A Study on Joint Availability forkout ofnand Consecutivekout ofnPoints and Intervals

AbstractThe performance of maintenance systems can be described by many indexes such as availability, mean up-time and mean down-time and so forth. The availability is the most important measure among them. Availability has many types, including instantaneous, steady-state and average availability, etc. In this paper, the joint availabilities for k out of n intervals and consecutive k out of n intervals under the Markov assumption are presented in recursive equations. When n = k , the k out of n and consecutive k out of n systems reduce to a series system, and in this situation, the corresponding results have been given by Csenki [9] and Cui et al. [17] using different methods. In contrast, the major contributions of the paper are the extensions of the known results for series systems; that is, the situations when k < n have not been covered in the previous studies and will be presented in the present paper. Some numerical examples and discussions are given to illustrate the results obtained in the paper. Finally, the conclusions are summarizedKey Words: Aggregated stochastic processesconsecutive k out of njoint interval availabilityk out of nMarkov repairable system. Additional informationNotes on contributorsShijia DuShijia Du B. S. degree in mathematics from China University of Mining and Technology, China in 2009, and is working towards the Ph.D. degree in Management Science and Engineering at the School of Management and Economics, Beijing Institute of Technology, Beijing, China. Her research interests are reliability, maintainability, stochastic modeling, and aggregated stochastic processes.Lirong CuiLirong Cui Professor in the School of Management & Economics, Beijing Institute of Technology, China. He received his Ph.D. degree in Probability and Statistics from the University of Wales, UK in 1994. He has worked on reliability related problems since 1986. In 2000, he co-authored of a book on reliability which was published by Kluwer Academic Publishers. Now he is only from mainland China to serve as an associate editor of IEEE Transactions on Reliability. He also is the Vice Chairman of Reliability committee of OR of China, and an associate editor of Journal of Application of Statistics and Management. In 2005, He was awarded the new century excellent talents in university of China. His recent research interests are stochastic modeling, quality and reliability engineering, simulation and optimization, operations research and applications of probability and statistics in various fields.Haijun LiHaijun Li Professor of Mathematics and Statistics in the Department of Mathematics, Washington State University, Pullman, WA. He received his Ph.D. degree in Mathematics from the University of Arizona, Tucson, AZ in 1994. He is currently an associate editor of the probability journal of Methodology and Computing in Applied Probability, and an associate editor of the reliability journal of IEEE Transactions on Reliability. His research interests include applied probability, stochastic processes and risk analysis.Xibin ZhaoXibin Zhao Lecturer at the School of Software, Tsinghua University, China. He received his Ph.D. in 2004 from the School of Computer Science and Telecommunication Engineering, Jiangsu University, China. His research interests include distributed system control, and system safety management.