Professor Toshio Nakagawa has already published more than two hundred research papers on subject of maintenance and reliability theory in main reliability journals, and has published four books titled on "Maintenance Theory of Reliability" in 2005, "Shock and Damage Models in Reliability Theory" in 2007, "Advanced Reliability Models and Maintenance Policies" in 2008, and "Stochastic Processes with Applications to Reliability Theory" in 2011 from Springer. His research group in Nagoya has continuously studied reliability and maintenance theory and their applications since 1988, and has published a large number of papers in reliability journals and at international conferences. Professor Nakagawa has active research interchange mainly with professors in Taiwan, Korea and China. Dr. Xufeng Zhao is currently engaged in reliability theory and maintenance policies of stochastic systems, shock models and applications in computer science. His research works related with above topics have been published in European Journal of Operational Research, IEEE Transactions on Reliability, Reliability Engineering & System Safety, International Journal of Systems Science, and so on. He also has finished several book chapters published from Springer, Wiley, and World Scientific. Dr. Zhao is a member of Nagoya Computer and Reliability Research organized by Professor Toshio Nakagawa twenty-five years ago in Japan. He has some joint works with experts in Canada, Korea, Taiwan, and China. Not only that, Professor Nakagawa has just finished his fifth book from Springer entitled "Random Maintenance Policies" which will be published in 2014. Some of the results obtained in the book has been used into some real models in computer science by his group. Furthermore, Dr. Zhao studied shock and damage models extensively for his Ph.D. dissertation entitled "Studies on Extensive Cumulative Damage Models and Their Applications to Garbage Collections". All of these works serve asfoundation for this note.

Professor Toshio Nakagawa has already published more than two hundred research papers on subject of maintenance and reliability theory in main reliability journals, and has published four books titled on "Maintenance Theory of Reliability" in 2005, "Shock and Damage Models in Reliability Theory" in 2007, "Advanced Reliability Models and Maintenance Policies" in 2008, and "Stochastic Processes with Applications to Reliability Theory" in 2011 from Springer. His research group in Nagoya has continuously studied reliability and maintenance theory and their applications since 1988, and has published a large number of papers in reliability journals and at international conferences. Professor Nakagawa has active research interchange mainly with professors in Taiwan, Korea and China. Dr. Xufeng Zhao is currently engaged in reliability theory and maintenance policies of stochastic systems, shock models and applications in computer science. His research works related with above topics have been published in European Journal of Operational Research, IEEE Transactions on Reliability, Reliability Engineering & System Safety, International Journal of Systems Science, and so on. He also has finished several book chapters published from Springer, Wiley, and World Scientific. Dr. Zhao is a member of Nagoya Computer and Reliability Research organized by Professor Toshio Nakagawa twenty-five years ago in Japan. He has some joint works with experts in Canada, Korea, Taiwan, and China. Not only that, Professor Nakagawa has just finished his fifth book from Springer entitled "Random Maintenance Policies" which will be published in 2014. Some of the results obtained in the book has been used into some real models in computer science by his group. Furthermore, Dr. Zhao studied shock and damage models extensively for his Ph.D. dissertation entitled "Studies on Extensive Cumulative Damage Models and Their Applications to Garbage Collections". All of these works serve asfoundation for this note.

Professor Toshio Nakagawa has already published more than two hundred research papers on subject of maintenance and reliability theory in main reliability journals, and has published four books titled on "Maintenance Theory of Reliability" in 2005, "Shock and Damage Models in Reliability Theory" in 2007, "Advanced Reliability Models and Maintenance Policies" in 2008, and "Stochastic Processes with Applications to Reliability Theory" in 2011 from Springer. His research group in Nagoya has continuously studied reliability and maintenance theory and their applications since 1988, and has published a large number of papers in reliability journals and at international conferences. Professor Nakagawa has active research interchange mainly with professors in Taiwan, Korea and China. Dr. Xufeng Zhao is currently engaged in reliability theory and maintenance policies of stochastic systems, shock models and applications in computer science. His research works related with above topics have been published in European Journal of Operational Research, IEEE Transactions on Reliability, Reliability Engineering & System Safety, International Journal of Systems Science, and so on. He also has finished several book chapters published from Springer, Wiley, and World Scientific. Dr. Zhao is a member of Nagoya Computer and Reliability Research organized by Professor Toshio Nakagawa twenty-five years ago in Japan. He has some joint works with experts in Canada, Korea, Taiwan, and China. Not only that, Professor Nakagawa has just finished his fifth book from Springer entitled "Random Maintenance Policies" which will be published in 2014. Some of the results obtained in the book has been used into some real models in computer science by his group. Furthermore, Dr. Zhao studied shock and damage models extensively for his Ph.D. dissertation entitled "Studies on Extensive Cumulative Damage Models and Their Applications to Garbage Collections". All of these works serve asfoundation for this note.