Economic optimization of off-line inspection in a process subject to failure and recovery

In certain types of processes, verification of the quality of the output units is possible only after the entire batch has been processed. We develop a model that prescribes which units should be inspected and how the units that were not inspected should be disposed of, in order to minimize the expected sum of inspection costs and disposition error costs, for processes that are subject to random failure and recovery. The model is based on a dynamic programming algorithm that has a low computational complexity. The study also includes a sensitivity analysis under a variety of cost and probability scenarios, supplemented by an analysis of the smallest batch that requires inspection, the expected number of inspections, and the performance of an easy to implement heuristic.