Afrika Statistika

State distribution and reliability of some multistate systems with complex configurations

Soheir Belaloui and Moussa Bouloudene

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Résumé

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

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

Dates
First available in Project Euclid: 13 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.as/1447439365

Mathematical Reviews number (MathSciNet)
MR3422847

Zentralblatt MATH identifier
1327.62496

Subjects
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]

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

Citation

Bouloudene, Moussa; Belaloui, Soheir. State distribution and reliability of some multistate systems with complex configurations. Afr. Stat. 10 (2015), no. 1, 751--762. https://projecteuclid.org/euclid.as/1447439365


Export citation