Constructing a Markov process for modelling a reliability system under multiple failures and replacements

•A multicomponent system under simultaneous failures is studied.•It is subject to inspections and multiple replacements of the failed components.•A Markov process for modeling the system is constructed.•The study is performed in transient regime.•An application to three systems is performed consider...

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Bibliographic Details
Published in:Reliability engineering & system safety 2018-05, Vol.173, p.34-47
Main Authors: Montoro-Cazorla, Delia, Pérez-Ocón, Rafael
Format: Article
Language:English
Subjects:
Availability
Failure
Inspection
Markov analysis
Markov chains
Markov process
Markov processes
Multiple failures
Multiple replacements
Poisson density functions
Poisson distribution
Reliability engineering
Reliability system
State vectors
System reliability
Systems design
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Summary:•A multicomponent system under simultaneous failures is studied.•It is subject to inspections and multiple replacements of the failed components.•A Markov process for modeling the system is constructed.•The study is performed in transient regime.•An application to three systems is performed considering operational cycles. We present a reliability system subject to shocks, internal failures, and inspections. Shocks cause damage or failure to several units simultaneously. The units undergo internal failures. After an inspection, the units that have failed are replaced by new and identical ones. The shocks are governed by a Poisson process, the internal failures and the inspection times are exponentially distributed. Under these assumptions a Markov process governing the system is constructed. The states of the system are formed by state-vectors associated to the units of the system. The instantaneous transitions among the states are constructed by using intermediate functions and indicators. A system with three components illustrating the procedure is studied and a numerical application is performed, comparing the performance measures of the k-out-of-3 systems for k = 1, 2, 3.
ISSN:0951-8320
1879-0836
DOI:10.1016/j.ress.2017.12.017