Reliability Comparison of Two Unit Redundancy Systems Under the Load Requirement

Abstract

This paper compares the reliability functions of the cold standby, hot standby, and load-sharing redundancy configurations, each of which is composed of two identical components for meeting a given system requirement. Thus far, no research has been done into the conditions that make one configuration more reliable than another because their reliability functions have no closed forms even when the component follows a Weibull lifetime distribution. In this paper, two analytical results are obtained given that the reliability of each configuration is expressed in terms of the design and operational loads of the component. First, higher reliability can be achieved in a cold standby configuration than in a load-sharing configuration if the increase in the component reliability obtained from the reduction in the operational load is not significant. Second, a cold standby configuration exhibits better reliability and carries a higher load than a hot standby configuration if the design load can be increased with a less decrease in the component reliability.

Reliability maximization of a load‐sharing system without redundant components

“…The power parameter 𝛿 measures the capability of the developer producing scaled down component. 28,21 A large value of 𝛿 indicates a fast decrease in the nominal failure rate as the component design load decreases from the baseline. Because 𝜓(𝑉 𝑛 ) approaches to zero as 𝑛 approaches infinity, and the corresponding elasticity is constant for all 𝑛, that is, 𝑔(𝑛) = 𝛿, the optimal 𝑛 can be infinite, for example, if 𝑝 = 0 and 𝛿 > 1.…”

“…Then, we have $$\theta = {V^\delta }$$ from the condition of $$\psi ( V ) = 1$$, implying that $$\psi ( {{V_n}} ) = {n^{ - \delta }}$$. The power parameter δ measures the capability of the developer producing scaled down component 28,21 . A large value of δ indicates a fast decrease in the nominal failure rate as the component design load decreases from the baseline.…”

“…9,10,18 In the case of an accelerated life test-based reliability model, the increased load accelerates the component age 4,6,16,19,20 or increases the component failure rate during operation. 2,5,21 Some of recent researches have superimposed a shock model over the component degradation model to incorporate the effect of the external shock that occur during operation. 10,22,23 Although these models are useful for computing the reliability of a given system, they are not applicable to compare reliability functions of different systems, because a component operating at the lowest load is selected as a baseline so that the baseline changes if the number of components used in the system changes.…”

“…Under the degradation‐based reliability model, the increased load raises the component degradation rate 7,8,12 or causes an additional damage to the component degradation 9,10,18 . In the case of an accelerated life test‐based reliability model, the increased load accelerates the component age 4,6,16,19,20 or increases the component failure rate during operation 2,5,21 . Some of recent researches have superimposed a shock model over the component degradation model to incorporate the effect of the external shock that occur during operation 10,22,23 .…”

Orderings of component level versus system level at active redundancies for coherent systems with dependent components

“…The research of this topic is mainly divided into two levels: active redundancy at the component level () and at the system level (). In the former case, the main problem is where to allocate active spares in a system to improve the reliability; see, for example, Boland et al [6], Li and Ding [25], Li et al [27], Zhao et al [52], Zhuang and Li [54], You et al [48], Fang and Li [12,13], Chen et al [8], Yan and Luo [43], You and Li [47], Zhang [49], Ling et al [28], Yan et al [45], Kim [21], Navarro et al [36] and Zhang et al [51]. In the later case, Barlow and Proschan [1] first proposed a well-known BP principle that is more reliable in the sense of usual stochastic ordering for the coherent system with independent components.…”