Optimal sequence of partial inspections subject to errors

Multiple inspections are necessary in some important areas of production systems. The quality of a product is enhanced by the inspections of a sequence of inspectors. Based on a cost-minimization model, Raz and Thomas proposed in 1983 a branch-and-bound method to determine the optimal sequence subject to inspection errors. Although their model is quite practical, the suggested branch-and-bound solution does not seem to be so attractive. By modifying their cost model slightly, under some regular conditions, we derived an analytic solution to determine the optimal number of inspectors and the optimal sequence of inspectors.