Uncertainty treatment for clearance measurement
IAEA Safety Standards General Safety Requirements Part 3  defines Clearance as the removal of regulatory control by a regulatory body from radioactive material or radioactive objects within notified or authorized practices. Clearance measurement should be performed with high reliability, and a conformity assessment of the measured or evaluated contamination values to the regulatory limit, considering the measurement’s uncertainty is necessary.
Generally, clearance measurements are employed to calculate the sum of ratios of the measured activity concentration (di) to the limit (ci) for all nuclides to be evaluated, as shown in Eq. (1). When the uncertainty is expressed as u(y), the upper limit for a certain level of confidence can be calculated as Eq. (2), which includes several components related to measurements, such as the counting uncertainty, calibration uncertainty, or uncertainty of the ratio of the activity concentration of the difficult to measure nuclide to that of easy to measure nuclide. Under the assumption that y is four times or greater than u(y) as shown in sub-clause 5.9 and clause nine of ISO 11929-1 , a one-sided level of confidence is 95% when the coverage factor k equals 1.645. The object can be released when the upper limit does not exceed one according to the conformity assessment for the clearance measurements.
Regarding the uncertainty of the clearance measurements, the uncertainty of the ratio of the activity concentration of the difficult to measure nuclide to that of the key nuclide often attracts attention. The ratio is obtained using sampling and radiochemical investigation before the clearance measurements, and its probability distribution is commonly considered log-normal . Regarding the clearance measurements, additional consideration of the probability distribution of the ratio employed for the evaluation is required since the log-normal probability distribution of the ratio is presented for very small sample volumes compared to the volume assumed for the clearance measurements. Assuming that the material to be measured is divided into 105 segments, the ratio for each small segment is distributed according to the log-normal probabilistic distribution, which has a geometric mean of 0.10 and a geometric standard deviation of 3.0. The probability distribution of the ratio was derived using the Monte Carlo approach to demonstrate a simplified example of the log-normal distribution of the ratios among small segments, which can be expected in the actual measurements as shown in Figure 1 (a). It is frequently debated whether the arithmetic mean or the geometric mean is more suitable for the representative ratio. The best estimate of the ratio to be employed for the clearance measurements is the population mean of the ratios of all small segments included in the material, or the arithmetic mean of the values of ratios from samples, because the release of the material is judged by the value of averaged activity concentration of a large volume of the materials to be measured. Figure 1 (b) shows the probability distributions of the estimated ratio for sample sizes N = 20, and 200. The result reveals that the estimated arithmetic mean is expected to be closer to the theoretical arithmetic mean (0.183), whose uncertainty is sufficiently small if the estimated arithmetic mean is derived by averaging large N sample measurement results.
In the Japanese regulation examination process for clearance measurement, the above treatments of the uncertainty and the conformity assessment have already been adopted . The detailed uncertainty treatment for clearance measurement were described in the published paper .
 IAEA Safety Standards General Safety Requirements Part 3, 2014. Radiation Protection and Safety of Radiation Sources: International Basic Safety Standards, International Atomic Energy Agency, Vienna.
 ISO 11929-1, 2019. Determination of the characteristic limits (decision threshold, detection limit and limits of the coverage interval) for measurements of ionizing radiation -- Fundamentals and application -- Part 1: Elementary applications, International Organization for Standardization, Geneva.
 Kashiwagi, M., Müller, W., 2000. Considerations on the activity concentration determination method for low-level waste packages and nuclide data comparison between different countries, Proceedings of international conference on the safety of radioactive waste management; Cordoba (Spain); 13-17 Mar 2000, IAEA, 175–179.
 Nuclear Regulation Authority (NRA), 2021. Standard of examination for approval of measurement and evaluation for solid materials clearance, Japan. (in Japanese)
 Sakai H., Yoshii, T., Kawasaki, S., 2021. Derivation of uncertainty propagation for clearance measurement, Applied Radiation and Isotopes, 170, 109630.
Nuclear Regulation Authority (NRA)