Linear Consecutive-k-out-of-n: G System Reliability Analysis

Authors

  • Garima Chopra Department of Mathematics, University Institute of Engineering & Technology, Maharshi Dayanand University, Rohtak, Haryana, India
  • Mangey Ram 1) Department of Mathematics, Computer Science & Engineering, Graphic Era Deemed to be University, Dehradun, Uttarakhand, India 2)Institute of Advanced Manufacturing Technologies, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia

DOI:

https://doi.org/10.13052/jrss0974-8024.15211

Keywords:

Consecutive-k-out-of-n: G system, SVT, common cause failure, copula, reliability measures

Abstract

The concerned study pertains to the development of a new stochastic model for the reliability analysis of linear consecutive-k-out-of-n: G system, where k>n2. In the developed model, system may collapse as a result of common cause failure or hardware failure in its units. The system has exponentially distributed failure rates, and in case of breakdown, it is repaired with the copula method. The developed model has been examined through supplementary variable technique (SVT) along with Laplace transform. The current paper has specifically studied consecutive-(n-1)-out-of-n: G system. The performance of such system having ten components is explored and its various reliability measures have been obtained and discussed with the help of graphs. The originality of this work lies in incorporating common cause failure in conjunction with copula repair in the reliability modeling of consecutive systems through the SVT. The study confirms that an increase in failure rates and the number of components of the concerned system decreases mean time to failure (MTTF). The profit of linear consecutive-9-out-of-10: G system is examined with the help of a numerical example.

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Author Biographies

Garima Chopra, Department of Mathematics, University Institute of Engineering & Technology, Maharshi Dayanand University, Rohtak, Haryana, India

Garima Chopra is presently working as Assistant Professor in the Department of Mathematics, University Institute of Engineering & Technology, Maharshi Dayanand University, Rohtak, Haryana, India. She received her Ph.D. degree in Mathematics from G. B. Pant University of Agriculture and Technology, Pantnagar, India in 2010. She is recipient of Certificate of Appreciation for excellent academic performance in M.Sc. by Ministry of HRD, Government of India. She has 11 years teaching experience. She has publications in renowned international journals. Her areas of interest are reliability analysis, wavelet transform and image processing.

Mangey Ram, 1) Department of Mathematics, Computer Science & Engineering, Graphic Era Deemed to be University, Dehradun, Uttarakhand, India 2)Institute of Advanced Manufacturing Technologies, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg 195251, Russia

Mangey Ram received the Ph.D. degree major in Mathematics and minor in Computer Science from G. B. Pant University of Agriculture and Technology, Pantnagar, India in 2008. He has been a Faculty Member for around thirteen years and has taught several core courses in pure and applied mathematics at undergraduate, postgraduate, and doctorate levels. He is currently the Research Professor at Graphic Era (Deemed to be University), Dehradun, India & Visiting Professor at Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, Russia. Before joining the Graphic Era, he was a Deputy Manager (Probationary Officer) with Syndicate Bank for a short period. He is Editor-in-Chief of International Journal of Mathematical, Engineering and Management Sciences; Journal of Reliability and Statistical Studies; Journal of Graphic Era University; Series Editor of six Book Series with Elsevier, CRC Press-A Taylor and Frances Group, Walter De Gruyter Publisher Germany, River Publisher and the Guest Editor & Associate Editor with various journals. He has published 300 plus publications (journal articles/books/book chapters/conference articles) in IEEE, Taylor & Francis, Springer Nature, Elsevier, Emerald, World Scientific and many other national and international journals and conferences. Also, he has published more than 60 books (authored/edited) with international publishers like Elsevier, Springer Nature, CRC Press-A Taylor and Frances Group, Walter De Gruyter Publisher Germany, River Publisher. His fields of research are reliability theory and applied mathematics. Dr. Ram is a Senior Member of the IEEE, Senior Life Member of Operational Research Society of India, Society for Reliability Engineering, Quality and Operations Management in India, Indian Society of Industrial and Applied Mathematics, he has been a member of the organizing committee of a number of international and national conferences, seminars, and workshops. He has been conferred with “Young Scientist Award” by the Uttarakhand State Council for Science and Technology, Dehradun, in 2009. He has been awarded the “Best Faculty Award” in 2011; “Research Excellence Award” in 2015; “Outstanding Researcher Award” in 2018 for his significant contribution in academics and research at Graphic Era Deemed to be University, Dehradun, India. Recently, he has been received the “Excellence in Research of the Year-2021 Award” by the Honourable Chief Minister of Uttarakhand State, India.

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Published

2023-02-10

How to Cite

Chopra, G. ., & Ram, M. . (2023). Linear Consecutive-k-out-of-n: G System Reliability Analysis. Journal of Reliability and Statistical Studies, 15(02), 669–692. https://doi.org/10.13052/jrss0974-8024.15211

Issue

2022: Vol 15 Iss 2

Section

Articles