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Relative Measurement and Its Generalization in Decision Making. Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors. The Analytic Hierarchy/Network Process.

Thomas L. Saaty (2008)

RACSAM

According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value...

Reliability design of complex systems by minimizing the lifetime variance

Ewa Lobos, Michał Momot (2002)

International Journal of Applied Mathematics and Computer Science

The problem considered in this paper is the minimization of the lifetime variance of a complex system subject to its expected life and economic constraints. The example of a bridge network, in which all elements have constant failure rates, illustrates the problem. A numerical algorithm for solving this optimization problem by using exact formulae for system lifetime moments is included. Using this algorithm, we can obtain results better than the solutions known from earlier papers.

Reliability modeling of fault tolerant control systems

Hongbin Li, Qing Zhao, Zhenyu Yang (2007)

International Journal of Applied Mathematics and Computer Science

This paper proposes a novel approach to reliability evaluation for active Fault Tolerant Control Systems (FTCSs). By introducing a reliability index based on the control performance and hard deadline, a semi-Markov process model is proposed to describe system operation for reliability evaluation. The degraded performance of FTCSs in the presence of imperfect Fault Detection and Isolation (FDI) is reflected by semi-Markov states. The semi-Markov kernel, the key parameter of the process, is determined...

Reliability of system with dependent units

Raimi Ajibola Kasumu (1985)

Aplikace matematiky

The availability of a system with dependent units is obtained in the case where the system fails when one of the essential units fails. Markov model is assumed. The system considered consists of n dependent units of which r n units are essential units. A unit is said to be essential if its failure causes the system to fail. The mean and variance of time to system failure are given. Unit reliability is also discussed.

Representation of equilibrium solutions to the table problem of growing sandpiles

Piermarco Cannarsa, Pierre Cardaliaguet (2004)

Journal of the European Mathematical Society

In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain Ω 2 . The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge–Kantorovich problem, is the object of this paper. Our main...

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