Using Bayesian models to assess the capability of a manufacturing process in the presence of unobserved assignable causes

Abstract

The capability of a manufacturing process is a measure of how well the process is able to manufacture items within required engineering specifications. A process capability analysis is traditionally considered only after all assignable causes of variation have been removed. Under these conditions, a manufacturing process is considered to be in control. This is often an idealized situation since assignable causes such as tool wear, environmental conditions and batch variation in raw materials are inherent in many processes. In this article, the capability of a process is modelled in such a way that the process distribution is allowed to change between observed subgroups due to assignable causes. Standard and hierarchical Bayesian models are used. The Bayesian framework allows for prior information that is known about the manufacturing processes to be formally incorporated into the model. The hierarchical Bayesian framework is useful when the within group variation dominates the between group variation, and when an overall measure of process capability is desired for the entire process. The usefulness of the proposed methods is demonstrated through the application of several examples and issues such as practical implementation and computation are addressed.

Keywords:

• Bayesian inference
• conjugate distribution
• dynamic process capability
• hierarchical model
• random effects model

Acknowledgements

We wish to thank the two referees whose valuable suggestions greatly improved both the presentation and content of the article.

Disclosure statement

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of this article.

Notes on contributors

Alan M. Polansky, received his Ph.D. in Statistics from Southern Methodist University in 1995. He is currently an Associate Professor in the Division of Statistics at Northern Illinois University. His current interests include statistical inference for networks, hierarchical models, nonparametric Bayesian methods, and resampling methods.

Adam Maple, received his M.S. in Statistics from Northern Illinois University in 2013.