Student-t Processes for Degradation Analysis

Abstract

Stochastic processes are widely used to analyze degradation data, and the Gaussian process is a particularly common one. In this article, we propose a robust statistical model using a Student-t process to assess the lifetime information of highly reliable products. This model is statistically plausible and demonstrates a substantially improved fit when applied to real data. A computationally accurate approach is proposed to calculate the first-passage-time density function of the Student-t degradation-based process; related properties are investigated as well. In addition, this article provides parameter estimation using the EM-type algorithm and a simple model-checking procedure to evaluate the appropriateness of the model assumptions. Several case studies are performed to demonstrate the flexibility and applicability of the proposed model with random effects and explanatory variables. Technical details, datasets, and R codes are available as supplementary materials.

Keywords:

• Conjugate distribution
• Gamma process
• Heavy tail
• Inverse Gaussian process
• Volterra integral equation

Acknowledgments

The authors thank the editor, associate editor, and referees for their helpful and valuable comments.

Additional information

Funding

This work was supported in part by Academia Sinica (AS-CDA-107-M09) and Ministry of Science and Technology (MOST-106-2118-M-001-013-MY3) of Taiwan, Republic of China.