Operating characteristic curves for single, double and multiple fraction defective sampling plans developed for Cronobacter in powder infant formula

Abstract

The microbiological criteria established in the EC 2073/2005 for Cronobacter in powder infant formula (PIF) are based on two-class attribute sampling plans, where the sample results are qualitative (sample indicates presence or absence) and the lot is rejected if any sample is positive. The performance of a sampling plan is revealed by its Operating Characteristic (OC) curve which plots the probability of acceptance against possible values of proportion defective. The objective of this study is to generate several OC curves for single, double and multiple sampling plans assuming different statistical distributions of Cronobacter in PIF in order to determine and compare the probabilities of rejecting/accepting the lot and the respective level of contamination. In this study, the microbial distribution of Cronobacter in the PIF is described by assuming to be Poisson-lognormal (PLN), Poisson-gamma (PG), Zero- inflated Poisson-lognormal (ZIPLN) and Zero-inflated Poisson-gamma (ZIPG). For each distribution the proportion defective of the population is estimated in order to determine the probability of acceptance for single, double and multiple sampling plans. Furthermore, the effect of clustering of the bacteria on the probability of acceptance of the lot was assessed through a Poisson-logarithmic (PLOG) and a PLogn distribution. Probabilities of accepting the lot at a given level of contamination change drastically according to the statistical distribution assumed and by changing the values of its own parameters. In addition, a procedure of multiple sampling plan based on resampling reveals that the producer's risk (α risk) can be reduced without affecting the consumer's risk (β risk).