A systematic approach for designing Bayesian-Lot Quality Assurance Sampling plans. (December 2018) - Duarte, Belmiro P.M.
Abstract: Design strategies using Bayesian-Lot Quality Assurance Sampling (B-LQAS) monitoring plans for vaccination coverage and disease eradication typically assume a model with prior information of the parameters. One of the goals B-LQAS plans is finding the minimum sample size so that the characteristics of the risk curve meet user-specified requirements; however, there is no systematic approach to find such optimal B-LQAS plans to date. This paper formulates the problem as a mixed integer linear program and uses a branch and cut method to find the solution. The method also works when we have a user-specified weight function to account for a different emphasis in the misclassification error rates and different priors. We apply our algorithm to construct a few B-LQAS plans for estimating vaccination coverage in a given population using different weighting functions, priors and target proportions of vaccination coverage/disease eradication and compare results with those obtained from current methods. Numerical results support that our proposed method is computationally efficient, produces more accurate estimates than those commonly used and the estimates are more robust to model assumptions. In practical applications, the B-LQAS plans incorporate prior information about the prevalence, thus allowing the governments implementing plans more adequate to the specificities of the communities.