Parametric analysis of time-censored aggregate lifetime data

Abstract

Many large organizations have developed ambitious programs to build reliability databases by collecting field failure data from a large variety of components. To make the database concise, only the number of component replacements in a component position during an operation time interval is reported in these databases. This leads to time-censoring in the aggregate failure data. Statistical inference for the time-censored aggregate data is challenging, because the likelihood function based on some common lifetime distributions can be intractable. In this study, we propose a general parametric estimation framework for the aggregate data. We first use the gamma distribution and the Inverse Gaussian (IG) distribution to model the aggregate data. Bayesian inference for the two models is discussed. Unlike the gamma/IG distribution, other lifetime distributions involve multiple integrals in the likelihood function, making the standard Bayesian inference difficult. To address the estimation problem, an approximate Bayesian computation algorithm that does not require evaluating the likelihood function is proposed, and its performance is assessed by simulation. As there are several candidate distributions, we further propose a model selection procedure to identify an appropriate distribution for the time-censored aggregate data. A real aggregate dataset extracted from a reliability database is used for illustration.

Keywords:

• Weibull distribution
• gamma distribution
• log-normal distribution
• inverse Gaussian distribution
• approximate Bayesian computation
• Monte Carlo sampling

Acknowledgments

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

Additional information

Funding

This work was supported by National Natural Science Foundation of China under grants 71601138, 71771221, and 71871191.

Notes on contributors

Piao Chen

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, reliability engineering and statistical inference.

Zhi-Sheng Ye

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.

Qingqing Zhai

Qingqing Zhai received his B.E. (2011) and Ph.D. (2015) degree from Beihang University, Beijing, China. He is currently an Associate Professor in School of Management, Shanghai University, China. His research interests mainly focus on degradation modeling and complex systems reliability modeling.