Reliability estimation of a consecutive k-out-of-n system for non-identical strength components with applications to wind speed data

ABSTRACT

In the stress-strength reliability literature, although identical components assumption may not be realistic due to the structure of a system, independent and identically distributed components have been commonly used. In this study, we aim to contribute to the literature by studying of non-identical distributed components in a consecutive $k$-out of-$n$ system when both stress and strength components follow the proportional hazard rate models. Estimation methods for the stress-strength reliability of this system are investigated from frequentist and Bayesian perspectives. Maximum likelihood and uniformly minimum variance unbiased estimations are obtained in the frequentist approach. Based on the suitability of the structure, approximate Bayes estimates methods: Lindley’s approximation, Markov Chain Monte Carlo through Metropolis-Hastings or Gibbs sampling algorithms and exact Bayes estimates are derived. Asymptotic confidence and highest posterior density credible intervals are also constructed for all cases. We provide comprehensive simulation experiments for investigating the performances of the considered estimates. Wind speed data from NASA’s satellite data source project are used in the application of the considered model and methods. We present the comparison of wind energy potentials of two districts on the Aegean coast of Turkey using our model structure after determining their wind speed distributions.

KEYWORDS:

• Stress-strength reliability
• consecutive $k$-out of-$n$:G system
• non-identical component
• proportional hazard rate model
• NASA POWER data

Acknowledgements

The authors thank the associate editor and the anonymous referees for their helpful comments and suggestions for the improvement of the paper.

The real data in this study were obtained from the NASA Langley Research Center POWER Project funded through the NASA Earth Science Directorate Applied Science Program.

Disclosure statement

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

Supplemental data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/16843703.2023.2173426

Additional information

Notes on contributors

Duygu Demiray

Duygu Demiray received her Ph.D. degree with full scholarship recipient in the Department of Mathematics at Yeditepe University, Istanbul, Turkey. She is working as an Assistant Professor in the Computer Engineering Department at Beykoz University, Istanbul, Turkey. Her main research interests include probability theory, statistical inference, reliability theory and analysis and Bayesian statistics.

Fatih Kızılaslan

Fatih Kızılaslan completed his Ph.D. degree in the Department of Mathematics at Gebze Technical University, Kocaeli, Turkey. Currently, he is an Associate Professor in the Department of Statistics at Marmara University, Istanbul, Turkey, and also he has worked as a Postdoctoral Fellow in the Department of Biostatistics at the University of Oslo, Norway since December 2021. His research interest is in statistical inference, reliability analysis, and survival analysis with high-dimensional data.