A NONLINEAR MODEL FOR DETERMINING THE MOST ECONOMIC PROCESS MEAN UNDER A BETA DISTRIBUTION

Abstract

The selection of the process mean (target) is critically important since it directly affects the process defective rate, material cost, scrap or rework cost, and the loss to the customer due to the deviation of product performance. The goal is to determine the optimum process target based on minimizing total cost relating to product quality. For mathematical convenience, normal distributions have been traditionally assumed in solving this problem. Under practical situations, however, typical process distributions are often either positively or negatively skewed. Consequently, the normal distribution may not be ideal for many situations. In this paper, we consider a beta distribution which can be shaped and scaled to fit most skewed and symmetric process distributions. Furthermore, this paper uses a quality loss function to capture and quantify the quality loss from the customer's perspective. Finally, we develop an economic model for selecting the optimum process target. An example is given to illustrate the model.