Balanced sampling of boxes from batches for assessing quality of fruits and vegetables in EU countries

The best evaluation for the proportion of defective units in a batch of fruits and vegetables can be achieved by an exhaustive checking of all the boxes in the batch, that is prohibitive to perform in most cases. Usually, only a sample of boxes is checked. In EU countries, EU regulations establish to estimate the proportion of defective units in a batch by the proportion of defective units in the sample, without giving any rule for selecting boxes. Therefore, results are highly dependent on the subjective choice of boxes. In the present study, an objective design-based approach is considered to select boxes from batches, adopting balanced spatial schemes with equal inclusion probabilities. The schemes are able to select samples of boxes evenly spread throughout the batch also ensuring good statistical properties for the proportion of defective units in the sample as estimator of the proportion of defective units in the batch. The performance of these strategies is evaluated by means of a simulation study performed on real and artificial batches of apples, peppers and strawberries. A case study is considered to estimate the proportion of defective units in a batch of courgettes stored in a distribution center of a supermarket chain in Central Italy.