Interval estimation for Wiener processes based on accelerated degradation test data

Abstract

Degradation is a primary cause of failures for many materials and products. Although stochastic processes have been widely applied to degradation data, there is a lack of efficient and accurate methods for interval estimation of model parameters and reliability characteristics given limited degradation data. Using the method of generalized pivotal quantities, this study develops interval estimation procedures for fixed-effects and mixed-effects Wiener degradation processes based on accelerated degradation test data. The fixed-effects processes are common for mature products and the mixed-effects model is capable of capturing heterogeneities in an immature product. The constructed confidence intervals are shown to have exact, or asymptotically exact, frequentist coverage probabilities. Extensive simulations are conducted to compare the proposed procedures to other competing methods, including the large sample normal approximation, and the bootstrap. The simulation results reveal that the proposed intervals have satisfactory performance in terms of the coverage probability and the average interval length. The proposed interval estimation procedures are successfully applied to accelerated degradation data from commercial white LEDs.

KEYWORDS:

• Accelerated degradation tests
• fixed-effects
• generalized pivotal quantity
• mixed-effects

Acknowledgments

We are grateful to the editor, the associate editor, and the two referees for their insightful comments that have lead to a substantial improvement of an earlier version of the paper.

Funding

This work was supported in part by the Natural Science Foundation of China [71601138], Singapore AcRF Tier 1 Funding [R-266-000-113-114], and the National Research Foundation Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE).

Notes on contributors

Lanqing Hong is a Ph.D. candidate in the Department of Industrial Systems Engineering and Management at the National University of Singapore. She received a B.Eng. degree (2014) from Shanghai Jiao Tong University. Her current research interests include reliability engineering, degradation modelling, stochastic process models, environmental risk evaluation, and data analysis for environmental sustainability problems.

Zhi-Sheng Ye received a joint B.E. (2008) in material science & engineering, and economics from Tsinghua University. He received his Ph.D. degree (2012) from the National University of Singapore. He is currently an assistant professor in the Department of Industrial Systems Engineering and Management, National University of Singapore. His research interests include reliability engineering, complex systems modeling, and industrial statistics.

Josephine Kartika Sari received her Ph.D. degree in industrial & systems engineering (2008) from the National University of Singapore. She is currently working at LedNed Holding B.V. in The Netherlands.