Fortunately traditional reliability theory, where the system and the components are always described simply as functioning or failed, is on the way to being replaced by a theory for multistate systems of multistate components. In this paper, we treat the consecutive k-out-of-n systems. Such systems have caught the attention of many engineers and researchers because of their wide range of application. We define a multistate consecutive k-out-of-n system: G as follows: Each component and the system can be in 1 of M + 1 possible states: 0, 1, 2, …, M. The system is in state ≥ j iff at least kj consecutive components are in state ≥ j. The value of kj can be different for different required minimum system state levels. We propose a method based on the combinatorial approach for computing the system's reliability and we give examples to illustrate this method.
Abstract. A consecutive k-out-of-n system consists of an ordered sequence of n components, such that the system functions if and only if at least k (k ≤ n) consecutive components function. The system is called linear (L) or circular (C) depending on whether the components are arranged on a straight line or form a circle. In the first part, we use a shock model to obtain the reliability function of consecutve-k-out-of-n systems with dependent and nonidentical components. In the second part, we treat some numerical examples to show the derive results and deduce the failure rate of each component and the system. Résumé. Un système k-consécutifs-parmi-n est un système constitué de n composants, tel que ce système fonctionne si et seulement si au moins k (k ≤ n) composants consécutifs fonctionnent. Le système est dit linéaire (L) ou circulaire (C) suivant la disposition des composants en ligne ou en cercle. Dans la première section, en utilisant le modèle de chocs, onétablit la fiabilité du système en question ayant des composants dépendants et non identiques. Dans la deuxième section, on traite des exemples numériques qui illustrent les résultats obtenus tout en déduisant le taux de panne de chaque composant et du système.
Abstract. In this paper, we focus on multi-state complex systems and their reliability. First, we provide a formula which computes the reliability of consecutive k-out-of-n: G systems. Then, we extend the used method to obtain the reliability of consecutive k-out-of-L n : G series and consecutive k-out-of-L n : G parallel systems. In the end, we illustrate all theoretical results by numerical examples.Résumé. Dans ce papier, nous nous intéressons aux systèmes multi-étatsà configurations complexes et leur fiabilité. Nous commençons parétablir une formule qui permet de calculer la fiabilité des systèmes k-consécutifs-sur-n : G. Ensuite, nousétendons la méthode utilisée pour obtenir la fiabilité des systèmes k-consécutifs-sur-L n : G série et k-consécutifs-sur-L n : G parallèle. Enfin, nous illustrons tous les résultats théoriques par des exemples numériques.
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