Reliability Evaluation of Repairable Parallel-Series Multi-State System Implementing Interval Valued Universal Generating Function

  • Renu Department of Mathematics, Statistics and Computer Science, G.B. Pant University of Agriculture and Technology, Pantnagar, India
  • Soni Bisht Department of Mathematics, Eternal University, Baru Sahib, Himachal Pradesh, India https://orcid.org/0000-0003-4715-5280
  • S.B. Singh Department of Mathematics, Statistics and Computer Science, G.B. Pant University of Agriculture and Technology, Pantnagar, India
Keywords: Interval valued universal generating function, Reliability, sensitivity, Mean time to failure, Repairable parallel-series multi-state system, Laplace-Steiltjes transform

Abstract

In this paper, we have studied a repairable parallel-series multi-state system. The proposed system consists of components in series and components in parallel in which each component has three possible states. The interval universal generating function (IUGF) is presented, and the corresponding composition operators are defined. The reliability assessment of the considered system is done with the help of the IUGF approach. It is worth mentioning that IUGF got attention from various researchers due to its straightforwardness, less complexity, and universal applications. In the present model, probabilities of different components, reliability, sensitivity, and mean time to failure are evaluated with the help of the Markov process; Laplace-Steiltjes transform method applying IUGF. A numerical example has also been taken to illustrate the proposed technique.

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Author Biographies

Renu , Department of Mathematics, Statistics and Computer Science, G.B. Pant University of Agriculture and Technology, Pantnagar, India

Renu received the B.Sc. degree in science from Kumaun University, Nainital, India in 2015 and M.Sc. degree in Mathematics from G. B. Pant University of Agriculture and Technology, Pantnagar, India, in 2017. She has cleared CSIR NET in Mathematics in 2019. She has also been selected for INSPIRE Programme of Government of India from 2012 to 2015. She has been published one research paper in Emerald. Her area of research is Reliability Theory.

Soni Bisht, Department of Mathematics, Eternal University, Baru Sahib, Himachal Pradesh, India

Soni Bisht received the B.Sc. and M.Sc. degree in science from H.N.B. Garhwal Central University, Srinagar, India in 2012 and 2014, and the Ph.D. degree major in Mathematics and minor in Computer science from G. B. Pant University of Agriculture and Technology, Pantnagar, India, in 2018. She is currently working as an Assistant Professor in Department of Mathematics, Eternal University, Baru Sahib, Himachal Pradesh in India. She has been published 12 research papers in IEEE Explore, Emerald, International Journal of Mathematical, Engineering and Management Sciences and many other national and international journals of repute and also presented her works at national and international conferences. She has been conferred with “Young Scientist Award” by the Uttarakhand State Council for Science and Technology, Dehradun, in 2018. Her area of research is Reliability Theory, Applied Mathematics, Network Reliability and Parallel and Distributed Systems.

S.B. Singh, Department of Mathematics, Statistics and Computer Science, G.B. Pant University of Agriculture and Technology, Pantnagar, India

S. B. Singh is a Professor in the Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar (Uttarakhand), India. He has around 25 years of teaching and research experience to Undergraduate and Post Graduate students at different Engineering Colleges and University. Prof. Singh is a member of Indian Mathematical Society, Operations Research Society of India, Member of Advisory board of Intellectual Society for Socio-Techno Welfare (ISST) and National Society for Prevention of Blindness in India and Member of Indian Science Congress Association. He is a regular reviewer of many books and International/National Journals. Prof. Singh has been a member of organizing committee of many international and national conferences and workshops. He is an Editor-in-Chief of the ‘Journal of Reliability and Statistical Studies’. He is member of Editorial board of seven journals and edited books as well. He has authored and coauthored eight books on different courses of Applied/Engineering Mathematics. Prof. Singh has been conferred with five national awards and the Best Teacher Award. He has been included in the special edition of Marquis Who’s Who in the World 2015, USA. His area of research is Reliability Theory/Engineering.

Published
2021-04-07
Section
Articles