Decision theoretic analysis of pollutant emission monitoring procedures

A decision theoretic problem is considered which arises in the context of monitoring point sources of pollution: The management of an industrial plant may be authorized to release per unit time some amount of pollutants into the environment, for example air or water. An environmental agency may control, i.e. decide with the help of randomly sampled measurements, whether or not the real releases are larger than the permitted ones. The analysis of the problem of determining the ‘best’ inspection procedure is performed with the help of a non-cooperative two-person game and can be constructed as follows: For a given value of the false alarm probability, only a zero-sum game has to be considered, where the probability of detecting illegal behavior is the payoff to the inspector. The solution of this game, i.e. the best inspection procedure, is then determined by use of the Neyman-Pearson Lemma.