A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process

• Published in: Reliability engineering & system safety Vol. 142; pp. 1 - 8
• Main Authors: Liu, Baoliang, Cui, Lirong, Wen, Yanqing, Shen, Jingyuan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2015
• Subjects: Arrivals; Interruption; Markov processes; Mathematical models; Multiple vacations; Phase-type distribution; Policies; Rate of occurrence of failure; Reliability; Reliability engineering; Repair time; Representations; Vacation interruptions; Working vacations; Working vacations; Multiple vacations; Phase-type distribution; Reliability; Rate of occurrence of failure; Vacation interruptions
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2015.04.010

This paper studies a cold standby repairable system with working vacations and vacation interruptions. The repairman׳s multiple vacation, the working vacation policy and the vacation interruption policy are considered simultaneously. The lifetime of component follows a Phase-type (PH) distribution. The repair time in the regular repair period and the working vacation period are other two Phase-type distributions with different representations, and the successive vacation times are governed by a Markovian arrival process (MAP). For this system, a vector-valued Markov process is constructed. We obtain several important performance measures for the system in transient and stationary regimes applying the matrix-analytic method. Finally, a numerical example is given to illustrate the results obtained in the paper. •The working vacations and vacation interruption policy is considered in the model.•A repairman can take multiple vacations when all of the components are good in the system.•The operational time and the repair time follow PH-distributions.•The successive vacation times are governed by a Markovian arrival process.•The system is studied in transient and stationary regime.