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1

Semi-Markov reliability model of two different units cold standby system

Grabski F.

Zeszyty Naukowe Akademii Marynarki Wojennej

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2017

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R. 58 nr 4 (211)

45--60

EN

A semi-Markov stochastic process is used for solving in a reliability problem in the paper. The problem concerns of two different component cold standby system and a switch. To obtain the reliability characteristic and parameters of the system we construct so called an embedded semi-Markov process in the process describing operation process of the system. In the model the conditional time to failure of the system is represented by a random variable denoting the first passage time from the given state to the specified subset of states. We apply theorems of the Semi-Markov processes theory concerning the conditional reliability functions to calculate the reliability function and mean time to failure of the system. Often an exact reliability function of the system by using Laplace transform is difficult to calculate, frequently impossible. The semi-Markov processes perturbation theory, allows to obtain an approximate reliability function of the system in that case.

PL

Do rozwiązania problemu z zakresu teorii niezawodności został zastosowany proces semi-Markowa. Problem dotyczy tak zwanego systemu z rezerwą zimną, który jest złożony z dwóch różnych podsystemów i przełącznika. Aby uzyskać charakterystyki i parametry niezawodności tego systemu, jako model funkcjonowania systemu konstruujemy proces semi-Markowa — tak zwany proces włożony w inny proces stochastyczny. W naszym modelu czas zdatności systemu jest reprezentowany przez zmienną losową oznaczającą czas pierwszego przejścia z danego stanu do określonego podzbioru stanów. W celu obliczenia funkcji niezawodności i średniego czasu do awarii systemu stosujemy twierdzenia teorii procesów semi-markowskich dotyczące warunkowej funkcji niezawodności. Najczęściej dokładna funkcja niezawodności systemu przy zastosowaniu transformaty Laplace’a jest trudna do wyliczenia. W takim przypadku teoria zaburzonych procesów semi-markowskich pozwala otrzymać przybliżoną funkcję niezawodności systemu.

2

Non-renewal multistate system with Semi-Markov components

Grabski F.

Journal of Polish Safety and Reliability Association

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2014

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Vol. 5, No. 1

63--70

EN

The paper deals with non-renewal multistate monotone systems consisting of multistate components which are modeled by the semi-Markov processes. In the case of a non-renewal system the multistate reliability functions of the system components and the whole system are discussed. All presented concepts and models are illustrated by simple numerical examples.

3

Complex technical systems safety prediction

Soszyńska-Budny J.

Journal of Polish Safety and Reliability Association

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2014

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Vol. 5, No. 2

127--142

EN

There are presented general safety analytical models of complex multistate technical systems related to their operation processes. They are the integrated general models of complex technical systems, linking their multistate safety models and their operation processes models and considering variable at the different operation states safety structures and their components safety parameters. The conditional safety functions at the system particular operation states and independent of the system particular operation states the unconditional safety function and the risk function of the complex technical systems are defined. These joint models of the safety and the variable in time system operation processes are constructed for multistate series, parallel, “m out of n”, consecutive “m out of n: F”, series-parallel, parallel-series, series-“m out of k”, “mi out of li”-series, series-consecutive “m out of k: F” and consecutive “mi out of li: F”-series systems. The joint models are applied to determining safety characteristics of these systems related to their varying in time safety structures and their components safety characteristics. Under the assumption that the considered systems are exponential, the unconditional safety functions of these systems are determined. The proposed models and methods are applied to the safety analysis, evaluation and prediction of the one subsystem of the port grain transportation system related to varying in time their operation processes, structures and components safety parameters.

4

An importance measure for multi-component systems with Semi-Markov dynamics

Hellmich M., Berg H. P.

Journal of Polish Safety and Reliability Association

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2012

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Vol. 3, No. 1

147--156

EN

We consider semi-Markov reliability models of multi-component systems with a discrete state space, general enough to include systems with maintenance or repair. We assume that for all system states the functioning or failure of each component is specified. In this setup we propose a component importance measure which is close in spirit to the classical steady state Barlow–Proschan importance measure for repairable binary coherent systems. We discuss our importance measure to some extent, highlighting the relation to the classical Barlow–Proschan measure, and present formulas expressing it in terms of quantities easily obtained from the building blocks of the semi-Markov process. Finally an example of a two-component cold standby system with maintenance and repair is presented which illustrates how our importance measure can be used in practical applications.