The stringer bound in case of uniform taintings

The Stringer bound is a widely used nonparametric 100(1 − α)% upper confidence bound for the fraction of errors in an accounting population. This bound has been found in practice to be rather conservative. In the present paper, we give recursive relations for obtaining the exact distribution of the Stringer bound in the case where the underlying distribution of the taintings is a uniform distribution on the interval [0,1], or a distribution with positive mass at zero and conditionally uniform on [0,1]. Based on these recurrence relations, we find a concrete counterexample which shows that the Stringer bound is not always conservative.