Sequential Sampling Statistics for Evaluating Low Concentrations

Abstract

The sampling of low concentrations of particles can be especially time consuming and thus expensive when one attempts to get enough particles for an acceptable statistical confidence interval. The "sequential analysis" technique originated in the 1940s by Wald was shown to minimize the number of samples needed, at the cost of increased data analysis. The technique can be extended from sampling items to sampling intervals, e.g., time, volume, area, etc. Sequential sampling analysis tests hypotheses about the probabilities of events, thus about concentrations. A brief description of the technique and an example are provided here. Upper and lower limits on counts versus sampling extent can be set to give a desired 1-α probability of accepting a specified low concentration and β probability of accepting a specified high concentration. At very low or very high probabilities of finding a particle compared with the levels hypothesized, sequential sampling can produce a decision with relatively very few samples. An approximation to sequential sampling, the taking of multiple samples with evaluation, after each sample, can produce a decision with almost as few samples. Such approaches deserve consideration for the next revision of Federal Standard 209 concerning cleanroom certification.