The optimal policy for a sampling plan in continuous production in terms of the clearance number

The first objective of this paper is to derive the total cost for one of the most commonly used continuous sampling plans in industry. The total cost includes the costs of inspection, reworks, and defective items returned by the customers. The continuous sampling plan under study is commonly known as CSP-1 which consists of alternate sequences of 100% inspection and random inspection used in continuous production systems. To achieve this objective, we employ the concepts of the renewal reward processes to obtain the long run average unit cost of the sampling plan. The second and the more important objective of this paper is to derive the minimum cost policy for the above sampling plan. The result of this effort is a simple and easy-to-apply rule which states that either a 100% inspection or a random inspection should be adopted to minimize the average unit cost. In addition, we arrive at the interesting result that the optimal clearance number is independent of the fraction of the units to be inspected during random inspection periods.