Non-parametric Bayesian modeling of hazard rate with a change point for nanoelectronic devices

Abstract

This study proposes a non-parametric Bayesian approach to the inference of the L-shaped hazard rate with a change point, which has been observed for nanoelectronic devices in experimental studies. Instead of assuming a restrictive parametric model for the hazard rate function, this article uses a flexible non-parametric model based on a stochastic jump process to describe the decreasing hazard rate in the infant mortality period. A Markov chain Monte Carlo simulation algorithm that implements a dynamic version of the Gibbs sampler is developed for posterior simulation and inference. The proposed approach is applied to analyze an experimental data set, which consists of the failure times of a novel nanoelectronic device: a metal oxide semiconductor capacitor with mixed oxide high-k gate dielectric. Results obtained from the analysis demonstrate that the proposed non-parametric Bayesian approach is capable of producing reasonable estimates of the hazard rate function and the change point. As a flexible method, the proposed approach has the potential to be applied to assess the reliability of novel nanoelectronic devices when the failure mechanisms are generally unknown, parametric reliability models are not readily available, and the availability of data is limited.

Keywords:

• Hazard rate
• change point
• non-parametric Bayesian modeling
• Gibbs sampler
• nanoelectronics

Acknowledgements

The authors would like to thank Alou C.-H. Lin for preparing the sample devices. The authors would like to thank the reviewers for their insightful comments and suggestions. This study was partially supported by the NSF projects CMMI-0926420, CMMI-0825908, and CMMI-0926379.