A new process capability index for multiple quality characteristics based on principal components

This paper presents a new multivariate process capability index (MPCI) which is based on the principal component analysis (PCA) and is dependent on a parameter (Formula presented.) which can take on any real number. This MPCI generalises some existing multivariate indices based on PCA proposed by several authors when (Formula presented.) or (Formula presented.). One of the key contributions of this paper is to show that there is a direct correspondence between this MPCI and process yield for a unique value of (Formula presented.). This result is used to establish a relationship between the capability status of the process and to show that under some mild conditions, the estimators of this MPCI is consistent and converge to a normal distribution. This is then applied to perform tests of statistical hypotheses and in determining sample sizes. Several numerical examples are presented with the objective of illustrating the procedures and demonstrating how they can be applied to determine the viability and capacity of different manufacturing processes.