The Skew-Normal Distribution in SPC

Abstract

Modeling real data sets, even when we have some potential (as)symmetric models for the underlying data distribution, is always a very difficult task due to some uncontrollable perturbation factors. The analysis of different data sets from diverse areas of application, and in particular from statistical process control (SPC), leads us to notice that they usually exhibit moderate to strong asymmetry as well as light to heavy tails, which leads us to conclude that in most of the cases, fitting a normal distribution to the data is not the best option, despite of the simplicity and popularity of the Gaussian distribution. In this paper we consider a class of skew-normal models that include the normal distribution as a particular member. Some properties of the distributions belonging to this class are enhanced in order to motivate their use in applications. To monitor industrial processes some control charts for skew-normal and bivariate normal processes are developed, and their performance analyzed. An application with a real data set from a cork stopper’s process production is presented.