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Calculation of Reliability Characteristics for Regenerative Models

Kalashnikov, Vladimir (1996)

Serdica Mathematical Journal

If a regenerative process is represented as semi-regenerative, we derive formulae enabling us to calculate basic characteristics associated with the first occurrence time starting from corresponding characteristics for the semi-regenerative process. Recursive equations, integral equations, and Monte-Carlo algorithms are proposed for practical solving of the problem.

Cálculo del número medio de máquinas activas en un grupo de un operario y N máquinas, con incidencias poissonianas y tiempos de servicio aleatorio.

Albert Corominas Subias (1988)

Qüestiió

Este artículo expone un método para el cálculo del número medio de máquinas en funcionamiento en un sistema formado por un operario y N máquinas iguales, con tiempos exponenciales de funcionamiento entre averías y tiempos de servicio aleatorios, idéntica e independientemente distribuidos. El modelo generaliza las conocidas fórmulas que se obtienen a partir de los modelos M/M/1 con centro emisor finito y de Ashcroft, que suelen utilizarse para el problema de asignación de máquinas.

Capacity bounds for the CDMA system and a neural network: a moderate deviations approach

Matthias Löwe, Franck Vermet (2009)

ESAIM: Probability and Statistics

We study two systems that are based on sums of weakly dependent Bernoulli random variables that take values ± 1 with equal probabilities. We show that already one step of the so-called soft decision parallel interference cancellation, used in the third generation of mobile telecommunication CDMA, is able to considerably increase the number of users such a system can host. We also consider a variant of the well-known Hopfield model of neural networks. We show that this variant proposed by Amari...

Cavity method in the spherical SK model

Dmitry Panchenko (2009)

Annales de l'I.H.P. Probabilités et statistiques

We develop a cavity method for the spherical Sherrington–Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.

Central Limit Theorem for Diffusion Processes in an Anisotropic Random Environment

Ernest Nieznaj (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove the central limit theorem for symmetric diffusion processes with non-zero drift in a random environment. The case of zero drift has been investigated in e.g. [18], [7]. In addition we show that the covariance matrix of the limiting Gaussian random vector corresponding to the diffusion with drift converges, as the drift vanishes, to the covariance of the homogenized diffusion with zero drift.

Central limit theorem for hitting times of functionals of Markov jump processes

Christian Paroissin, Bernard Ycart (2004)

ESAIM: Probability and Statistics

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.

Central limit theorem for hitting times of functionals of Markov jump processes

Christian Paroissin, Bernard Ycart (2010)

ESAIM: Probability and Statistics

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.

Characterization of equilibrium measures for critical reversible Nearest Particle Systems

Thomas Mountford, Li Wu (2008)

Open Mathematics

We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than 7 + 41 2 and obeys some natural regularity conditions.

Characterization of the departure process from an ME/ME/1 queue

Jayesh Kumaran, Kenneth Mitchell, Appie Van de Liefvoort (2004)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper we propose a family of finite approximations for the departure process of an ME/ME/1 queue indexed by a parameter k defined as the system size of the finite approximation. The approximations capture the interdeparture times from an ME/ME/1 queue exactly and preserve the lag correlations of inter-event times of the departures from an ME/ME/1 queue up to lag ( k - 1 ) .

Characterization of the departure process from an ME/ME/1 queue

Jayesh Kumaran, Kenneth Mitchell, Appie van de Liefvoort (2010)

RAIRO - Operations Research

In this paper we propose a family of finite approximations for the departure process of an ME/ME/1 queue indexed by a parameter k defined as the system size of the finite approximation. The approximations capture the interdeparture times from an ME/ME/1 queue exactly and preserve the lag correlations of inter-event times of the departures from an ME/ME/1 queue up to lag (k - 1).

Characterization of the first operating period of a two-unit standby redundant system with three states of units

Antonín Lešanovský (1982)

Aplikace matematiky

A two-unit cold-standby redundant system with one repair facility is considered. Each unit can be in three states: good (I), degraded (II), and failed (III). We suppose that only the following state-transitions af a unit are possible: I I I , I I I I I , I I I , I I I I . The paper is devoted to the problems which arise only provided that the units of the redundant system can be in more than two states (i.e. in operating and failed states). The following characteristics dealing with a single operating period of the system are studied...

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