsevier Academic Press, 641 p.
16. Mykhailov O. V., Bezmylov V. M., Terzi A. K. (2020). Analysis of radionuclide contamination features in solid radwaste of “light” eastern compartment of solid waste repository of Chornobyl NPP. Nuclear Power and the Environment, vol. 16, no. 1, pp. 40–48.

Full Text(PDF)


If the article is accepted for publication in the journal «Industrial Heat Engineering» the author must sign an agreement on transfer of copyright. The agreement is sent to the postal (original) or e-mail address (scanned copy) of the journal editions.

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a  Creative Commons Attribution License International CC-BY that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal.

Insert math as
Additional settings
Formula color
Text color
Type math using LaTeX
Nothing to preview