Efficiency of the sampling plan for Cronobacter spp. assuming a Poisson lognormal distribution of the bacteria in powder infant formula and the implications of assuming a fixed within and between-lot variability

The introduction of Microbiological Criteria (MC) by the European Regulators (European Commission, 2005) has required the food industry to implement sampling plans in order to monitor food pathogens such as Cronobacter spp. in powder infant formula (PIF). In order to determine the performance of the sampling plans, Operating Characteristic curves (OC curves) were developed based on the assumption that Cronobacter spp. follow a Poisson lognormal (PLN) distribution in powder infant formula (PIF). The limitations of the mathematical models introduced by other authors based on the assumption of a fixed within-lot (S) and between-lot variability (Sb) for any sample weight (w) adopted are mathematically explored. In this study an alternative approach is suggested based on the assumption that for any sample of mass w employed, the variance-to-mean ratio of the PLN distribution (IPLN) is fixed and the within-lot variability changes accordingly. The implication of relating the probabilities of accepting/rejecting a lot to the mean expressed in the log10 scale (M) rather than to the arithmetic mean (μ) is also developed. A case study based on published data was also assessed and presented as example.