Sampling particulate matter for analysis – Controlling uncertainty and bias using the theory of sampling

Abstract

Sampling particulate matter for measuring the content of an analyte is a routine operation in many fields of engineering and science. However, sampling can lead to important bias and variance in concentration estimation because of sampling errors stemming from particulate matter heterogeneity. The goal of this study was to quantify bias, reproducibility and the degree of representativeness of a probabilistic sampling (PS) technique following principles from the Theory of sampling (TOS) and grab sampling (GS). PS was designed to control sampling errors, while GS did not exert any control over them. GS also included a step of sieve screening, which is common during sampling in some fields (e.g. soil sampling). Both techniques were used with two different analytes, namely steel microspheres and copper sulfate, at two different concentrations, in order to assess sampling errors and sampling performance.The sampling method had the most significant effect on sampling bias and relative variance, and therefore, on the degree of sampling representativeness. The most important result is the demonstration that probabilistic sampling improves the degree of representativeness of concentrations measurements by more than two orders of magnitudes by significantly decreasing bias and relative variance. The lot containing the physical analyte lead to larger bias and relative variance compared to the lot containing the chemical analyte. GS resulted in largely biased results and a poor degree of representativeness. The results have also highlighted a significant problem associated with the screening of larger particles as performed in GS. This alteration of the primary sample decreased the variability of the resulting concentration measurements, but it also biased them significantly.