Bayesian analysis of the sequential inspection plan via the Gibbs sampler

A complex product, such as a software system, is often inspected more than once in a sequential manner to further improve its quality and reliability. In such a case, a particularly important task is to accurately estimate the number of errors still remaining in the product after a series of multiple inspections. In the paper, we first develop a maximum likelihood method of estimating both the number of undiscovered errors in the product and the detection probability. We then compare its performance with that of an existing estimation method that has several limitations. We also propose a Bayesian method with noninformative priors, which performs very well in a Monte Carlo simulation study. As the prior knowledge is elicited and incorporated in the analysis, the prediction accuracy of the Bayesian method improves even further. Thus, it would be worthwhile to use various estimation methods and compare their estimates in a specific inspection environment.