Reliability of Linear and Circular Consecutive-k-out-of-n Systems with shock model

Abstract

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.

On the modification of GL-models by adding edges to a cyclic graph

“…The results of the experiments show that the obtained model demonstrates the system's operable state on all vectors with two zeros, as well as on the next 29 = 1 such that both the 1st and 3rd, as well as the 4th, 5th, and 7th components have the value 1 (which corresponds to the situation when both of the above conditions are simultaneously met): 10111010. It is easy to see that their total number is indeed 20 + 10 -1 = 29, and that they do indeed constitute that the set obtained from experiments with the GL-model built above.…”

“…The methods of the first group are based on the construction of analytical expressions for calculating the corresponding parameters. Their advantage is the ability to obtain results with high accuracy, but their disadvantage is non-universality: for each type of system, it is often necessary to create a new calculation method [23,24], [25,26], [27,28], [29,30], [31,32], [33,34], [35,36], [37,38], [39,40], [41,42], [43,44], [45,46], [47,48], [49,50], [51,52], [53,54]. The methods of the second group are based on conducting statistical experiments with models of system behavior in the failure flow [55,56], [57].…”

On the method of building of non-basic GL-models which are formed on combination of edge functions of basic models

“…The advantage of such approaches is the relative simplicity of the calculation process itself, as well as the ability to achieve high calculation accuracy. The disadvantage, is the complexity of building these expressions for different types of systems: for each of them, a new calculation method often has to be created [23,26], [27,28], [29,30], [31,32], [33,34], [35,36], [37,38], [39,40], [41,42], [43,44], [45,46], [47,48], [49,50], [51,52], [53,54].…”