International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Note on History of Age Replacement Policies

Note on History of Age Replacement Policies

Toshio Nakagawa
Department of Business Administration, Aichi Institute of Technology, Toyota 470-0392, Japan.

Mingchih Chen
Graduate Institute of Business Administration, Fu Jen Catholic University, New Taipei City 24205, Taiwan.

Xufeng Zhao
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China.

DOI https://dx.doi.org/10.33889/IJMEMS.2018.3.2-012

Received on March 22, 2017
Accepted on September 27, 2017


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).


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