Superposed Poisson process models with a modified bathtub intensity function for repairable systems

Abstract

Bathtub-shaped failure intensity is typical for large-scaled repairable systems with a number of different failure modes. Sometimes, repairable systems may exhibit a failure pattern different from the traditional bathtub shape, due to the existence of multiple failure modes. This study proposes two superposed Poisson process models with modified bathtub intensity functions to capture this kind of failure pattern. The new models are constructed by the superposition of the generalized Goel–Okumoto process and power law process (or log-linear process). The proposed models can be applied to masked failure-time data from repairable systems where the modes of collected failure-times are unobserved or unavailable. Bayesian posterior computation algorithms based on the data augmentation method are developed for the inference on the parameters or their functions of the superposed Poisson process models. This study also examines the best model selection among the candidate models in the Bayesian framework and modeling check using the residuals. A practical case study with a data set of unscheduled maintenance events for complex artillery systems illustrates potential applications of the proposed models for the purpose of reliability prediction for the repairable systems.

Keywords:

• Bayesian inference
• data augmentation
• modified bathtub intensity
• Goel–Okumoto process
• superposed Poisson process

Acknowledgments

The authors are grateful to three referees and AE for their careful reading and helpful suggestions.

Additional information

Funding

The work of S. J. Bae was supported in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education under Grant 2018R1D1A1A09083149, and in part by the National Research Foundation of Korea (NRF) funded by the Korea Government (MSIT) under Grant 2020R1A4A407990411.

Notes on contributors

Tao Yuan

Tao Yuan received a BE degree in thermal engineering from Tsinghua University, China; an MS degree in aerospace engineering and an ME degree in industrial engineering from Texas A&M University, College Station; and a PhD degree in industrial engineering from the University of Tennessee, Knoxville. He is a professor in the Department of Industrial and Systems Engineering at Ohio University. His research interests mainly include reliability modeling and prediction, as well as reliability testing and characterization for electronic devices. He is a member of IISE, INFORMS and IEEE.

Tianqiang Yan

Tianqiang Yan earned his BE degree in electronic information science and technology at Nanjing Agricultural University, China. He also received an MS degree in industrial and system engineering from the Russ College of Engineering and Technology at Ohio University. His primary research interests involve reliability modeling and data analysis.

Suk Joo Bae

Suk Joo Bae is a professor in the Department of Industrial Engineering at Hanyang University, Seoul, South Korea. He received his PhD degree from the School of Industrial and Systems Engineering at the Georgia Institute of Technology in 2003. He served as a reliability engineer at Samsung SDI, Korea from 1996 to 1999. His research interests are centered on reliability evaluation of light displays, nanodevices, and battery systems including fuel cells via accelerated life and degradation testing, fault diagnoses and prognostics for condition-based maintenance, and process monitoring for large-volumed on-line sensing data. He has published more than 60 papers in journals such as Technometrics, Journal of Quality Technology, IISE Transactions, Reliability Engineering & System Safety, and IEEE Transactions on Reliability. Currently he is an associate editor of IEEE Transactions on Reliability. He is a member of INFORMS and IEEE.