TY - JOUR
T1 - A multiple warm standby repairable system under -policy with multiple vacations following Markovian arrival process
AU - Liu, Baoliang
AU - Wen, Yanqing
AU - Kang, Shugui
AU - Qiu, Qingan
N1 - Publisher Copyright:
© 2020, © 2020 Taylor & Francis Group, LLC.
PY - 2020/8/2
Y1 - 2020/8/2
N2 - The paper considers a warm standby (Formula presented.) -unit system under (Formula presented.) -policy with one repairman taking multiple vacations. The system is operational as long as one of the units is normal. The online unit is subject to internal failures and external shocks. The lifetime of the online unit due to an internal failure follows a phase-type (PH) distribution. The inter-arrival time of shocks and the random amount of shock damage are governed by other two different PH distributions, respectively. When the damage of a shock is larger than the given threshold, the online unit is considered to be failed. Standby units are subject to shocks from a different cause, which are governed by a Markovian arrival process (MAP). A repairman who can take multiple vacations repairs the failed units based on the (Formula presented.) -policy. The successive repair times and the successive vacation times of the repairman are governed by other two different MAPs, respectively. In this paper, first, a Markov process is constructed to describe the warm standby (Formula presented.) -unit system. Then the system is studied in a transient and stationary regime using matrix-analytical approaches. Finally, two numerical applications are given to illustrate the results obtained in the paper.
AB - The paper considers a warm standby (Formula presented.) -unit system under (Formula presented.) -policy with one repairman taking multiple vacations. The system is operational as long as one of the units is normal. The online unit is subject to internal failures and external shocks. The lifetime of the online unit due to an internal failure follows a phase-type (PH) distribution. The inter-arrival time of shocks and the random amount of shock damage are governed by other two different PH distributions, respectively. When the damage of a shock is larger than the given threshold, the online unit is considered to be failed. Standby units are subject to shocks from a different cause, which are governed by a Markovian arrival process (MAP). A repairman who can take multiple vacations repairs the failed units based on the (Formula presented.) -policy. The successive repair times and the successive vacation times of the repairman are governed by other two different MAPs, respectively. In this paper, first, a Markov process is constructed to describe the warm standby (Formula presented.) -unit system. Then the system is studied in a transient and stationary regime using matrix-analytical approaches. Finally, two numerical applications are given to illustrate the results obtained in the paper.
KW - Markov models
KW - Markovian arrival process
KW - matrix-analytical approach
KW - multiple vacations
KW - phase-type distribution
UR - http://www.scopus.com/inward/record.url?scp=85078057161&partnerID=8YFLogxK
U2 - 10.1080/03610926.2019.1710758
DO - 10.1080/03610926.2019.1710758
M3 - Article
AN - SCOPUS:85078057161
SN - 0361-0926
VL - 49
SP - 3609
EP - 3634
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 15
ER -