Development of an optimization model to determine sampling levels

Abstract

As the complexity of multi-component products increases the quality of these products becomes increasingly difficult to control. The first step to manufacturing a quality product is making sure that the components of the product meet specifications. Product quality can be controlled through sampling inspection of the components. Two models were developed in this research to determine the optimal sampling levels for incoming lots containing parts for production and assembly of multi-component systems. The main objective of the first model is to minimize the expected cost that is associated with a nonconforming item reaching assembly. In this model the time available for inspection is limited. The main objective in the second model is to minimize total cost, which includes the appraisal cost (inspection cost) and the cost associated with nonconformance reaching assembly. In this model the time available is not a constraint. The distribution of defects is assumed to follow the binomial distribution, and the distribution of accepting the lot with defects follows the hypergeometric distribution. In addition, the inspection is considered to be accurate and, if a nonconforming item is found in the inspected sample, the entire lot is rejected. An example is given with real world data and the results are discussed --Abstract, page iv