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Reliability evaluation for multi-state repairable systems with hybridization the markov stochastic process and the universal generating function

Mohamed Amara, Abdelkader Zeblah, Mohamed Mostefai

Przegląd Elektrotechniczny

2021

R. 97, nr 1

109--114

Multistate reliability models are generally complicated and the state space has a large number of states. Evaluating the performance distribution of complex series parallel to the repairable multi-state system with dependent linear components. They are much more complex and present major difficulties in defining the system and the performance of the MSS multistate reliability assessment system. A new approach is introduced to extend the classical theory of reliability based on the binary hypothesis to the repairable multi-state system (MSS). Generally, some of the stochastic processes of traditional methods did not provide an assessment of the reliability of the MSS system due to the enormous states of the system. This article is based on the hybridization of the Markov stochastic process and the universal generation function technology (UGF) which deals with the most sophisticated and realistic models ranging from perfect operation to complete failure in which components and systems can take many states. We consider the case where the performance and probability distributions of certain components depend on the linear of another component or group of components.

Zaprezentowano nowa metodę rozszerzająca klasyczną teorię niezawodności bazującą na hipotezie naprawialnych systemów wielostanowych MSS. Artykuł bazuje na hybrydyzacji stochastycznego procesu Markova i technologii uniwersalnej funkcji UGF. Rozważono przypadek kiedy gęstość prawdopodobieństwa pewnych składowych zależy liniowo od innych składowych.

K-extreme point of generalized Orlicz sequence spaces with Luxemburg norm

Shi Z., Wang X.

Commentationes Mathematicae

2013

Vol. 53, No. 2

147--162

In this paper,we give necessary and sufficient conditions in order that a point u∈S(l(Φ)) is a k-extreme point in generalized Orlicz sequence spaces equipped with the Luxemburg norm, combing the methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between the classical Orlicz spaces and generalized Orlicz spaces.