On total capacity of k‐out‐of‐n systems with random weights

Abstract

In engineering applications, many reliability systems can be modeled as k-out-of-n systems with components having random weights. Before putting such kind of system into a working state, it is of great significance for a system designer to find out the optimal assembly of the random weights to the components. In this article, we investigate the performance levels of k-out-of-n systems with random weights. Optimal assembly policies are obtained by maximizing the total capacity according to different criteria, including the usual stochastic order, the increasing convex [concave] order, and the expectation order. Based on the optimal assembly strategy derived by maximizing the expected total capacity, we further investigate stochastic properties of the resulting weighted system with respect to the vector of expectations of random weights. Numerical examples are provided to highlight our theoretical findings as well. KEYWORDS expected total capacity, LWSAI, optimal assembly, random weighted k-out-of-n system, RWSAI, SAI, stochastic orders, total capacity 1 Hereafter, for convenience, we denote the k-out-of-n system with random weights by r-w-k-out-of-n system. Formally, the definition of a r-w-k-out-of-n system is recalled as follows. Let X = (X 1 , … , X n ) be the component lifetimes vector, and W = (W 1 , … , W n ) be the random weights vector with W i denoting the weight of the ith component. Let (t; k, Naval Res Logistics 2018;65:347-359 wileyonlinelibrary.com/journal/nav

Ordering properties of generalized aggregation with applications

“…In such models, component i contributes not only reliability but also capacity w i to the entire system when it functions, then the system functions if and only if the total weight due to operational components is above some predetermined threshold . For more discussions on (random) weighted k ‐out‐of‐ n systems, we refer the readers to References 38‐41.…”

“…Then, the failure time of this system can be represented as from which we have Now, assume that the components lifetimes X is positively dependent and stochastically ordered in the sense of RWSAI accompanied with comonotonic random decay coefficients such that . This assumption is reasonable since in general we put the weaker component in the node suffered from more drastic shocks (ie, stochastically larger decay coefficient), which phenomenon is also discussed in Reference 41 for the case of random weighted k ‐out‐of‐ n systems.…”

“…Proposition 5 implies that the system with a larger weight (ie, a slower random decay rate) assigned to a more reliable component has longer lifetime in the sense of the increasing convex order, and this conclusion is consistent with intuition and agrees with some existing results; see theorem 4.5 in Reference 41.…”

ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

“…This kind of system is functional provided that the total contribution of components is above a specified performance level. The past two decades have witnessed extensive developments on different aspects of weighted k -out-of-n systems, including studies on extensions of these systems with multiple states or random weights [33]. However, to the best of the author's knowledge, there are only a few papers studying stochastic properties of weighted k -out-of-n systems in the literature [11,18].…”

Reliability-based evaluation of hybrid wind–solar energy system

“…Recently, the weighted -k -out-of- n system has attracted a great deal of attention in reliability literature. 11–13 For a weighted- k -out-of- n system with n binary components, its reliability is defined to be the probability that the total weight of all working components is at least k . The reliability of weighted- k -out-of- n system has been evaluated using various methods.…”