Model of uncertainty for the variability of water microbiological enumeration in a proficiency testing scheme

Abstract

Data processing of microbial enumeration expressed as colony counts requires the use of specific statistical approaches due to the particular aspect of the analyte and the consideration of the variability related to the growth of microorganisms. A challenging matter in the organization of proficiency testing (PT) schemes for water microbiology is to provide representative, homogeneous and stable enough samples with the aim of assessing participants’ performance but also characterizing the accuracy of measurement. As a consequence, the proficiency testing design may help to make clear distinction between the different sources of variation and facilitate the subsequent error analysis associated with the analytical procedures of the participants. Besides, the statistical tools may be selected to provide explicit outcomes which enable the participants to interpret the data in line with other existing indicators such as those arising from validation studies or measurement uncertainty procedures in the laboratory quality assurance system. In this paper, the suitability of a Poisson–Gamma hierarchical generalized linear model is tested in order to evaluate the interlaboratory error, the batch homogeneity and the repeatability error from water microbiology PT. A probabilistic approach deriving from the negative binomial distribution is proposed for assessing the participating laboratories performance in terms of generalized z-score.