Iterative method for steady state reliability analysis of complex Markov systems

In the actual study, we carried out a reliability analysis of a repairable redundant data transmission system with the use of the elaborated mathematical and simulation model of a closed heterogeneous cold standby system. The system consists of one repair unit and two different data sources with an exponential cumulative distribution function (CDF) of their uptime and a general independent CDF of their repair time. We consider five special cases of the general independent CDF; including Gamma, Weibull-Gnedenko, Exponential, Lognormal and Pareto. We study the system-level reliability, defined as the steady-state probability (SSP) of failure-free system operation. The proposed analytical methodology made it possible to assess the reliability of the whole system in the event of failure of its components. Specific analytic expressions and asymptotic valuations are obtained for the steady-state probabilities of the system and the SSP of failure-free system operation. A simulation model of the system in cases where it is not workable to obtain expressions for the steady-state probabilities of the system in an explicit analytical form was considered, in particular for constructing the empirical system reliability function. The issue of sensitivity analysis of reliability characteristics of the considered system to the types of repair time distributions was also studied. The simulation modeling was done with the R statistics package.

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A SPLITTING ITERATIVE METHOD FOR SOLVING THE NEUTRON TRANSPORT EQUATION

Mathematical Modelling and Analysis ◽

10.3846/1392-6292.2009.14.271-289 ◽

2009 ◽

Vol 14 (3) ◽

pp. 271-289 ◽

Cited By ~ 1

Author(s):

Onana Awono ◽

Jacques Tagoudjeu

Keyword(s):

Steady State ◽

Iterative Method ◽

Transport Equation ◽

Multigrid Method ◽

Neutron Transport ◽

Dimensional Space ◽

Two Dimensional ◽

Numerical Treatment ◽

Neutron Transport Equation ◽

Slab Geometry

This paper presents an iterative method based on a self‐adjoint and m‐accretive splitting for the numerical treatment of the steady state neutron transport equation. Theoretical analysis shows that this method converges unconditionally to the unique solution of the transport equation. The convergence of the method is numerically illustrated and compared with the standard Source Iteration method and multigrid method on sample problems in slab geometry and in two dimensional space.

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Steady-state hierarchical control for the drift correction of a constellation in highly elliptical orbits

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1243/09544100jaero501 ◽

2009 ◽

Vol 223 (8) ◽

pp. 1125-1139 ◽

Cited By ~ 3

Author(s):

P A Capó-Lugo ◽

P M Bainum

Keyword(s):

Steady State ◽

Iterative Method ◽

Boundary Value ◽

Hierarchical Control ◽

Separation Distance ◽

Point Boundary ◽

Computational Process ◽

Drift Correction ◽

Control Scheme ◽

Elliptical Orbits

The hierarchical control scheme is used to obtain the solutions of two-point boundary value problems to correct the separation distance drifts of a pair of satellites within a constellation in highly elliptical orbits according to mission constraints. One of these solutions is the drift correction that shows a faster correction than the solution of the two-point boundary value problem for the station-keeping process of a pair of satellites within a constellation. For the drift correction, the hierarchical control scheme uses an iterative method to obtain the solution for the drift correction. Thus, the hierarchical control scheme is re-expressed as a steady-state system to reduce the computational process and time. In summary, the steady-state hierarchical control scheme is used to correct the drift between a pair of satellites within a constellation in which the computational process is minimized.

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