Allocating active redundancies to k‐out‐of‐n reliability systems with permutation monotone component lifetimes

Abstract

This paper studies k-out-of-n redundant systems with component lifetimes having lower tail permutation decreasing probability density. For matched redundancies with stochastic arrangement increasing lifetimes, the allocation of a more reliable component to a weaker component is proved to enhance system reliability. For redundancies with independent and identically distributed lifetimes, more allocations to a weaker component are shown to stochastically increase the system lifetime. In addition, using a real data set, we illustrate the statistical aspects of developing lifetimes with lower tail permutation decreasing density.

On matched active redundancy allocation for coherent systems with statistically dependent component lifetimes

“…If the system is symmetric w.r.t. components , then , Proof According to the proof of Theorem 4.3 of You et al (), when , the bivariate random vector is SAI. By the independence among , the result follows directly from Theorem 3.3.…”

“…Except for Kotz, Lai, and Xie (), Belzunce, Martínez‐Puertas, and Ruiz (), You and Li (), Jeddi and Doostparast () and You, Fang, and Li (), fewer works on redundancy allocation for coherent systems with mutually dependent component lifetimes are found in the literature. Among the references in the literature regarding dependent component lifetimes, one line presumes that the base and redundancy component lifetimes may be dependent, and the other assumes independence between the base component lifetimes and the redundancy component lifetimes.…”

“…Later on, Jeddi and Doostparast () derived some sufficient and necessary conditions guaranteeing the existence of the usual stochastic order on the resultant system lifetime and partially generalized the findings of Belzunce et al (). Following the second line, for ‐out‐of‐ systems with dependent component lifetimes, You and Li () and You et al () studied the optimal allocation of active redundancy components with their lifetimes independent of the base component lifetimes.…”

On allocating one active redundancy to coherent systems with dependent and heterogeneous components' lifetimes

“…Later, You and Li [24] generalized this result to k-out-of-n systems with SAI components' lifetimes. Recently, by relaxing SAI components' lifetimes to lower tail permutation decreasing components' lifeimes 2 t ≤ x j ., You et al [25] further extended the theoretical result of [24] to the case of multiple active redundancies. Note that, for a k-out-of-n system, any two positions are symmetric in the sense that switching positions i and j resulting in the same system structure.…”

“…For a series system without any specification on the dependence structure of components' lifetimes and one active redundancy's lifetime, [9] proved that allocating the active redundancy to one component leads to a system with stochastically longer lifetime if and only if a more reliable minimal path is introduced by the redundancy. Recently, You et al [25] studied k-out-of-n redundant systems with components' lifetimes having a lower tail permutation decreasing density and with multiple redundancies having possibly dependent lifetimes.…”