System Reliability Analysis: Transition from Binary to Multi-state Models
暫譯: 系統可靠性分析：從二元模型轉換到多狀態模型

這段文字涵蓋了基於狀態性能系統和二進制系統的基本與進階技術。它展示了使用 Petri 網進行安全關鍵系統的動態可靠性分析，以及對具有修補功能的軟體進行的動態資源分配建模。

Akshay Kumar received the B.Sc. and M.Sc. degree in science from Chaudhary Charan Singh University, Meerut, India, in 2010 and 2012, 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 2017. He is currently working as an Assistant Professor in the Department of Mathematics, Graphic Era Hill University, Dehradun in India. He currently teaching LLP and Probability and Statistics in B.Sc.(H) and taught Group Theory, Numerical Methods, Business Statistics, Discrete Mathematics, Engineering Mathematics-III and in PG level taught OR, Linear Algebra and Discrete Structure. He is a regular Reviewer for more than 43 international journals. He has published 80 plus research papers in Communications in Statistics - Simulation and Computation., Emerald, Inderscience, International Journal of Mathematical, Engineering and Management Sciences, IGI Global Publisher, MDPI, Cambridge Scientific Publishers, Springer nature, Elsevier Multimedia Tools and Applications and many other national and international journals of repute and presented his works at national and international conferences. Also, he has published 3 books (edited) with international publishers. His fields of research are reliability theory, fuzzy reliability, signature reliability and applied Mathematics. He has been awarded recently "Outstanding Researcher Award" in 2019-2020 at Graphic Era Hill University Dehradun India and in 15th and 16th Uttarakhand State Science and Technology Congress 2020-2022 for his significant contribution in academics and research at Graphic Era Deemed to be University, Dehradun, India.

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 fifteen 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. 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 the 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 reputed publishers and the Guest Editor & Associate Editor with various journals. He has published 400 plus publications (journal articles/books/book chapters/conference articles) in many national and international journals and conferences. Also, he has published more than 60 books (authored/edited) with international publishers. His fields of research are reliability theory and applied mathematics. Dr. Ram is a Senior Member of the IEEE, the Senior Life Member of the Operational Research Society of India, the 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 the "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; the "Research Excellence Award" in 2015; "Outstanding Researcher Award" in 2018 for his significant contribution to academics and research at Graphic Era Deemed to be University, Dehradun, India. Also, he has received the "Excellence in Research of the Year-2021 Award" by the Honourable Chief Minister of Uttarakhand State, India, and the "Emerging Mathematician of Uttarakhand" state award by the Director, Uttarakhand Higher Education. Recently, he received the "Distinguished Service Award-2023" for the subject & nation development by Vijñāna Parishad of India.

Rajesh S. Prabhu Gaonkar is presently a Professor on Deputation at School of Mechanical Sciences, Indian Institute of Technology Goa (IIT Goa). He is B.E. (Mechanical Engg., 1993), M.E. (Industrial Engg., 1997), P.G.D.O.M. (I.G.N.O.U., 2000), Ph.D. (I.I.T. Bombay, 2007) and a Research Fellow at National University of Singapore (2010-2011). He is Former Professor and Head of the Mechanical Engineering Department at Goa College of Engineering and Former Dean of Faculty of Engineering at the Goa University. He is Associate Editor of the International Journal of System Assurance Engineering and Management and Editorial Board Member of the International Journal of Mathematical, Engineering and Management Sciences. He is on reviewer panel of more than 20 International Journals. Prof. Rajesh S. Prabhu Gaonkar is first recipient (awardee) of the Goa State Award for Meritorious Teacher in Technical Education for the year 2015. This is awarded in public recognition of valuable services to the community as a teacher of outstanding merit. He is recipient of prestigious Fellowship of Indian Institution of Industrial Engineering (IIIE) for his immense contribution in the field of industrial engineering in the state of Goa and recipient of Dr. J. M. Mahajan Award for the year 2016-17 by Indian Institution of Industrial Engineering for contributing substantially to the spread/ propagation of Industrial Engineering in Education i.e. in Institutes and in university. He is also a Fellow of the Institution of Engineers (India). Prof. Rajesh S. Prabhu Gaonkar was awarded "Diploma of Excellence" for the paper presentation at DQM International Reliability Summer School by D.Q.M. Research Center in Serbia in 2005. He has also bagged best paper award at four International Conferences. He has published over 90 research papers in various National & International Conferences and Journals; co-authored a book on "Fuzzy Reliability -- Concepts and Applications" (2007) and co-authored a monograph "Six-Sigma: A Key to Enterprise Excellence" (2008). He was involved in organization of about 30 International Conferences in various capacities. He has total 30 years of teaching and research experience. He has four book chapters, three Indian Patents and two Australian Innovation Patents to his credit. He has successfully guided four Ph.D. students as on date. Prof. Rajesh S. Prabhu Gaonkar is Founder Chairman of Mechanical Engineering Students Association (MESA) formed to organize technical events in Mechanical Engineering and related fields at Goa College of Engineering and founder Chairman of Indian Institution of Industrial Engineering (IIIE) Goa Chapter. He conceived and implemented MESSERGY (Mechanical Engineering Students' Social and Education Responsibility and Green Initiates) voluntary sustainable project for Mechanical Engineering Students of Goa College of Engineering. His teaching areas include Industrial Engineering, Operations Research, Advanced Optimization, Reliability Engineering/ Reliability based Design, CAD/CAM, Maintenance Engineering and Management, Operations Management, System Modeling and Simulation. His research areas include Fuzzy Set Applications in Reliability and Maintenance Engineering, Multi-Attribute Decision Making etc.

Yury Klochkov holds the post of Rector of Tyumen Industrial University. He has the degree of mechanical engineering from the Samara State Transport University in 2001, Postgraduate studies majoring in 05.02.23 Standardization and quality management from Samara State Aerospace University (National Research University) (SSAU) in 2006 and Doctorate degree majoring in 05.02.23 Standardization and quality management from Samara State Aerospace University (National Research University) (SSAU) 2012. He has achieved many awards, certificates and acknowledgements like in 2007 the Potanin Foundation for young teachers grant holder, in 2014 the certificate of little Russian Quality Leader, Amity University Professor Emeritus certificate in 2016. In 2018 Dr. Yury Klochkov was the St. Petersburg Government prize winner for excellence in higher education and secondary professional education and in 2019 he got the acknowledgment for dedicated work and high standard of professionalism by Peter the Great St. Petersburg Polytechnic University. He is also the guest editor of many special issues of magazines like Key Engineering Materials, Scientific.net, Resources, MDPI, International Journal of System Assurance Engineering and Management, Springer, International Journal of Reliability, Quality and Safety Engineering, World Scientific and International Journal of Mathematical, Engineering and Management Sciences (IJMEMS). He is the visiting professor in Amity University and University of Kragujevac conferences. His total number of published research articles is 193. His H-index in Scopus with 58 publications is 20 and in WoS with 45 publications is 15. His total number of Teaching and Learning publications is 16. He also was certified by the Academic Methodological Association and the Ministry of Education and Science of the Russian Federation of the most significant Teaching and Learning publications.

**阿克沙伊·庫馬爾**（Akshay Kumar）於2010年和2012年分別在印度梅魯特的查烏達里·查蘭·辛格大學（Chaudhary Charan Singh University）獲得理學士（B.Sc.）和理學碩士（M.Sc.）學位，並於2017年在印度潘塔納加爾的G.B.潘特農業與技術大學（G. B. Pant University of Agriculture and Technology）獲得數學博士（Ph.D.）學位，主修數學，輔修計算機科學。他目前在印度德拉敦的圖形時代山大學（Graphic Era Hill University）數學系擔任助理教授，教授B.Sc.(H)的線性規劃（LLP）和機率與統計，並教授群論、數值方法、商業統計、離散數學、工程數學-III等課程，於研究生階段教授運籌學（OR）、線性代數和離散結構。他是超過43本國際期刊的定期審稿人，已在《統計通訊 - 模擬與計算》（Communications in Statistics - Simulation and Computation）、Emerald、Inderscience、國際數學、工程與管理科學期刊（International Journal of Mathematical, Engineering and Management Sciences）、IGI Global Publisher、MDPI、劍橋科學出版社（Cambridge Scientific Publishers）、施普林格自然（Springer nature）、Elsevier多媒體工具與應用（Multimedia Tools and Applications）及其他多本國內外知名期刊上發表了80篇以上的研究論文，並在國內外會議上展示了他的研究成果。此外，他還與國際出版社共同編輯出版了3本書籍。他的研究領域包括可靠性理論、模糊可靠性、簽名可靠性和應用數學。他最近在2019-2020年獲得了圖形時代山大學的「傑出研究者獎」，並在2020-2022年第15屆和第16屆烏塔拉坎德州科學與技術大會上因其在學術和研究方面的重大貢獻而獲獎。

**曼基·拉姆**（Mangey Ram）於2008年在印度潘塔納加爾的G.B.潘特農業與技術大學獲得數學博士（Ph.D.）學位，主修數學，輔修計算機科學。他擔任教職約十五年，教授多門純數學和應用數學的核心課程，涵蓋本科、研究生和博士階段。他目前是印度德拉敦的圖形時代（被認定為大學）研究教授。在加入圖形時代之前，他曾在辛迪克銀行擔任副經理（見習官）一段時間。他是《國際數學、工程與管理科學期刊》（International Journal of Mathematical, Engineering and Management Sciences）、《可靠性與統計研究期刊》（Journal of Reliability and Statistical Studies）、《圖形時代大學期刊》（Journal of Graphic Era University）的主編，並擔任六本書系列的系列編輯，還是多本期刊的客座編輯和副編輯。他在許多國內外期刊和會議上發表了400篇以上的出版物（期刊文章/書籍/書章/會議文章）。此外，他還與國際出版社共同出版了60本以上的書籍（作者/編輯）。他的研究領域包括可靠性理論和應用數學。拉姆博士是IEEE的高級會員、印度運籌學會的高級終身會員、印度可靠性工程、質量與運營管理學會的會員、印度工業與應用數學學會的會員。他曾參與多個國際和國內會議、研討會和工作坊的組織委員會。他於2009年獲得烏塔拉坎德州科學與技術委員會頒發的「青年科學家獎」。他於2011年獲得「最佳教職員獎」，2015年獲得「研究卓越獎」，2018年因其在圖形時代被認定為大學的學術和研究方面的重大貢獻而獲得「傑出研究者獎」。此外，他還獲得了烏塔拉坎德州首席部長頒發的「2021年研究卓越獎」和烏塔拉坎德州教育部長頒發的「烏塔拉坎德新興數學家」州獎。最近，他因對學科和國家的發展作出的貢獻而獲得了印度科學院的「傑出服務獎-2023」。

**拉傑什·S·普拉布·高卡爾**（Rajesh S. Prabhu Gaonkar）目前在印度理工學院果阿分校（IIT Goa）機械科學學院擔任教授。他擁有1993年的機械工程學士（B.E.）、1997年的工業工程碩士（M.E.）、2000年的運營管理研究生文憑（P.G.D.O.M.）、2007年的博士學位（Ph.D.，印度理工學院孟買）以及2010-2011年在新加坡國立大學的研究員經歷。他曾擔任果阿工程學院機械工程系的教授及系主任，並曾擔任果阿大學工程學院的院長。他是《系統保證工程與管理國際期刊》（International Journal of System Assurance Engineering and Management）的副編輯，以及《國際數學、工程與管理科學期刊》的編輯委員會成員。他是超過20本國際期刊的審稿小組成員。拉傑什·S·普拉布·高卡爾教授是2015年果阿州技術教育優秀教師獎的首位獲獎者，該獎項是對他作為優秀教師對社會的寶貴服務的公開認可。他還因在果阿州工業工程領域的巨大貢獻而獲得印度工業工程學會（IIIE）的榮譽獎學金，並因對工業工程在教育（即在學院和大學）的推廣作出重大貢獻而獲得2016-17年印度工業工程學會的Dr. J. M. Mahajan獎。他還是印度工程師學會的會員。拉傑什·S·普拉布·高卡爾教授於2005年在塞爾維亞的DQM國際可靠性夏季學校上因論文發表獲得「卓越文憑」。他在四個國際會議上獲得最佳論文獎，並在各種國內外會議和期刊上發表了90篇以上的研究論文；共同撰寫了《模糊可靠性——概念與應用》（2007）一書，並共同撰寫了專著《六西格瑪：企業卓越的關鍵》（2008）。他參與組織了約30個國際會議，擁有30年的教學和研究經驗。他擁有四個書章、三項印度專利和兩項澳大利亞創新專利。他至今成功指導了四名博士生。拉傑什·S·普拉布·高卡爾教授是機械工程學生協會（MESA）的創始主席，該協會旨在組織果阿工程學院的機械工程及相關領域的技術活動，並是印度工業工程學會（IIIE）果阿分會的創始主席。他構思並實施了MESSERGY（機械工程學生的社會與教育責任及綠色倡議）自願可持續項目，旨在為果阿工程學院的機械工程學生提供支持。他的教學領域包括工業工程、運營研究、高級優化、可靠性工程/基於可靠性的設計、CAD/CAM、維護工程與管理、運營管理、系統建模與模擬。他的研究領域包括可靠性和維護工程中的模糊集應用、多屬性決策等。

**尤里·克洛奇科夫**（Yury Klochkov）擔任秋明工業大學（Tyumen Industrial University）校長。他於2001年在薩馬拉國立交通大學獲得機械工程學位，於2006年在薩馬拉國立航空航天大學（國立研究型大學）完成標準化與質量管理的研究生學習，並於2012年獲得該校的博士學位，主修標準化與質量管理。他獲得了許多獎項、證書和表彰，例如2007年獲得波塔寧基金會的年輕教師獎學金，2014年獲得小俄羅斯質量領導者證書，2016年獲得阿米提大學名譽教授證書。2018年，尤里·克洛奇科夫博士因在高等教育和中等職業教育方面的卓越表現而獲得聖彼得堡政府獎，2019年因其專業水平和奉獻精神而獲得彼得大帝聖彼得堡理工大學的表彰。他還是多本期刊的特刊客座編輯，如《關鍵工程材料》（Key Engineering Materials）、Scientific.net、Resources、MDPI、《系統保證工程與管理國際期刊》、《施普林格》（Springer）、《可靠性、質量與安全工程國際期刊》和《國際數學、工程與管理科學期刊》（IJMEMS）。他是阿米提大學和克拉古耶瓦茨大學會議的訪問教授。他的研究文章總數為193篇，Scopus的H指數為20（58篇出版物），WoS的H指數為15（45篇出版物）。他的教學與學習出版物總數為16篇。他還獲得了俄羅斯聯邦教育科學部和學術方法學協會的認證，成為最重要的教學與學習出版物的作者。