OPTIMAL INSPECTION POLICY FOR CSP-T WITH RETURN COST USING GERT

Abstract

In contrast to single-level continuous sampling plans, CSP-T, a multilevel continuous sampling procedure, is a more economic and tightened scheme. Traditional performance measures for CSP-T plan had been developed via the technique of Markov chain which is more tedious and complex than the Graphical Evaluation and Review Technique (GERT). The main purpose of this paper is to deal with the problem of designing a CSP-T with return cost by employing GERT. First, the traditional performance measures for CSP-T are re-built using GERT. Second, the concept of a renewal process is employed to obtain the long run average unit cost of the inspection policy. Then, by minimizing the long run average unit cost, we determine the optimal inspection policy (including the optimal clearance number and sampling frequency). Overall, the analytical results indicate that depending on four parameters (the unit rework cost, the unit return cost, the unit inspection cost, and the defective percentage), there are three possible optimal inspection policies for CSP-T: “Do not inspect”, “Do 100% inspection”, or any setting for (i, f). An interesting result is that by suspending the restriction cost of rework and imposing the sampling fraction, we can easily obtain Dr. Deming's statement: “Do 100% inspection” if the ratio of the unit inspection cost to the unit return cost is less than the defective percentage and “Do not inspect” otherwise.

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