The Analysis of a Simple Class of Multistage Inspection Plans

A simple class of multistage inspection plans is considered for an ordered production process consisting of N − 1 manufacturing stages and a final inspection stage. The plans are applied to batches of items of size S. At each stage any number of items from 0 to S may be inspected. Defectives found are replaced with non-defectives. Costs of inspection, replacement, and the cost of undetected defectives are included. It is shown that under certain conditions an optimal inspection plan has the property that at every stage either the whole batch is inspected or no inspection is performed. In such cases a very simple dynamic program can be solved to find the optimal plan.