A cold standby repairable system with the repairman having multiple vacations and operational, repair, and vacation times following phase-type distributions. Issue 4 (16th February 2016)

• Record Type: Journal Article
• Authors: Liu, Baoliang; Cui, Lirong; Wen, Yanqing; Guo, Furi
• Is Part Of: Communications in statistics. Volume 45:Issue 4(2016)
• Page Start: 850
• Page End: 858
• Publication Date: 2016-02-16
• Subjects: Markov process -- multiple vacations -- phase-type distribution -- rate of occurrence of failure -- reliability; 90B25; 60K10.; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.851239
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: This paper studies a cold standby repairable system with two identical components and one repairman having multiple vacations applying matrix-analytic methods. The lifetime of the component follows a phase-type distribution. The repair times and the vacation times of the repairman are governed by different phase-type distributions, respectively. 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, respectively. A numerical application is performed to illustrate the calculations.