Sequencing of imperfect inspection operations subject to constraints on the quality of accepted and rejected units

Several imperfect inspection operations are available in a discrete production environment. A decision regarding acceptance or rejection of the produced items needs to be made without exceeding specified limits for the probabilities of accepted units being non-conforming and rejected units conforming to quality specifications. A branch and bound approach is used to find the inspection sequence resulting in least expected total inspection cost. Following the heuristic construction of a trial solution, a dominance relationship is applied to search the tree of possible sequences for the optimal sequence. A numerical example is included.     

Location and sequencing of imperfect inspection operations in serial multi-stage production systems

An integrated approach to the problem of allocation of inspection effort in multistage production systems is presented. The problem addresses multiple inspection operations, different disposition policies and inspection, production and repair errors. Quality and cost transfer functions are developed to model production operations and different types of inspection operations in a unified manner and to facilitate the recursive computations required to evaluate alternative system configurations. We formulate the combined inspection location and sequencing problem as a nonlinear mathematical programming problem and solve it with a branch and bound technique, using a heuristic to generate a feasible solution and upper bound. These developments are illustrated with a numerical example.