Discrete Repairable Systems With External and Internal Failures Under Phase-Type Distributions

We study a multi-component system subject to internal, and external failures. The external failures may be repairable, or not. The unit enters the repair channel when a repairable failure occurs and there is a repairman available. The random times involved in the study of the system are phase-type d...

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Bibliographic Details
Published in:IEEE transactions on reliability 2009-03, Vol.58 (1), p.41-52
Main Authors: Ruiz-Castro, J.E., Fernandez-Villodre, G., Perez-Ocon, R.
Format: Article
Language:English
Subjects:
Availability
Channels
Computation
Conditional probability
Conditional probability of failure
Failure
Failure analysis
History
Markov processes
Mathematical analysis
Matlab
multi-component system
phase-type distribution
Probability
Queueing analysis
Reliability theory
Repair
repairable system
stationary distribution
Statistics
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Description
Summary:We study a multi-component system subject to internal, and external failures. The external failures may be repairable, or not. The unit enters the repair channel when a repairable failure occurs and there is a repairman available. The random times involved in the study of the system are phase-type distributed. From this system, new ones are developed. General systems with internal, and external repairable, or non-repairable failures are built, generalizing the initial system. The availability, and the conditional probability of failure for the different types of failures and systems are calculated for finite, and infinite numbers of units. The results are implemented computationally with Matlab, and illustrated using examples.
ISSN:0018-9529
1558-1721
DOI:10.1109/TR.2008.2011667