Optimal inspection policies for a manufacturing station

The authors consider the quality control problem of a single automated service facility modeled as a simple queueing system with feedback. The objective is to minimize a finite or infinite time horizon discounted cost measure. It is shown that the optimal inspection policy is based on a threshold applied to the input queue length, both for an infinite and a finite queue capacity station; in the latter case, blocking costs are included in the model. These results apply to the long-run average cost minimization problem as well. Given the difficulty of determining the value of the threshold parameter, the authors also present an approach for estimating the cost sensitivity with respect to the threshold along a single observed sample path of the system, and hence adjusting it on-line. Numerical and simulation results are included to validate our analysis and to illustrate the on-line threshold-setting process.