A Bayesian estimation of the concentration of microbial organisms in powdered foods arising from repeat testing for microbial contamination

Microbial food safety sampling in the food industry is generally based on single sampling schemes, with the results dictating the acceptance/rejection of the entire food lot. Resampling plans are generally only used to discern quality of ingredients or food items where food safety is not part of the evaluation. This paper developed a Bayesian model to quantify the uncertainty in the concentration of a bacterial organism in a batch of product considering the results from the primary sampling, as well as from subsequent resampling. Bayesian consideration of the primary sampling outcomes allowed formulation of a prior distribution which was then used to revise the uncertainty in the concentration present. Uncertainty distributions for microbial concentration were calculated for a range of resampling scenarios, in the event where one sample from an initial sampling tested positive. The study demonstrated that even in the event of large numbers of negative retest results, there was only a small shift in the uncertainty distributions of the concentrations of microorganisms present compared to the results from the initial sampling results. When the second set of testing includes positive outcomes, the peak of the uncertainty distribution moves to the right, as the retest outcomes revise upwards the initial estimate of the concentration of the microbial organism present. The study demonstrated the potential value of additional sampling to better estimate the likely microorganism concentration present in the food product. Especially in the events where a large proportion of the retests were negative, the magnitude of uncertainty was improved. The approach may be especially valuable for any investigation into a wider root cause analysis undertaken after the original positive test.