Analysis of a Stochastic Model with Rework System

  • Mangey Ram 1) Department of Mathematics, Computer Science and Engineering, Graphic Era Deemed to be University, Dehradun, India 2) Institute of Advanced Manufacturing Technologies, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, Russia
  • Ganga Negi 3) Department of Mathematics, Graphic Era Deemed to be University, Dehradun, India 4) Department of Mathematics, Dev Bhoomi Uttarakhand University, Dehradun, India
  • Nupur Goyal Department of Mathematics, Graphic Era Deemed to be University, Dehradun, India
  • Anuj Kumar Department of Mathematics, University of Petroleum & Energy Studies, Dehradun, India
Keywords: Multi state model, Markov process, reliability measures and sensitivity analysis

Abstract

The demand in the present global industrial system, requires the challenge to meet the growing consumer capabilities and requirements constantly. So, there is always a need to improve different parameters, one of them being different types of failures involved in the working of different engineering systems related to communication systems, manufacturing goods, nuclear and hydro power plants, automobiles and many others. Human error occurring in the working of various systems has always been the challenge to the researchers and is being constantly worked upon by the researchers in the analysis and improvement of reliability and availability of different complex and multistate systems. In the present paper, there is a three-unit system consisting of the unit A with two subunits in parallel and other units B and C are connected in series with A. The authors have investigated and analysed different reliability measures like availability, MTTF and sensitivity taking into account the human failure and carrying out rework system. This research work aims at the study of reliability and availability measures of a multi-state system incorporating human error so as to increase the efficiency of industrial systems by taking maintenance and rework measures to enhance the availability factors. This would help to understand and estimate the reliability measures of any such systems in the field of telecommunication, any electronic devices like that in small power plants, robot systems and such others. Also, a comparison has been made between the availability and reliability estimates in the presence and in the absence of human error. The techniques used are Markov process, Laplace transformation and supplementary variable technique.

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Author Biographies

Mangey Ram, 1) Department of Mathematics, Computer Science and Engineering, Graphic Era Deemed to be University, Dehradun, India 2) Institute of Advanced Manufacturing Technologies, Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, 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 SciencesJournal of Reliability and Statistical StudiesJournal of Graphic Era University; Series Editor of six Book Series with ElsevierCRC Press-A Taylor and Frances GroupWalter 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 55 books (authored/edited) with international publishers like ElsevierSpringer NatureCRC Press-A Taylor and Frances GroupWalter 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.

Ganga Negi, 3) Department of Mathematics, Graphic Era Deemed to be University, Dehradun, India 4) Department of Mathematics, Dev Bhoomi Uttarakhand University, Dehradun, India

Ganga Negi is pursuing her Ph.D. in Mathematics from Graphic Era Deemed to be university, Dehradun, India. Currently, she is currently working as an Assistant Professor at the Department of Allied Sciences, Dev Bhoomi Uttarakhand University, Dehradun, India. Her research areas include reliability analysis and optimization.

Nupur Goyal, Department of Mathematics, Graphic Era Deemed to be University, Dehradun, India

Nupur Goyal received the Bachelor’s degree in Computer science in 2009 from Kurukshetra University, Kurukshetra, Haryana, India. She received the master’s degree in mathematics in 2011 from H.N.B. Garhwal University, Srinagar, Uttarakhand, India and Ph.D. degree from Graphic Era University, Dehradun, Uttarakhand, India in November 2016. Her research interests are in the area of reliability theory and operation research. She has been an Assistant Professor in the Mathematics Department of the Suraj Degree College, Mahendergarh, Haryana in 2016. She has been an Assistant Professor in the Mathematics Department of the Garg Degree College, Laksar, Haridwar from 2017 to October 2018. She has been an Assistant Professor and Head of the Department of Applied Science and Humanities Department, Roorkee Institute of Technology, Roorkee from 2018 to January 2020. Currently, she is an Assistant Professor in department of Mathematics, Graphic Era Deemed to be University, Dehradun, India. She is a reviewer of various international journals including Springer, Emerald and IEEE, IJMEMS. She has published around 50 research papers in various reputed national and international journals, book chapters including Springer, Emerald, Taylor & Francis, Inderscience and many other and also presented her research works at national and international conferences. She is the guest editor in many special issues of some journals. She is associate editor in the International Journal of Mathematical, Engineering and Management Sciences. She has published one book in CRC Press – Taylor & Francis group. She has been a member of the organizing committee of a number of international and national conferences, seminars, and workshops.

Anuj Kumar, Department of Mathematics, University of Petroleum & Energy Studies, Dehradun, India

Anuj Kumar received his Master’s and doctorate degree in Mathematics from G. B. Pant University of Agriculture and Technology, Pantnagar, India. Currently, he is working as an Associate Professor of Mathematics at University of Petroleum and Energy Studies, Dehradun, India. His current area of interest is reliability analysis, nature inspired optimization and Multi-criteria decision-making (MCDM). He has Published around 35 research articles in the journals of national/international repute and authored/edited 03 books in his area of interest. In addition, he is instrumental in various other research related activities like editing/reviewing for various reputed journals, organizing/participating in conferences.

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Published
2022-08-03
Section
Articles