Optimal Numbers of Repeat Inspections with Decreasing Detection Probability

Optimal numbers of repeat inspections are obtained for a single inspector who has a fixed probability of detecting a nonconforming item on each inspection and will continue to inspect until further inspection is not warranted when comparing the expected increase of total gain with the inspection cost. It is assumed that the detection probability decreases as the number of repeat inspections increases, and that the lot to be inspected contains an unknown but Poisson distributed number of nonconforming items.