Shortest Route Models for the Allocation of Inspection Effort on a Production Line

Two shortest route models for determining where to allocate inspection effort on a production line are developed for the cases where this effort is unlimited or limited in its availability. A production line is defined as an ordered sequence of production stages, each stage consisting of a manufacturing operation followed by a potential inspection station. Items flow through the line in batches and may incur defects at any stage. Defects are assumed to be repairable or non-repairable. The defect generating process at any stage is taken to be an independent Bernoulli process with a known parameter. Two levels of inspection effort may be applied at any stage: no inspection or 100% inspection. Thus, both models are used to determine the stages at which batches are to be 100% inspected. A general cost structure is postulated first for the case where items with repairable defects are immediately repaired and items with non-repairable defects are discarded, and then for the case where all items found to be defective are replaced immediately with non-defectives. An expected cost per batch criterion is used to determine an optimal inspection plan in all cases. Examples are included.