Department of Business Administration, Aichi Institute of Technology, Toyota 470-0392, Japan.
Graduate Institute of Business Administration, Fu Jen Catholic University, New Taipei City 24205, Taiwan.
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China.
This paper tries to trace our research history briefly from Barlow and Proschan to attain general replacement models. We begin with a random age replacement policy that is planned at a random time Y and call it as random replacement. When the distribution of Y becomes a degenerate distribution placing unit mass at T, age replacement is formulated. We obtain the general formulas for optimum replacement times. We next suppose the unit works for a job with random works, and replacement policies with N cycles are discussed. As follows, we combine age and random replacement models and discuss replacement first, replacement last, replacement overtime, replacement overtime first and replacement overtime last. By formulating the distributions of replacement times with n variables, general replacement models with n replacement times are obtained.
Keywords- Age replacement, Replacement first, Replacement last, Replacement overtime, General replacement.
Nakagawa, T., Chen, M., & Zhao, X. (2018). Note on History of Age Replacement Policies. International Journal of Mathematical, Engineering and Management Sciences, 3(2), 151-166. https://dx.doi.org/10.33889/IJMEMS.2018.3.2-012.
Conflict of Interest
The authors thank the Grant-in-Aid for Scientific Research (C), Grant No. 15K03562 (2015-2017) from the Ministry of Education, Culture, Sports, Science in Japan and the Ministry of Science and Technology in Taiwan (No. MOST 104-2221-E-030-010).
Barlow, R. E., & Proschan, F. (1996). Mathematical theory of reliability. Society for Industrial and Applied Mathematics.
Chen, M., Qian, C., Zhao, X., & Nakagawa T. (2016). Replacement policy with a general model. Advanced Reliability and Maintenance Modeling VII (pp. 49-56). Magraw-Hill, Taiwan.
Karlin, S., & Taylor, H. M. (1975). A first course in stochastic process. Academic Press, New York.
Nakagawa, T. (2005). Maintenance theory of reliability. Springer Science & Business Media.
Nakagawa, T. (2008). Advanced reliability models and maintenance policies. Springer Science & Business Media.
Nakagawa, T. (2014). Random maintenance policies. Springer, London.
Nakagawa, T., & Zhao, X. (2015). Maintenance overtime policies in reliability theory: models with random working cycles. Springer.
Sarkar, A., Panja, S. C., & Sarkar, B. (2011). Survey of maintenance policies for the last 50 years. International Journal of Software Engineering and Applications, 2(3), 130-148.
Zhao, X., & Nakagawa, T. (2012). Optimization problems of replacement first or last in reliability theory. European Journal of Operational Research, 223(1), 141-149.
Zhao, X., Al-khalifa, K. N., Hamouda, A. M., & Nakagawa, T. (2015). What is middle maintenance policy? Quality and Reliability Engineering International, 32(7), 2403-2414.