Phase II Monitoring of Dirichlet Profiles

Abstract

ABSTRACT The quality of a product or a process is usually maintained by monitoring one or more of its quality characteristics. In some cases, these quality characteristics are highly correlated, and their sum must be equal to a constant, such data are referred to as compositional data. The Dirichlet distribution is a multivariate extension of the Beta distribution and can be used to model compositional data under certain conditions. Sometimes we are interested in monitoring functional relationships like monitoring Dirichlet regression profiles. No studies have been presented yet to monitor Dirichlet regression profiles in Phase II. Thus, the main objective of this paper is to present some procedures to monitor Dirichlet profiles in Phase II. A MEWMA control chart is presented to monitor the Dirichlet regression parameters in Phase II (Method A). In addition, a MEWMA chart is proposed to solve the high dimensionality problem by monitoring the difference between the observed and the reference profiles (Method B). Moreover, a third method is proposed to detect which Dirichlet random variable is the source of the out‐of‐control signal (Method C). Simulations and an illustrative example based on a real case application are used to assess the performance of the proposed methods.