On Birnbaum importance assessment for aging multi-state system under minimal repair by using Lz-transform method

Figure Legend: Principal scheme of the water cooling system.

minimal repair by using the Lz-transform method-advances in engineering

Lz-transform method

Figure Legend: State-transition diagram of the water cooling system.

About the author

Anatoly Lisnianski, PhD

Expert-engineer in the Reliability Department of The Israel Electric Corporation Ltd., Israel and Scientific Supervisor of the Center for Reliability and Risk Management , SCE – Shamoon College of Engineering, Beer Sheva, Israel

E-mail: [email protected][email protected]

URL http://www.angelfire.com/oz/lisninanski/

Anatoly LISNIANSKI received his M.Sc. degree in Electrical Engineering from the University of Information Technologies, Precision Mechanics and Optics, Sankt-Petersburg, Russia; and Ph.D. degree in Reliability in 1984 from Federal Scientific and Production Center ‘‘Aurora’’ in Sankt-Petersburg. From 1975 through 1989, he was a researcher at this center. Starting in 1991 he is working in the Reliability Department of the Israel Electric Corporation as an engineering expert. He is specialized in reliability assessment and optimization for complex technical systems. He is the author and co-author of more than 120 journal papers, two books, some book chapters, and inventions in the field of reliability and applied statistics. He is a senior member of IEEE and a member of Israel Statistical Association.

About the author

Ilia Frenkel, PhD

Chair of the Center for Reliability and Risk Management and Senior Lecturer of the Industrial Engineering and Management Department, SCE – Shamoon College of Engineering, Beer Sheva, Israel

E-mail: [email protected]

URL http://www.sce.ac.ilhttp://www.frenkel-online.com

He has obtained M.Sc. degree in Applied Mathematics from Voronezh State University, Russia, and PhD degree in Operational Research and Computer Science from Institute of Economy, Ukrainian Academy of Science, formerly USSR. He has more then 40 years of academic experience and teaching in Universities and Institutions of Russia and Israel. From 1988 till 1991 he worked as Department Chair and Associate Professor in the Applied Mathematics Department and at Computers Department, Volgograd Civil Engineering Institute, Russia .From 2005 he is served as Chair of the Center for Reliability and Risk Management and Senior Lecturer of the Industrial Engineering and Management Department, SCE-Shamoon College of Engineering, Beer Sheva, Israel.

He has specialized in applied statistics and reliability with application to preventive maintenance. He is an Editor and a member of editorial board of scientific and professional journals .

He published one book and more than 50 scientific articles and book chapters in the fields of reliability, applied statistics and production and operation management.

About the author

Lev Khvatskin, PhD

Researcher of the Center for Reliability and Risk Management and Senior Lecturer of the Industrial Engineering and Management Department, SCE – Shamoon College of Engineering, Beer Sheva, Israel

E-mail: [email protected] , URL http://www.sce.ac.il

Dr. Khvatskin has obtained his M.Sc. degree in Mechanical Engineering from University of Railway Transport, Moscow, Russia and PhD degree in Reliability Engineering and Inventory Control from Railway Research Institute, Moscow, Russia.

He has specialized in statistical and probabilistic methods in reliability of power and refrigeration equipment, scheduled and unscheduled repair and service, refrigeration, heating and air-conditioning systems.

He published more than 30 scientific articles and book chapters in the fields of reliability, applied statistics and production and operation management.

 

Journal Reference

Reliability Engineering & System Safety, Volume 142, October 2015, Pages 258-266.

Anatoly Lisnianski1 , Ilia Frenkel2, Lev Khvatskin2 

Show Affiliations
  1. The Israel Electric Corporation Ltd., P. O. Box 10, Bait Amir, Haifa 3100, Israel
  2. Center for Reliability and Risk Management, Industrial Engineering and Management Department, SCE – Shamoon College of Engineering, Beer-Sheva, Israel

Abstract

This paper considers a reliability importance evaluation for components in an aging multi-state system. In practical reliability engineering a “curse of dimensionality” (the large number of states that should be analyzed for a multi-state system model) is a main obstacle for importance assessment. In order to challenge the problem, this paper proposes a new method that is based on an LZ-transform of the discrete-state continuous-time Markov process and on Ushakov׳s Universal Generating Operator. The paper shows that the proposed method can drastically reduce a computational burden. In order to illustrate the method, a solution of a real world problem is presented as a numerical example.

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