A multiple warm standby δ-shock system with a repairman having multiple vacations

Yanqing Wen, Lirong Cui, Shubin Si, Baoliang Liu

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)3172-3186
Number of pages15
JournalCommunications in Statistics: Simulation and Computation
Volume46
Issue number4
DOIs
StatePublished - 21 Apr 2017

Keywords

  • Multiple vacations
  • Phase-type distribution
  • Rate of occurrence of failure
  • Reliability
  • δ-Shock

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