This paper proposes an approach for monitoring the average number of non-conformities per items in short-run productions of N items. After every m produced items, the last r items are inspected. For each inspected item, the number of defects is counted; each inspected item is classified as approved if it meets the control limit criterion. If all r inspected items are approved, then the production goes on, otherwise it is stopped for adjustment. The inspected items are all discarded in case of production stoppage. After a production of N items, an additional lot is produced to complete the size ordered, but this additional lot does suffer inspection. A finite discrete state Markov chain is used to determine the transitory probabilities, which will be considered in terms of cost, to determine the optimal strategy for monitoring, obtained by optimizing three parameters: sampling interval (m), retrospective sample size (r), and control limit (cl). These parameters are obtained computationally by direct search to minimize the expression of the average cost per item produced. A numerical example illustrates the proposal.
on-line control; Average number of defects; Short-run production; Economic model
