Statistical model for assessing the quality and cost of inspection procedures in forensic and environmental analysis

Abstract

Legal regulations on the composition and safety of food products require inspection programmes to maintain the standards required or to obtain an insight in the real situation. Such programmes consist of a sampling procedure followed by analysis of the samples. When monitoring environmental contamination similar programmes are required. When large numbers of samples have to be analysed in order to monitor contaminants in either environmental or food-chain samples, and the majority fulfil the legal requirements, a two-stage control system is desirable. Firstly, samples are analysed by a simple ‘screening method’, to sift out the large number of samples that fulfil the requirements (negative results). The minority not fulfilling the requirements (positive results) are investigated further by a more sophisticated confirmatory method, specific for the analyte(s) of interest, for an ultimate judgement. For this type of inspection a simple model is used in this study, in order to calculate the fraction of false negative results in the final decision. It is assumed, that, when the quality criteria for the confirmatory method are appropriate, the fraction of false positive results is negligibly small. The quality of the inspection is expressed in terms of the fraction f of false negative results with respect to the real positive samples and is related to labour and costs. In an example given, the costs of analysing 40 000 samples with f= 6.6% are ecu 7 800 000. Improving f down to 3.2% creates additional costs of ecu 16 000 000. The proposed model might not be sufficiently realistic, but more realistic models can be implemented. The proposed approach can be applied to determine the quality of an inspection for a given method of analysis, or, in reverse, to determine the requirements for a method of analysis for a given inspection quality.