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 μUμU with the de facto mean μWμW. An essential design parameter of variables schemes is the unknown variance σW2 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 σW2 with the known book value variance σU2 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 σW2. The present paper presents bounds for the variance σW2 and for the variance σU−W2 under various stochastic models for the relationship between book values and de facto values.