Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

Chien-Pai Han


Process capability indices (PCIs) play an important role in the field of Statistical Process Control. Prior to the last 25 years, PCIs had been formulated to assess the quality of a single product characteristic. Product quality, however, is typically dependent on several related variables. Therefore, there is a great need for multivariate process capability indices (MPCIs). The quality of a product is almost always determined from sample data. Thus, it is imperative that an MPCI has a corresponding confidence interval. In that way, conclusions may be drawn regarding the capability of the process that makes that product. Of the MPCIs proposed over the last 25 years, few have an accompanying confidence interval. Under the assumption of multivariate normality, we propose four new MPCIs, each having a corresponding confidence interval, as well as a decision rule for determining whether a process can be declared capable or not at a given level of significance. Two of the indices are based on principal component analysis (PCA) while the other two rely on non-PCA linear transformations. The indices we propose represent multivariate extensions of the popular univariate index, C_p. Current indices that extend C_p to the multivariate domain are referred to as MC_p s. From this group we select four indices that have accompanying confidence intervals to use in a comparative study with our own. The selected indices have been criticized in the past by other authors for different reasons. Upon investigation we find that our proposed indices do not suffer from the same limitations as the others and that they may serve as adequate tools for assessing multivariate capability in a manufacturing environment.


Mathematics | Physical Sciences and Mathematics


Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons