Displaying similar documents to “Construction of a class of stationary processes with applications in reliability”

Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin

Alexander Zeifman, Anna Korotysheva, Yacov Satin, Victor Korolev, Sergey Shorgin, Rostislav Razumchik (2015)

International Journal of Applied Mathematics and Computer Science

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Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, timedependent analysis...

Semi-Markov processes for reliability studies

Christiane Cocozza-Thivent, Michel Roussignol (2010)

ESAIM: Probability and Statistics

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We study the evolution of a multi-component system which is modeled by a semi-Markov process. We give formulas for the avaibility and the reliability of the system. In the r-positive case, we prove that the quasi-stationary probability on the working states is the normalised left eigenvector of some computable matrix and that the asymptotic failure rate is equal to the absolute value of the convergence parameter r.