Determining optimal target values for two processes in series

Abstract

Recently, there has been much interest among researchers in the economics of quality control. One of the most important areas in quality control is "process targeting". The majority of the process targeting models in the literature deal with single-stage production systems. However, in real world industrial settings, products are often processed through multistage production systems. In this thesis, a production system of two machines in series that produces a single product is considered. The product is assumed to have two quality characteristics, in which the first one is impacted by the first process and the second one is impacted by the two processes. Four process targeting models are developed using different approaches for product quality control to maximize the expected profit. The models provide the optimal parameters for both processes. The first targeting model is developed for single sampling plans with error-free inspection. The second model considers the effect of inspection error on the sampling plan. In the third model, a 100 percent inspection is used instead of sampling. The 100 percent inspection with inspection error is studied in the fourth model. Sensitivity analysis is conducted to study the effect of different parameters and inspection errors on expected profit and optimal process means. It has been shown that the models are very sensitive to the variance of the two processes, selling prices, and rework cost and insensitive to the inspection cost. However, in the case of error-prone inspection the models are more sensitive to type I error (rejecting conforming items) than type II error (accepting nonconforming items). A realistic case study from local industry is used to demonstrate the utility of the models.