## 1 Introduction
These considerations support attributing a uniform random variable to the targeted analyte mass. It is worth noting that the concentration of the analyte, its uncertainty (standard or expanded), and the aliquot mass are the only data that a laboratory can provide for a sample that has undergone a chain of preparatory operations to produce the analytical specimen, also known as the aliquot. Laboratory practice shows that the aliquot mass is weighed with high accuracy using a calibrated balance, whose uncertainty is certified. Usually, the calibration certificate of a balance does not specify the **pdf** which is assigned to the measurand. When a calibration certificate specifies the volume of a flask as 1000 \(\pm\) 5 mL, it is recommended to use a triangular distribution [26]. Therefore, a triangular **pdf** is the best choice for the aliquot mass when it is considered as a random variable [25; 26]. The theoretical model addresses both the ideal measurement case, where the analytical process does not introduce uncertainty, and the practical one, where the analytical process distorts the results through unavoidable LOQ and measurement uncertainty. The model emphasizes the critical role of mass reduction; i.e., the primary sample mass of the order of kilograms is reduced to an aliquot mass of a few grams. Accordingly, the weighing operation plays a critical role in the modeling of the probability distribution function ascribed to the concentration of a trace element. The conservative approach for data analysis was applied when surveying iron ore tailings for CRMs through incremental sampling. The concentrations of major, minor, and trace elements of the collected samples were measured using energy-dispersive X-ray fluorescence spectrometry (ED-XRFS). Handheld and benchtop ED-XRFS techniques are frequently used for surveying purposes as they are fast, accessible, and reliable for elemental analysis. There are some other X-ray based techniques that can be used for advanced studies of solid waste, such as X-ray absorption spectrometry and total reflection X-ray fluorescence spectrometry, that have the ability to measure trace levels of elements in the ppb range to provide important information on the local state of the atoms, etc. [27; 28]. It is beyond the scope of this paper to discuss the advantages offered by recent developments of these techniques. The reader interested in the application of advanced X-ray-based techniques may find valuable information in dedicated literature such as [27; 28]. The raw data processing method for each X-ray-based technique depends on the intellectual property of the producer. The statistical analysis of a suite of results provided by an X-ray technique in a laboratory is performed based on the classical statistical approach [26]. The data analysis in the proficiency testing scheme is carried out both on classical and robust statistics [29]. This study contributes novel insights into the statistical analysis of data when surveying for trace elements, including CRMs, by addressing the entire process of data acquisition, i.e., sampling, subsampling, and laboratory analysis. Furthermore, we introduce the novel idea of disregarding the analyte concentration from its specific carriers; for example, analytes can be found in any particle as atoms in compounds or nuggets, among others. This approach avoids the use of discrete distributions of particles carrying the targeted analyte that are unfit for the interpretation of data when screening for trace elements. The superiority of the proposed conservative approach over classical and robust statistical data analyses is demonstrated in cases where uniform data distribution is found to be close to the detection limit. Additionally, the decision risk associated with solid waste recycling is highlighted, particularly when traditional statistical analyses lead to overestimated analyte concentrations and underestimated uncertainties.