TY - JOUR
T1 - A multiple warm standby δ-shock system with a repairman having multiple vacations
AU - Wen, Yanqing
AU - Cui, Lirong
AU - Si, Shubin
AU - Liu, Baoliang
N1 - Publisher Copyright:
© 2017 Taylor & Francis Group, LLC.
PY - 2017/4/21
Y1 - 2017/4/21
N2 - In this article, a warm standby n-unit system is studied. The system is operational as long as there is one unit normal. The unit online, which has a lifetime distribution governed by a phase-type distribution, is also attacked by a shock from some external causes. Assume that shocks arrive according to a Poisson process. Whenever an interarrival time of shock is less than a threshold, the unit online fails. The lifetimes of the units in warm standby is exponentially distributed. A repairman who can take multiple vacations repairs the failed units based on the “first-in-first-out” rule. The repair times and the vacation times of repairman are governed by different phase-type distributions. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime; the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated. A numerical application is performed to illustrate the calculations.
AB - In this article, a warm standby n-unit system is studied. The system is operational as long as there is one unit normal. The unit online, which has a lifetime distribution governed by a phase-type distribution, is also attacked by a shock from some external causes. Assume that shocks arrive according to a Poisson process. Whenever an interarrival time of shock is less than a threshold, the unit online fails. The lifetimes of the units in warm standby is exponentially distributed. A repairman who can take multiple vacations repairs the failed units based on the “first-in-first-out” rule. The repair times and the vacation times of repairman are governed by different phase-type distributions. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime; the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated. A numerical application is performed to illustrate the calculations.
KW - Multiple vacations
KW - Phase-type distribution
KW - Rate of occurrence of failure
KW - Reliability
KW - δ-Shock
UR - http://www.scopus.com/inward/record.url?scp=85006934256&partnerID=8YFLogxK
U2 - 10.1080/03610918.2015.1078471
DO - 10.1080/03610918.2015.1078471
M3 - 文章
AN - SCOPUS:85006934256
SN - 0361-0918
VL - 46
SP - 3172
EP - 3186
JO - Communications in Statistics: Simulation and Computation
JF - Communications in Statistics: Simulation and Computation
IS - 4
ER -