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.

scholarly journals On the Survival Time of a Duplex System: A Sokhotski-Plemelj Problem

2008 ◽  
Vol 2008 ◽  
pp. 1-13
Author(s):  
Edmond J. Vanderperre
Keyword(s):  
Survival Time ◽  
Survival Function ◽  
Solution Procedure ◽  
Security Level ◽  
Duplex System ◽  
Coupled Partial Differential Equations ◽  
System A ◽  
Risk Criterion ◽  
The Laplace Transform ◽  
Warm Standby

We analyze the survival time of a renewable duplex system characterized by warm standby and subjected to a priority rule. In order to obtain the Laplace transform of the survival function, we employ a stochastic process endowed with time-dependent transition measures satisfying coupled partial differential equations. The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. Finally, we introduce a security interval related to a prescribed security level and a suitable risk criterion based on the survival function of the system. As an example, we consider the particular case of deterministic repair. A computer-plotted graph displays the survival function together with the security interval corresponding to a security level of 90%.

scholarly journals On the reliability of a renewable multiple cold standby system

2005 ◽  
Vol 2005 (3) ◽  
pp. 269-273
Author(s):  
E. J. Vanderperre
Keyword(s):  
Reliability Analysis ◽  
Queuing Theory ◽  
Survival Function ◽  
Exact Result ◽  
Duplex System ◽  
Cold Standby ◽  
Standby System ◽  
General Reliability

We present a general reliability analysis of a renewable multiple cold standby system attended by a single repairman. Our analysis is based on a refined methodology of queuing theory. The particular case of deterministic failures provides an explicit exact result for the survival function of the duplex system.

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 Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain

1992 ◽  
Vol 122 (3-4) ◽  
pp. 317-340 ◽  
Author(s):  
Oscar P. Bruno ◽  
Fernando Reitich
Keyword(s):  
Boundary Value Problem ◽  
Helmholtz Equation ◽  
Electromagnetic Waves ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Simple Algorithm ◽  
Holomorphic Functions ◽  
Power Series Expansions ◽  
Image Position ◽  
Derivatives Of

SynopsisIn this paper we deal with the problem of diffraction of electromagnetic waves by a periodic interface between two materials. This corresponds to a two-dimensional quasi-periodic boundary value problem for the Helmholtz equation. We prove that solutions behave analytically with respect to variations of the interface. The interest of this result is both theoretical – the legitimacy of power series expansions in the parameters of the problem has indeed been questioned – and, perhaps more importantly, practical: we have found that the solution can be computed on the basis of this observation. The simple algorithm that results from such boundary variations is described. To establish the property of analyticity of the solution for the gratingwith respect to the height δ, we present a holomorphic formulation of the problem using surface potentials. We show that the densities entering into the potential theoretic formulation are analytic with respect to variations of the boundary, or, in other words, that the integral operator that results from the transmission conditions at the interface is invertible in a space of holomorphic functions of the variables (x, y, δ). This permits us to conclude, in particular, that the partial derivatives of u with respect to δ at δ = 0 satisfy certain boundary value problems for the Helmholtz equation, in regions with plane boundaries, which can be solved in a closed form.

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