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Discrete time analysis of a repairable machine

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Attahiru Sule Alfa  and
I. T. Castro
Attahiru Sule Alfa*
Affiliation:
University of Windsor
I. T. Castro*
Affiliation:
Universidad de Extremadura
*
∗ Current address: Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6. Email address: alfa@cc.umanitoba.ca
∗∗ Postal address: Departamento de Matemáticas, Facultad de Ciencias, Avenida de Elvas s/n, 06071 Badajoz, Spain.
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Abstract

We consider, in discrete time, a single machine system that operates for a period of time represented by a general distribution. This machine is subject to failures during operations and the occurrence of these failures depends on how many times the machine has previously failed. Some failures are repairable and the repair times may or may not depend on the number of times the machine was previously repaired. Repair times also have a general distribution. The operating times of the machine depend on how many times it has failed and was subjected to repairs. Secondly, when the machine experiences a nonrepairable failure, it is replaced by another machine. The replacement machine may be new or a refurbished one. After the Nth failure, the machine is automatically replaced with a new one. We present a detailed analysis of special cases of this system, and we obtain the stationary distribution of the system and the optimal time for replacing the machine with a new one.

Keywords

Discrete phase-type distributionsreplacement optimization reward

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 503 - 516
Copyright
Copyright © Applied Probability Trust 2002 

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References

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