Monetary Unit Acceptance Sampling: Sequential and Fixed Sample Size Plans for Substantive Tests in Auditing
Rohrbach, Kermit John
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https://hdl.handle.net/2142/71387
Description
Title
Monetary Unit Acceptance Sampling: Sequential and Fixed Sample Size Plans for Substantive Tests in Auditing
Author(s)
Rohrbach, Kermit John
Issue Date
1983
Department of Study
Accountancy
Discipline
Accountancy
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Business Administration, Accounting
Abstract
Monetary unit acceptance sampling (MUAS) is a statistical model suitable for audit substantive testing. The model is stated entirely in the statistical testing framework. Nominal risks of the test are achieved against a binomial error distribution (i.e. relative errors in the population are 0% or 100% only). For typical error distributions, the test is generally conservative in that actual risks are bounded by nominal risks. Both sequential and fixed sample size plans are developed, and, for these plans, both classical and Bayesian models are proposed. MUAS is derived from physical unit acceptance sampling and thereby provides a conceptual unification of statistical compliance and substantive testing that should facilitate both the implementation and teaching of audit sampling.
Classical sequential MUAS is essentially a classical sequential probability ratio test (SPRT) truncated at the optimal fixed sample size. Bayesian sequential MUAS is a new Bayesian SPRT, with a similar truncation rule, based on the constraints of the audit testing setup. A Monte Carlo study on MUAS is performed to provide some empirical evidence on the conservatism of MUAS against some typical accounting population error distributions and on the efficiency of sequential MUAS. The study results tend to support the use of MUAS for audit substantive tests. Sequential MUAS, in particular, can be an efficient method for the early detection of populations with lower than expected, or higher than tolerable, error rates (i.e. percentages of misstatement). Thus, if implemented sequentially, MUAS can significantly reduce the inefficiency associated with conservative tests under typical conditions while providing nominal protection against possible, but atypical, conditions.
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