Reliability for k-out-of-n:F balanced systems with m sectors

ABSTRACT

Rapid technological developments have resulted in the development of new reliability systems, such as unmanned aerial vehicles with balanced engine systems, whose reliability analysis cannot be covered by currently existing techniques. Thus, research on this topic is very important and significant. In this article, a k-out-of-n:F balanced system with m sectors is introduced based on some real background and then four related system reliability models are developed. Several methods, such as the order statistics technique, Markov process imbedding technique, recursive method, and convolution method, are used on the various models for different situations. The elegant Markov process imbedding technique is extensively considered in order to obtain the smallest number of system states. The labeling of system states is presented and the state labeling formula is given for exponential distributions and the presented models, which is very convenient for usage. To the best of our knowledge, this is the first report in the literature on such a balanced system, and the corresponding research results are new contributions. In addition to system reliability formulas, the moments of the system lifetime are given. Finally, some numerical examples are presented to illustrate the results obtained in this article.

KEYWORDS:

• k-out-of-n
• balanced system
• system reliability
• Markov process imbedding technique
• order statistics
• recursive method

Acknowledgements

We thank the two anonymous referees and the associate editor for their comments and suggestions.

Additional information

Funding

This work is supported by the NSF of China under Grants 71631001 and 61572442.

Notes on contributors

Lirong Cui

Lirong Cui is a professor in the School of Management & Economics at Beijing Institute of Technology. He received his Ph.D. degree in probability and statistics from the University of Wales in 1994. He has worked on quality and reliability-related problems since 1986 and published more than 100 papers and technical reports. In 2000, he co-authored a book on reliability published by Kluwer Academic Publishers. He served as an associate editor of IEEE Transactions on Reliability from 2005 to 2015. He also serves as an associate editor for Quality Technology & Quantitative Management and Communications in Statistics: Theory and Methods, Simulation and Computation. In 2005, he received the New Century Excellent Talents in China award. His recent research interests are in stochastic modeling, quality and reliability engineering, simulation and optimization, operations research, and applications of probability and statistics in various fields.

Hongda Gao

Hongda Gao is currently a Ph.D. student in the School of Management and Economics at Beijing Institute of Technology. He received his bachelor's degree in engineering management from China University of Petroleum, Qingdao, P.R. China, in 2013. His research interests focus on reliability modeling, maintenance optimization, and Monte Carlo simulation. He is now supported by the China Scholarship Council as a visiting scholar at Penn State University.

Yuchang Mo

Yuchang Mo is currently a distinguished professor with the School of Mathematical Sciences, Huaqiao University, Quanzhou, People's Republic of China. He received his Ph.D. degree in computer science from Harbin Institute of Technology, Harbin, P.R. China. He was a visiting scholar with the Department of Electrical and Computer Engineering, University of Massachusetts (UMass) Dartmouth from September 2012 to August 2013. He was the Program Chair of the 5th Conference on Dependable Computing in China. He is currently a senior expert at the Reliability Research Society of China and a senior expert at the Technical Committee on Fault Tolerant Computing of China. His current research focuses on the reliability analysis of complex systems and networks using combinatorial models.