Optimal process parameters for two processes based on product uniformity criteria

Abstract

One of the most important problems in the economics of quality control is the process targeting problem. The process targeting problem is concerned with the determination of the optimal process parameters, namely the mean and the variance of the process. The majority of the target models in the literature deals with a single-stage production system. In the real world industrial settings, products are often processed through multi-stage production systems. In this thesis, we consider two processes in series that produce a product. The product is assumed to have two quality characteristics; the first quality characteristic is determined by the setting of the first process and the second quality characteristic is determined by the setting of the two processes. Four process targeting models have been developed based on product uniformity criteria that is represented via Taguchi quadratic loss function using both acceptance sampling and 100 percent inspection with and without error. The first model is developed for the two processes using lot by lot inspection sampling plan and assuming inspection is error free. Sensitivity analysis is conducted to study the effect of model's parameters on its solution. The second model is developed from the first model assuming inspection is error prone. Sensitivity analysis is performed on the above developed model and the results obtained show that the type I and type II errors have tremendous impact on the optimal process parameters. In the third model, quality of products is performed through 100 percent inspection instead of sampling plan. The fourth model extends to the situation where the inspection is considered error prone. Sensitivity analysis has been performed to study the effect of cost parameters on expected loss and optimal process means. The models have been tested on a real case. The results indicated that the errors have tremendous impact on product quality and process. The thesis concluded by a set of possible directions for further research.