A multiple warm standby δ-shock system with a repairman having multiple vacations. Issue 4 (21st April 2017)

• Record Type: Journal Article
• Authors: Wen, Yanqing; Cui, Lirong; Si, Shubin; Liu, Baoliang
• Is Part Of: Communications in statistics. Volume 46:Issue 4(2017)
• Page Start: 3172
• Page End: 3186
• Publication Date: 2017-04-21
• Subjects: δ-Shock -- Multiple vacations -- Phase-type distribution -- Rate of occurrence of failure -- Reliability; 90B25 -- 60k10; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2015.1078471
• Languages: English
• ISSNs: 0361-0918

Abstract

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.