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A functional equation related to a repairable system subjected to priority rules

Published online by Cambridge University Press:  18 March 2016

E. J. VANDERPERRE  and
S. S. MAKHANOV
E. J. VANDERPERRE
Affiliation:
Reliability Engineering Research Unit, Ruzettelaan 183, Bus 158, 8370 Blankenberge, Belgium email: evanderperre@yahoo.com
S. S. MAKHANOV*
Affiliation:
School of Information and Computer Technology, Sirindhorn International Institute of Technology, Thammasat University, Tiwanont Road, T. Bangkadi, A. Muang, Pathum Thani 12000, Thailand email: makhanov@siit.tu.ac.th
*
†Corresponding author
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Abstract

We analyse the survival time of a general duplex system sustained by an auxiliary cold standby unit and subjected to priority rules. The duplex system is attended by two general repairmen Rp and Rh. Repairman Rp has priority in repairing failed units with regard to repairman Rh provided that both repairmen are jointly idle. Otherwise, the priority is overruled. The auxiliary unit has its own repair facility. The duplex system has overall, break-in priority (often called pre-emptive priority) in operation and in standby with regard to the auxiliary unit. The analysis of the survival time is based on advanced complex function theory (sectionally holomorphic functions). The main problem is to convert a functional equation into a (parameter dependent) Sokhotski–Plemelj problem.

Keywords

duplex systempriority rulesurvival functionstopping timesecurity intervalsectionally holomorphic function
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 1 , February 2017 , pp. 123 - 140
Copyright
Copyright © Cambridge University Press 2016 

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