Uncertainty quantification for monotone stochastic degradation models

ABSTRACT

Degradation data are an important source of product reliability information. Two popular stochastic models for degradation data are the Gamma process and the inverse Gaussian (IG) process, both of which possess monotone degradation paths. Although these two models have been used in numerous applications, the existing interval estimation methods are either inaccurate given a moderate sample size of the degradation data or require a significant computation time when the size of the degradation data is large. To bridge this gap, this article develops a general framework of interval estimation for the Gamma and IG processes based on the method of generalized pivotal quantities. Extensive simulations are conducted to compare the proposed methods with existing methods under moderate and large sample sizes. Degradation data from capacitors are used to illustrate the proposed methods.

KEYWORDS:

• coverage probability
• Gamma process
• generalized pivotal quantity
• inverse Gaussian process

About the authors

Piao Chen received the B.E. degree in industrial engineering from Shanghai Jiao Tong University, China, in 2013, and the Ph.D. degree in industrial systems engineering and management from the National University of Singapore, in 2017. He is currently a research scientist in the Institute of High Performance Computing, Singapore. His research interests include data analysis and industrial statistics.

Zhi-Sheng Ye received the joint B.E. degree in material science and engineering and economics from Tsinghua University, Beijing, China, in 2008, and the Ph.D. degree in industrial and systems engineering from the National University of Singapore, in 2012. He is currently an Assistant Professor with the Department of Industrial Systems Engineering and Management, National University of Singapore. His research interests include reliability engineering, complex systems modeling, and industrial statistics.

Acknowledgments

We are grateful to the editors and two referees for their insightful comments that have led to a substantial improvement to an earlier version of the article.

Additional information

Funding

This work was supported by the Natural Science Foundation of China (71601138), Singapore AcRF Grant (R-266-000-113-114), and the National Research Foundation Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program.