Random or systematic sampling to detect a localised microbial contamination within a batch of food

Pathogenic microorganisms are known to be distributed heterogeneously in food products that are solid, semi-solid or powdered, like for instance peanut butter, cereals, or powdered milk. This complicates effective detection of the pathogens by sampling. Two-class sampling plans, which are deployed when the health hazard is severe and direct, specify how many samples have to be drawn. In order to take a representative sample, the sampling strategy is important, especially when the microorganisms are distributed heterogeneously or localised. This theoretical study shows the impact of random versus systematic sampling on the probability to detect localised microbial contamination in a batch of food. A statistical model was used to compare these sampling strategies. The microbial contamination was modelled as being present in one specific localised fraction of the batch in which the cells were randomly distributed, while no cells were present in the remaining part of the batch. The probability that the entire sampling scheme contains at least one cell was calculated for various numbers of samples drawn either randomly or systematically and was shown to depend on the size of the contaminated fraction, the microbial concentrations, and the number of samples drawn. The probability of detection was either equal or higher for systematic sampling as compared to random sampling. The maximal improvement in probability of detection was 0.37, when the sampling interval was equal to the size of the contaminated fraction, meaning that exactly one systematic sample hits the contaminated fraction. In those cases where the size of the contaminated fraction can be estimated, this study may assist in selecting the sampling strategy that is most optimal regarding probability of detection.