Off-line inspections under inspection errors

Abstract

The problem of off-line inspection is of both practical and theoretical interest. It has been the subject of research in somewhat simplistic scenarios. In this paper, the theoretical coverage of this problem is extended to include inspection errors. In particular, a process which is subject to random failures that sequentially produces a batch of units is investigated. After the batch is complete, off-line inspections are performed. In the proposed model it is these inspections that are subject to errors. The optimal inspection policy, i.e., which units should be inspected and the inspection order so as to minimize the expected number of inspections, is determined. The considered objective function is to find the point at which the machine fails with a given confidence level. The optimal policy is found by a dynamic programming algorithm and four different heuristic policies are investigated. An extensive computational study that examines the behavior of both the optimal and heuristic policies is presented. In particular, the effect of the model parameters on the behavior of the optimal policy is analyzed. The heuristic policies are computationally studied with the goal of comparing their quality to the optimal solution, and also to compare the heuristics themselves.

Keywords:

• Off-line inspection
• quality control
• dynamic programming

Notes

¹ Another possibility exists, i.e., that we determine that no transition occurred with the given confidence level. In this case we will say that we have achieved our goal. For clarity of exposition we will only refer to this case when explicitly needed.