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In this paper, we address an optimization problem for minimizing the inspection and rework cost in an inspection-rework system, which forms a network of nodes including a K-stage inspection system, storage areas for items, a source inspection shop, and a re-inspection shop. We assume that (n, 0) acceptance sampling is performed in the source inspection shop and that only 100(1-r)% of items of rejected lots are re-inspected in the re-inspection shop. Since all the nodes are interrelated, in order to formulate our steady-state objective function, we make a steady-state network flow analysis between nodes, and derive both the steady-state amount of flows between nodes and the steady-state fraction defectives by solving a nonlinear balance equation. Finally we provide some fundamental properties and an enumeration procedure for determining the optimal values of (K, r) which both minimizes our objective function and attains a given target average outgoing quality.

Analysis of (K, r) Incomplete Inspection Policy for Minimizing Inspection Cost subject to a Target AOQ