A nonlinear quantile regression for accelerated destructive degradation testing data

Abstract

Traditional regression approaches to Accelerated Destructive Degradation test (ADDT) data have modeled the mean curve as being representative. However, maximum likelihood estimates of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear Quantile Regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the $\tau$th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

Keywords:

• Accelerated destructive degradation test
• asymmetric Laplace distribution
• bootstrap estimator
• generalized EM algorithm
• order statistic estimator

Acknowledgments

The authors are sincerely grateful to the editor and anonymous reviewers for their detailed comments and many valuable suggestions.

Conflict of interest

The authors report there are no competing interests to declare.

Additional information

Funding

This work was supported by the Technology Innovation Program (20015756, Development of Fuel Cell Highly Durable Operation Technique for Fuel Cell Powered Heavy Duty Vehicle) funded By the Ministry of Trade, Industry & Energy (MOTIE, Korea). This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy of the Republic of Korea (No. 2021202090056C).

Notes on contributors

Suk Joo Bae

Suk Joo Bae is a professor in the Department of Industrial Engineering at Hanyang University, Seoul, Korea. He received his PhD. from the ISyE Department at Georgia Tech, 2003. Prof. Bae was the editor-in-chief of the Journal of the Korean Society for Quality Management, The Journal of Applied Reliability, and the associate editor of IEEE Transactions on Reliability. He has published more than 100 papers in journals such as Technometrics, Journal of Quality Technology, Reliability Engineering & System Safety, IISE Transactions, and IEEE Transactions on Reliability. His research interests include reliability evaluation and modeling of light displays, batteries and fuel cells via accelerated life and degradation testing, and prognostics and diagnostics health monitoring systems.

Munwon Lim

Munwon Lim is a post-doc in the Department of Industrial Engineering, Hanyang University, Seoul, Korea. She received her PhD from the Department of Industrial Engineering at Hanyang University, 2024. Her current research interests include anomaly detection of large complex systems based on signal and image processing, prognostics, and health management of big-sized sensor data.