The overestimation and underestimation of the radioactivity concentration of difficult-to-measure radionuclides can occur during the implementation of the scaling factor (SF) method because of the uncertainties associated with sampling, radiochemical analysis, and application of SFs. Strict regulations ensure that the SF method as an indirect method does not underestimate the radioactivity of nuclear wastes; however, there are no clear regulatory guidelines regarding the overestimation. This has been leading to the misuse of the SF methodology by stakeholders such as waste disposal licensees and regulatory bodies. Previous studies have reported instances of overestimation in statistical implementation of the SF methodology. The analysis of the two most popular linear models of the SF methodology showed that severe overestimation may occur and radioactivity concentration data must be dealt with care. Since one major source of overestimation is the use of minimum detectable activity (MDA) values as true activity values, a comparative study of instrumental techniques that could reduce the MDAs was also conducted. Thermal ionization mass spectrometry was recommended as a suitable candidate for the trace level analysis of long-lived beta-emitters such as iodine-129. Additionally, the current status of the United States and Korea was reviewed from the perspective of overestimation.

There always exist nonzero inspection errors whether inspectors are humans or automatic inspection machines. Inspection errors can be categorized by two types, type I error and type II error, and they can be regarded as either a constant or a random variable. Under the assumption that two types of random inspection errors are distributed with the “uniform” distribution on a half-open interval starting from zero, it was proved that inspectors overestimate any given fraction defective with the probability more than 50%, if and only if the given fraction defective is smaller than a critical value, which depends upon only the ratio of a type II error over a type I error. In addition, it was also proved that the probability of overestimation approaches one hundred percent as a given fraction defective approaches zero. If these critical phenomena hold true for any error distribution, then it might have great economic impact on commercial inspection plans due to the unfair overestimation and the recent trend of decreasing fraction defectives in industry. In this paper, we deal with the same overestimation problem, but assume a “symmetrical triangular” distribution expecting better results since our triangular distribution is closer to a normal distribution than the uniform distribution. It turns out that the overestimation phenomenon still holds true even for the triangular error distribution.