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Geometric processes and replacement problem

Geometric processes and replacement problem In this paper, we introduce and study the geometric process which is a sequence of independent non-negative random variablesX 1,X 2,... such that the distribution function ofX n isF (a n−1 x), wherea is a positive constant. Ifa>1, then it is a decreasing geometric process, ifa<1, it is an increasing geometric process. Then, we consider a replacement model as follows: the successive survival times of the system after repair form a decreasing geometric process or a renewal process while the consecutive repair times of the system constitute an increasing geometric process or a renewal process. Besides the replacement policy based on the working age of the system, a new kind of replacement policy which is determined by the number of failures is considered. The explicit expressions of the long-run average costs per unit time under each replacement policy are then calculated, and therefore the corresponding optimal replacement policies can be found analytically or numerically. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Geometric processes and replacement problem

Acta Mathematicae Applicatae Sinica , Volume 4 (4) – Jul 13, 2005

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 1988 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02007241
Publisher site
See Article on Publisher Site

Abstract

In this paper, we introduce and study the geometric process which is a sequence of independent non-negative random variablesX 1,X 2,... such that the distribution function ofX n isF (a n−1 x), wherea is a positive constant. Ifa>1, then it is a decreasing geometric process, ifa<1, it is an increasing geometric process. Then, we consider a replacement model as follows: the successive survival times of the system after repair form a decreasing geometric process or a renewal process while the consecutive repair times of the system constitute an increasing geometric process or a renewal process. Besides the replacement policy based on the working age of the system, a new kind of replacement policy which is determined by the number of failures is considered. The explicit expressions of the long-run average costs per unit time under each replacement policy are then calculated, and therefore the corresponding optimal replacement policies can be found analytically or numerically.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

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