Afrika Statistika

State distribution and reliability of some multistate systems with complex configurations

Soheir Belaloui and Moussa Bouloudene

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In this paper, our goal is to investigate, first, the multi-state consecutive $k_{n}$-out-of-$m_{n}$ : $G$ series systems and second, the multi-state consecutive $k_{n}$-out-of-$% m_{n} $ : $G$ parallel systems (see definitions 1 and 2). We begin by giving a non recursive formula which calculates the state distribution and the reliability of multi-state consecutive $k$-out-of-$n$ : $G$ system in the case where the number $k$ of functioning components depends on the system state level (see agreement 1), then we extend the used method to the multi-state consecutive $k_{n}$-out-of-$m_{n}$ : $G$ series and multi-state consecutive $k_{n}$-out-of-$m_{n}$ : $G$ parallel systems. In the end, we illustrate the obtained theoretical results by a numerical application.


Dans ce papier, notre but est d'étudier, premièrement, les systèmes $k_{n}$-consécutifs-sur-$m_{n}$ : $G$ série à multi-états, et deuxièment, les systèmes $k_{n}$-consécutifs-sur-$m_{n}$ : $G$ parallèle à multi-états (voir définitions 1 et 2). Nous commençons par donner une formule non récursive permettant le calcul de la distribution d'état des systèmes $k$-consécutifs-sur-$n$ : $G$ à multi-états et donc de déduire leur fiabilité dans le cas où le nombre $k$ des composants qui fonctionnent dépend du niveau d'état du système (voir agreement 1). Ensuite, nous faisons une extension de la méthode utilisée aux systèmes $k_{n}$-consécutifs-sur-$m_{n}$ : $G$ série à multi-états et $k_{n}$-consécutifs-sur-$m_{n}$ : $G$ parallèle à multi-états. Enfin, nous illustrons les résultats théoriques obtenus par une application numérique.

Article information

Afr. Stat., Volume 10, Number 1 (2015), 751-762.

First available in Project Euclid: 13 November 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62N05: Reliability and life testing [See also 90B25] 68M15: Reliability, testing and fault tolerance [See also 94C12]
Secondary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

Reliability Multi-state system Consecutive k-out-of-n G systems


Bouloudene, Moussa; Belaloui, Soheir. State distribution and reliability of some multistate systems with complex configurations. Afr. Stat. 10 (2015), no. 1, 751--762.

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