A multi-objective optimization model for process targeting using sampling plans

The process targeting problem is usually formulated as a single objective optimization model. In this paper, a multi-objective optimization model is developed for the process targeting problem. The process under consideration produces a product with a normally distributed quality characteristic with unknown mean and known variance. The quality characteristic has a lower specification limit. The quality of the product is controlled via lot-by-lot acceptance sampling. The objectives used in the model are to maximize profit, income and product uniformity using the Taguchi quadratic loss function as a surrogate for product uniformity. An algorithm is proposed to obtain and rank the set of Pareto optimal points. The utility of the model is demonstrated using a numerical example from the literature. Sensitivity analysis on the model parameters showed that the results of the model are sensitive to changes in process variance. In addition, the optimal objectives of the profit function and product uniformity are more sensitive to changes in model parameters than the income function.