A Bayesian nonparametric system reliability model which integrates multiple sources of lifetime information

Abstract

We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may exist. However, traditional Bayesian reliability models are quite computationally complex, relying on MCMC techniques. Our approach utilizes the conjugate properties of the beta-Stacy process, which is the fundamental building block of our model. These individual models are linked together using a method of moments estimation approach. This model is computationally fast, allows for right-censored data, and is used for estimating and predicting system reliability.

Keywords:

• beta-Stacy process
• conjugate models
• Dirichlet process
• method of moments
• right censoring

Acknowledgments

The authors thank the B61 Life Extension Program at Los Alamos National Laboratory for providing funding which made a part of this work possible. We also thank Brandon Greenwell for his work and insights on this project. We also thank the editor and two anonymous reviewers whose comments have substantially improved this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors thank the B61 Life Extension Program at Los Alamos National Laboratory for providing funding which made a part of this work possible. We also thank Brandon Greenwell for his work and insights on this project. We also thank the editor and two anonymous reviewers whose comments have substantially improved this work.

Notes on contributors

Richard L. Warr

Richard L. Warr is an Assistant Professor of Statistics at Brigham Young University. He obtained a Ph.D. in Statistics from the University of New Mexico.  His research interests include Bayesian statistics, Bayesian nonparametric methods, and reliability.

Jeremy M. Meyer

Jeremy M. Meyer earned a master’s degree from Brigham Young University with a research emphasis in Bayesian nonparametric methods. He is currently working as a data scientist for MScience doing big data analytics.

Jackson T. Curtis

Jackson T. Curtis earned his Master’s degree in statistics from Brigham Young University. He currently works as a data scientist at a software company.