Comparative study of the C_p and S_pmk indices for logistic regression profile using different link functions

Abstract

In some process control applications, the quality of a process or a product can be characterized by a relationship between a response variable and one or more independent variables which is typically referred to as a profile. For an in-control process, process capability indices are widely used for the characterization of the capability of a process. Although there are several studies in monitoring profiles, there are a few studies to evaluate the process capability of the profiles. In the majority of cases, the response variable in the profile follows a normal distribution, but, sometimes, this assumption is violated. In many industrial applications, the response variable is binary or binomial, as in the case of whether a product can be classified as defective or nondefective. In this article, we calculate the $C_{\mathrm{p}}$ and $S_{\text{pmk}}$ indices to measure the process capability when the quality of a process is characterized by a logistic regression profile with three well-known link functions, the logit, the probit and the complementary log-log.

Keywords:

• Link function
• logistic regression profile
• process capability index
• profile monitoring

Acknowledgment

The authors would like to thank the Editor and the referees for their useful comments which resulted in improving the quality of this article.

Additional information

Notes on contributors

Vasileios Alevizakos

Vasileios Alevizakos received his MSc in Mathematical Modeling in Modern Technologies and Financial Engineering in 2018 from the National Technical University of Athens. He is currently a PhD candidate at the National Technical University of Athens. His research interests are statistical process control, process capability analysis and robust parameter design.

Christos Koukouvinos

Christos Koukouvinos is a Professor at the National Technical University of Athens, Department of Mathematics. He received his Bachelor in Mathematics in 1983 and PhD in 1988 in Statistics both from the University of Thessaloniki. He is the author of numerous papers in the field of statistics and combinatorics and he served on the editorial board of 10 related journals and a guest editor for three special issues. He was awarded the prestigious Hall Medal of the ICA in 1996. He is a fellow of the ICA and a member of the Council of ICA from 2000 to 2003. His research interests include statistical experimental and optimal designs, biostatistics, statistical quality control, and combinatorial designs.

Angeliki Lappa

Angeliki Lappa received her Bachelor in Applied Mathematical and Physical Sciences in 2014 from the National Technical University of Athens and her MSc in Applied Mathematical Sciences in 2016 from the National Technical University of Athens. She is currently a PhD candidate at the National Technical University of Athens. Her research interests are factorial designs, generalized linear models, and quality control techniques.