Wyniki wyszukiwania - BazTech

1

Modeling reliability of systems with repair by stochastic processes with long memory

Filus Jerzy K., Filus Lidia Z.

Safety and Reliability of Systems and Processes

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2023

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Summer Safety and Reliability Seminar 2023

69--78

EN

In modelling reliability of systems with repair by stochastic processes of times between consecutive failures the usual Markovianity assumption was significantly relaxed. Instead of the Markovian stochastic processes, processes with long memory were constructed for the reliability and maintenance applications. The Markovianity restriction on the process’s memory could be omitted as two (relatively) new methods of the processes construction were employed. In this work, one of the two available methods, the ‘method of triangular transformations’, is presented. Other, the ‘method of parameter dependence’, is shortly described in Section 5. Since using an arbitrarily long memory has serious drawbacks in modelling process we, on the other hand, limited it by introducing the notion of k-Markovianity (k = 1,2,…), where the memory is reduced to the last k previous (discrete) time epochs. The discussion of this kind of problems together with construction of some new classes of stochastic processes with discrete time and their reliability application is provided.

2

On Derivation of Discrete Time Fourier Transform from Its Continuous Counterpart

Borys Andrzej

International Journal of Electronics and Telecommunications

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2020

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Vol. 66, No. 2

355-360

EN

This paper is devoted to some problems that appear in derivations of the discrete time Fourier transform from a formula for its continuous time counterpart for transformation from the time into the frequency domain as well as to those regarding transformation in the inverse direction. In particular, the latter ones remained so far an unresolved problem. It is solved for the first time here. Many detailed explanations accompanying the solution found are presented. Finally, it is also worth noting that our derivations do not exploit any of such sophisticated mathematical tools as the so-called Dirac delta and Dirac comb.

3

Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy Lz -transform

Hu L., Zhang Z., SU P., Peng R.

Eksploatacja i Niezawodność

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2017

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Vol. 19, no. 2

179--190

PL

W niniejszej pracy badano metodę oceny dynamicznej, rozmytej gotowości eksploatacyjnej (dostępności) dyskretnego w czasie systemu wielostanowego pracującego w trybie drobnych uszkodzeń i napraw. Tradycyjnie zwykło się zakładać, że analiza niezawodności dostarcza dokładnych danych niezawodnościowych na temat danego dyskretnego w czasie komponentu/systemu. W praktyce inżynieryjnej jednak trudno jest uzyskać dokładne dane do oceny właściwości komponentu/systemu. W niniejszej pracy zaproponowano jak problem ten można rozwiązać wykorzystując do oceny dynamicznej gotowości dyskretnego w czasie systemu wielostanowego, teorię zbiorów rozmytych. Rozmyty model Markowa z dyskretnym czasem i rozmytą macierzą prawdopodobieństw przejść zastosowano do analizy rozmytego prawdopodobieństwa stanu każdego elementu w dowolnym czasie dyskretnym. Opracowano rozmytą transformatę Lz rozmytego, dyskretnego w stanach i czasie łańcucha Markowa, która pozwala poszerzyć transformatę Lz modelu Markowa dyskretnego w stanach i ciągłego w czasie o zbiory ostre. W oparciu o metodę alfa przekrojów oraz rozmytą transformatę Lz, obliczono dynamiczną rozmytą gotowość eksploatacyjną systemu, wykorzystując do tego celu technikę programowania parametrycznego. Zastosowanie proponowanej metody zilustrowano na przykładzie liczbowym analizując układ przesyłu.

EN

This paper studies assessment approach of dynamic fuzzy availability for a discrete time multi-state system under minor failures and repairs. Traditionally, it was assumed that the exact reliability data of a component/system with discrete time are given in reliability analysis. In practical engineering, it is difficult to obtain precise data to evaluate the characteristics of a component/system. To overcome the problem, fuzzy set theory is employed to deal with dynamic availability assessment for a discrete time multi-state system in this paper. A fuzzy discrete time Markov model with fuzzy transition probability matrix is proposed to analyze the fuzzy state probability of each component at any discrete time. The fuzzy Lz-transform of the discrete-state discrete-time fuzzy Markov chain is developed to extend the Lz-transform of the discrete-state continuous-time Markov model with crisp sets. Based on the α-cut approach and the fuzzy Lz-transform, the dynamic fuzzy availability of the system is computed by using parametric programming technique. To illustrate the proposed method, a flow transmission system is analyzed as a numerical example.

4

Optimal dividend policy in discrete time

Marciniak E., Trybuła J.

Demonstratio Mathematica

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2014

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Vol. 47, nr 1

258--270

EN

A problem of optimal dividend policy for a firm with a bank loan is considered. A regularity of a value function is established. A numerical example of calculating value function is given.

5

Stochastic Petri Box Calculus with Discrete Time

Tarasyuk I.V.

Fundamenta Informaticae

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2007

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Vol. 76, nr 1-2

189-218

EN

In the last decades, a number of stochastic enrichments of process algebras was constructed to allow one for specification of stochastic processes within the well-developed framework of algebraic calculi. In [], a continuous time stochastic extension of finite Petri box calculus (PBC) was proposed called sPBC. The algebra sPBC has interleaving semantics due to the properties of continuous time distributions. At the same time, PBC has step semantics, and it could be natural to propose its concurrent stochastic enrichment. We construct a discrete time stochastic extension dtsPBC of finite PBC. A step operational semantics is defined in terms of labeled transition systems based on action and inaction rules. A denotational semantics is defined in terms of a subclass of labeled discrete time stochastic Petri nets (LDTSPNs) called discrete time stochastic Petri boxes (dts-boxes). A consistency of both semantics is demonstrated. In addition, we define a variety of probabilistic equivalences that allow one to identify stochastic processes with similar behaviour which are differentiated by too strict notion of the semantic equivalence. The interrelations of all the introduced equivalences are investigated.