A Mixed Model for Double Checking Fallible Auditors

Abstract

This article discusses the problem of a fallible auditor who assesses the values of sampled records, but may make mistakes. To detect these mistakes, a subsample of the checked elements is checked again, now by an infallible expert.

We propose a model for this kind of double check, which takes into account that records are often correct; however, if they are incorrect, the errors can take on many different values—as is often the case in audit practice. The model therefore involves error probabilities as well as distributional parameters for error sizes.

We derive maximum likelihood estimators for these model parameters and derive from them an estimator for the mean size of the errors in the population. A simulation study shows that the latter outperforms some other—previously introduced—estimators.

Keywords:

• Audit
• Inspection errors
• Maximum likelihood
• Mixed distribution
• Monotone missing data

Mathematics Subject Classification:

• C13
• C19