Importance of components in k-out-of-n system with components having random weights

Abstract

a b s t r a c tThe purpose of this paper is to study the component importance in k-out-of-n system with components having random weights. The system works if at least k components work and the total weight of all working components is above the required level c. A new measure of component importance, called weighted importance, for such a system is introduced and its relation with Birnbaum reliability measure of importance is studied. It is shown that the larger weight stochastically implies the larger weighted measure of importance. It is also shown that if two components are identically distributed then the larger weight stochastically implies the larger Birnbaum reliability measure of importance. Finally, it is proved that if the weight of a component is stochastically increased, then the weighted and Birnbaum reliability measures of importance are increased accordingly.

Stochastic comparisons of total capacity of weighted-k-out-of-n systems

“…The components 1 importance of weighted-k-out-of-n systems has been studied by Eryilmaz and Bozbulut (2014) and Rahmani et al (2016). 2 Eryilmaz and Sarikaya (2014), because of complexity of the stochastic model, obtained a closed form of survival function 3 of T T w for the case when the components and weights are only of two types.…”

Reliability Analysis of Weighted- k-out-of- n: G System Consisting of Two Different Types of Nonidentical Components Each with its Own Positive Integer-Valued Weight

“…Eryilmaz and Bozbulut [7] studied a multi-state weighted-k-out-of-n:G system model in a dynamic setup and yielded an algorithmic approach for its dynamic reliability analysis. In order to measure the components importance in k-out-of-n system with random weights, Rahmani et al [8] defined the weighted importance (WI) measure that depends only on the distribution of component weights and also, Meshkat and Mahmoudi [9] generalized this measure for two component i and j and the relation of these measures is investigated with Birnbaum reliability importance measure.…”

Reliability analysis of weighted-k-out-of-n system consisting of three-state components

“…Li et al 12 presented some ordering results on the total system weight with respect to component weight vector. Rahmani et al 13 and Meshkat and Mahmoudi 14 studied reliability and importance measures for the weighted- k -out-of- n system having random weights. Some results on stochastic comparisons of total capacity of weighted- k -out-of- n systems have been presented by Rahmani et al 15 Zhang 16 investigated optimal allocation of active redundancies for weighted- k -out-of- n systems.…”