Inference for reliability in a multicomponent stress–strength model for a unit inverse Weibull distribution under type-II censoring

ABSTRACT

In this paper, a unit inverse Weibull distribution as well as its basic structural properties is proposed. Furthermore, classical inferences for multicomponent reliability are discussed under type-II censoring when stress and strength components have a common parameter. The maximum likelihood estimator of the reliability is obtained and in sequel an asymptotic interval is constructed. Pivotal quantities are constructed and then generalized point and interval estimators are obtained for the reliability. Likelihood and pivotal quantities-based estimations are presented when all parameters are unequal as well. The performance of different estimators is investigated using simulation studies and real-life examples are studied from an application viewpoint. Finally, some concluding remarks are given.

KEYWORDS:

• Inverse Weibull distribution
• Multicomponent stress–strength model
• Generalized confidence interval
• Maximum likelihood estimation
• Generalized pivotal quantity

Acknowledgements

The authors wish to our thank the Editor and referees for their valuable suggestions, which led to the improvement of the paper. The research work of Yogesh Mani Tripathi is partially supported under a grant MTR/2022/000183 by Science and Engineering Research Board, India. This work of Liang Wang was supported by the National Natural Science Foundation of China (No. 12061091) and the Yunnan Fundamental Research Projects (No. 202101AT070103).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Kundan Singh

Kundan Singh is a Ph.D. student in the Department of Mathematics, Indian Institute of Technology Patna, India. He received his MTech degree in Mathematics and Computing from Indian Institute of Technology, Patna, India and MSc in Mathematics from Indian Institute of Technology, Kharagpur, India. His research interests include reliability estimation, censoring, Bayesian estimation, competing risks model.

Amulya Kumar Mahto

Dr. Amulya Kumar Mahto is an assistant professor at School of Mathematical & Statistical Sciences, IIT Mandi India. He received his PhD in Statistics and MTech in Mathematics and Computing from Indian Institute of Technology, Patna, India and MSc in Mathematics and Computing from Indian School of Mines, Dhanbad, India. His research interest includes accelerated life testing, competing risks, multicomponent stress-strength reliability and has published number of research papers in journals of repute. His research interest also extends to transfer learning.

Yogesh Tripathi

Yogesh Mani Tripathi received his Ph.D. degree from the Department of Mathematics, Indian Institute of Technology Kharagpur, India, under the guidance of Prof. Somesh Kumar. He was a Postdoctoral Fellow with Prof. Éric Marchand with the Department of Mathematics at University of Sherbrooke, Canada and with G. S. Shieh at Institute of Statistical Science, Academia Sinica, Taiwan. Currently, he is an Associate Professor with the Department of Mathematics, Indian Institute of Technology Patna, India. His research interests are in decision theory, life-testing and reliability analysis.

Liang Wang

Liang Wang was born in 1983. He received the Ph.D. degree in Applied Mathematics from Northwestern Polytechnical University, Xi’an, China, in 2012. He is currently an Associate Professor with the School of Mathematics, Yunnan Normal University, Kungming, China. His research interests include applied probability and statistics, reliability analysis and life testing.