On the survival time of a repairable duplex system sustained by a cold standby unit subjected to a priority rule

2016 ◽  
Vol 46 (16) ◽  
pp. 7872-7886
Author(s):  
E. J. Vanderperre ◽  
S. S. Makhanov
Keyword(s):  
Survival Time ◽  
Priority Rule ◽  
Duplex System ◽  
Cold Standby ◽  
A Priority

scholarly journals A Markov time related to a priority system

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
Edmond J. Vanderperre
Keyword(s):  
Stochastic Process ◽  
Differential Equations ◽  
Stochastic Analysis ◽  
Recovery Time ◽  
Holomorphic Functions ◽  
Priority Rule ◽  
Stieltjes Transform ◽  
Duplex System ◽  
Cold Standby ◽  
A Priority

We consider a basic renewable duplex system characterized by cold standby and subjected to a priority rule. Apart from a general stochastic analysis presented in the previous literature, we introduce a Markov time called the recovery time of the system. In order to obtain the corresponding Laplace-Stieltjes transform, we employ a stochastic process endowed with transition measures satisfying generalized coupled differential equations. The solution is provided by the theory of sectionally holomorphic functions.

scholarly journals Long-run availability of a priority system: a numerical approach

2005 ◽  
Vol 2005 (1) ◽  
pp. 75-85 ◽  
Author(s):  
Edmond J. Vanderperre ◽  
Stanislav S. Makhanov
Keyword(s):  
Stochastic Process ◽  
Numerical Approach ◽  
Priority Rule ◽  
Twin System ◽  
System A ◽  
Long Run ◽  
Random Behavior ◽  
Cold Standby ◽  
Standby System ◽  
A Priority

We consider a two-unit cold standby system attended by two repairmen and subjected to a priority rule. In order to describe the random behavior of the twin system, we employ a stochastic process endowed with state probability functions satisfying coupled Hokstad-type differential equations. An explicit evaluation of the exact solution is in general quite intricate. Therefore, we propose a numerical solution of the equations. Finally, particular but important repair time distributions are involved to analyze the long-run availability of theT-system. Numerical results are illustrated by adequate computer-plotted graphs.

scholarly journals Reliability of an engineering system characterized by hot and cold standby: A compound boundary value problem

2021 ◽  
pp. 16-16
Author(s):  
Edmond Vanderperre ◽  
Stanislav Makhanov
Keyword(s):  
Boundary Value Problem ◽  
Survival Time ◽  
Boundary Value ◽  
Survival Function ◽  
Holomorphic Functions ◽  
Engineering System ◽  
Entire System ◽  
Duplex System ◽  
Cold Standby ◽  
Auxiliary Unit

We analyse the reliability (survival function) of a duplex system characterized by hot standby and sustained by an auxiliary unit in cold standby. The entire system is attended by two heterogeneous repairmen. Our methodology is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. Finally, we also study the total occupational time of the repairman responsible for the repair of the failed priority unit during the survival time of the system.

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

2016 ◽  
Vol 28 (1) ◽  
pp. 123-140
Author(s):  
E. J. VANDERPERRE ◽  
S. S. MAKHANOV
Keyword(s):  
Functional Equation ◽  
Survival Time ◽  
Function Theory ◽  
Complex Function ◽  
Priority Rules ◽  
Complex Function Theory ◽  
Duplex System ◽  
Repair Facility ◽  
Parameter Dependent ◽  
Auxiliary Unit

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 repairmenRpandRh. RepairmanRphas priority in repairing failed units with regard to repairmanRhprovided 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.

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