The determination of product and process parameters under the non-normal distribution

Abstract

Burr developed a density function that is able to represent a wide range of normal and non-normal distributions, and it has been shown that this density function can be easily applied to investigate the effect of non-normality in the studies of statistical process control (SPC). The process mean setting problem is one of the important topic for SPC. Traditionally, the product/process characteristic is assumed to be normally distributed. However, this assumption may not be true and there may exist non-normal characteristic in many practical production processes. In this paper, the work of process mean setting is examined by introducing Burr's density function as the underlying probability distribution of product/ process characteristic, such that the effect of non-normality to the determination of optimal process mean, standard deviation and specification limits of product/process characteristic can be studied. The linear asymmetrical quality loss function is addressed for measuring the quality loss of conforming product. The expected total cost of product includes the quality loss of conforming products, the rework cost of non-conforming product and the scrap cost of non-conforming product. A numerical example is provided for illustration.