Monetary Unit Acceptance Sampling

Abstract

In this paper, I propose a new statistical sampling strategy appropriate for use in a variety of substantive audit testing situations. I call it monetary (dollar) unit acceptance sampling (MUAS). The advantage of MUAS over currently available monetary (or dollar) unit sampling (MUS) plans is that the former may be implemented sequentially, yielding smaller average sample sizes, without increasing audit decision risks. Savings in sample size will vary depending on the true error in the balance tested and the power function of the applied test. However, relative to fixed sample size MUS plans with comparable (nominal) risks, savings of 40% or more are possible if the true error is at an acceptable level, and 60% or more if the true error is at an unacceptable level. Currently, no sequential substantive procedure is available for audit use.' A sampling plan is more effective if it reduces (actual) decision risks for comparable sample sizes, and more efficient if it reduces sample size at comparable risk levels. Sequential MUAS, as presented below, is more efficient than current MUS plans. It is, of course, possible to trade off effectiveness for efficiency. If a procedure is conservative (i.e., actual risk is no greater than nominal risk and sometimes less), such a trade-off is acceptable as long as nominal risk levels are not exceeded. Thus, analyt-