Partial inspection problem with double sampling designs in multi-stage systems considering cost uncertainty

The nature of input materials is changed as long as the product reaches the consumer in many types of manufacturing processes. In designing and improving multi-stage systems, the study of the steps separately may not lead to the greatest possible improvement in the whole system, therefore the study of inputs and outputs of each stage can be effective in improving the output quality characteristics. In this study, the double sampling method is applied for inspection where decision variables are the sample size per sampling time and the maximum amount of defective items in the first and second samples in each stage. Furthermore, uncertainty in parameters such as production, inspection, and replacement costs are included in the objective function and handled by a Monte-Carlo based optimization method. In order to show the efficacies of the proposed method, a numerical example has been designed, and further analyses on solutions have been conducted.