Economic optimization of acceptance interval in conformity assessment: 1. Process with no systematic effect

In inspections for conformity assessment, an acceptance interval smaller than the tolerance interval is often determined in order to reduce the risk of consumers obtaining non-conforming items in the market. The presence of non-conforming items in the market impairs the evaluation of items by customers and may have an impact on revenue by decreasing prices. However, setting too small an acceptance interval reduces the revenue from the process by decreasing the number of the items available in the market. We thus propose a method to determine the optimum acceptance interval in conformity assessment by means of maximization of the revenue from processes. For this purpose, we give a mathematical model for the price of an item and its cost in the production process. Through theoretical analysis and simulations, it is shown that a parameter in the price model is the key in the optimization. In this paper we report a method for processes where no systematic effect component of measurement uncertainty exists, and in part 2 of this series we will report an extended method in which systematic effects are taken into consideration.