Variance bounds for the design of audit sampling

Audit sampling tests the conformance of monetary book values U kept in lists and databases on items like accounts, articles in an inventory, transactions, with the corresponding de facto values W of the items in reality. Variables sampling schemes focus on the conformance of the book value mean μ U with the de facto mean μ W . An essential design parameter of variables schemes is the unknown variance σ W 2 of the de facto values. It is a common practice to exploit the information conveyed by the book values in a naive way by equating σ W 2 with the known book value variance σ U 2 for design purposes. However, the de facto value variance may differ substantially from the book value variance. A robust design should be based on some reliable upper bound for the variance of σ W 2 . The present paper presents bounds for the variance σ W 2 and for the variance σ U − W 2 under various stochastic models for the relationship between book values and de facto values.