Reliability analysis of J-out-of-N system with Nadarajah-Haghighi component under generalised progressive hybrid censoring

Abstract

In reliability analysis of the J-out-of-N system, people usually assume that the lifetime of components in the system follows the exponential, Weibull or gamma distribution. However, this assumption has some limitations in fitting real-life data. Nadarajah–Haghighi distribution has more advantages than exponential, Weibull and gamma distributions in reliability modelling of real data. This paper investigates the reliability analysis of a J-out-of-N system in which the lifetimes of components follow Nadarajah–Haghighi distribution. Based on the generalised progressive hybrid censoring (GPHC) sample, the maximum likelihood estimates (MLEs), and the asymptotic confidence intervals of unknown parameters and the reliability function of the system are obtained by using the numerical procedure and asymptotic normality theory of MLEs, respectively. The Bayesian estimates under squared error loss are derived using the Tierney–Kadane’s (T–K) method. Furthermore, the Bayesian credible intervals are constructed based on Metropolis–Hastings method. Monte Carlo simulations are carried out to evaluate the performance of the proposed estimation methods. Finally, two real data sets are analysed for illustrative purposes.

KEYWORDS:

• J-out-of-N system
• Nadarajah–Haghighi distribution
• reliability analysis
• generalised progressive hybrid censoring
• Metropolis–Hastings method

Acknowledgments

The author thanks the editor-in-chief, editors and anonymous reviewers for the useful suggestions which helped improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 71571144, 71401135 and 11701406] and the Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province [2016KW-033].

Notes on contributors

Xiaolin Shi

Xiaolin Shi received her B.Sc. degree and M. Eng. from Northwestern Polytechnical University and then received her M. Phil. degrees from City University of Hong Kong. She received her Ph.D. degree from Northwestern Polytechnical University. She currently works as an associate professor of School of Electronics Engineering at Xi’an University of Posts & Telecommunications, China. Her research interests include system reliability modelling and analysis.

Yimin Shi

Yimin Shi is a full professor at School of Mathematics and Statistics, Northwestern Polytechnical University. Xian, Chaina. His research interests include system reliability modelling and analysis, information fusion theory.

Qiankun Song

Qiankun Song is a full professor at the Department of Mathematics, Chongqing Jiaotong University, Chongqing, China. He has published two books and about 120 papers in journals. His research interests are stability analysis of neural networks, system reliability modelling and statistical inference.