Note on History of Age Replacement Policies

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 placi...

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Main Authors: Toshio Nakagawa, Mingchih Chen, Xufeng Zhao
Format: Article
Language:English
Published: International Journal of Mathematical, Engineering and Management Sciences 2018-06-01
Series:International Journal of Mathematical, Engineering and Management Sciences
Subjects:
Online Access:https://www.ijmems.in/assets//12-vol.-3%2c-no.-2%2c-151%E2%80%93166%2c-2018.pdf
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spelling doaj-3ad40442090745dc924bc046f9ab6fae2020-11-25T01:18:48ZengInternational Journal of Mathematical, Engineering and Management SciencesInternational Journal of Mathematical, Engineering and Management Sciences2455-77492455-77492018-06-013215116610.33889/IJMEMS.2018.3.2-012Note on History of Age Replacement PoliciesToshio Nakagawa0Mingchih Chen1Xufeng Zhao2Department of Business Administration, Aichi Institute of Technology, Toyota 470-0392, JapanGraduate Institute of Business Administration, Fu Jen Catholic University, New Taipei City 24205, TaiwanCollege of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, ChinaThis 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.https://www.ijmems.in/assets//12-vol.-3%2c-no.-2%2c-151%E2%80%93166%2c-2018.pdfAge replacementReplacement firstReplacement lastReplacement overtimeGeneral replacement.
collection DOAJ
language English
format Article
sources DOAJ
author Toshio Nakagawa
Mingchih Chen
Xufeng Zhao
spellingShingle Toshio Nakagawa
Mingchih Chen
Xufeng Zhao
Note on History of Age Replacement Policies
International Journal of Mathematical, Engineering and Management Sciences
Age replacement
Replacement first
Replacement last
Replacement overtime
General replacement.
author_facet Toshio Nakagawa
Mingchih Chen
Xufeng Zhao
author_sort Toshio Nakagawa
title Note on History of Age Replacement Policies
title_short Note on History of Age Replacement Policies
title_full Note on History of Age Replacement Policies
title_fullStr Note on History of Age Replacement Policies
title_full_unstemmed Note on History of Age Replacement Policies
title_sort note on history of age replacement policies
publisher International Journal of Mathematical, Engineering and Management Sciences
series International Journal of Mathematical, Engineering and Management Sciences
issn 2455-7749
2455-7749
publishDate 2018-06-01
description 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.
topic Age replacement
Replacement first
Replacement last
Replacement overtime
General replacement.
url https://www.ijmems.in/assets//12-vol.-3%2c-no.-2%2c-151%E2%80%93166%2c-2018.pdf
work_keys_str_mv AT toshionakagawa noteonhistoryofagereplacementpolicies
AT mingchihchen noteonhistoryofagereplacementpolicies
AT xufengzhao noteonhistoryofagereplacementpolicies
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