Optimal Screening Plans for Nonserial Production Systems

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Abstract
Quality control screening programs are defined and evaluated for the general n-stage nonserial production process. A total expected cost criterion, developed as a function of the screening applied at each inspection station, embraces the various costs of inspection, defect repair and defects passing through the process undetected. Absorbing Markov chains aid in the identification of probabilistic flows of defective materials through the production network. Minimum cost screening programs are developed, giving the optimal level of screening at every potential inspection station. For a quasi-concave cost structure, it is shown that the optimal screening program will employ either zero or 100 percent effective screening throughout. A standard branch and bound “backtrack” strategy readily identifies optimal screening programs for the unconstrained (0, 1) nonlinear integer programming problem. An illustrative problem is presented.

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