Sequential Audit Sampling for Finite Populations with Exact and Simulation-based Guarantee

Financial statement auditors use a risk-based approach to evidence collection to obtain reasonable assurance. When an initial sample does not support a conclusion, they may inspect additional items. We develop a sampling procedure by formulating this additional inspection as sequential hypothesis testing for a fixed finite population sampled without replacement. A tolerable deviation rate and a margin below that rate define the composite hypotheses and the intervening indifference region, and lower and upper stopping boundaries control the two probabilities of incorrect conclusions. Under simple random sampling, a hypergeometric recursion computes the boundaries, decision probabilities, and expected sample size exactly. The procedure permits decisions at prespecified times, including fixed intervals. A separate extension imposes a fixed maximum sample size. We also consider one-sided error control and complete examination of selected items. When the state is multidimensional or has too many possible values for direct enumeration, Monte Carlo simulation constructs candidate boundaries. An independent simulation then provides one-sided upper confidence bounds for the two error probabilities at the least-favorable population counts.