GERT Analysis of m-Consecutive-k -Out-of-n Systems

An m-consecutive-k-out-of-n:F system, introduced by W.S. Griffith, consists of an ordered linear sequence of n i.i.d. components that fails iff there are at least m non-overlapping runs of k consecutive failed components. However, a situation may occur in which an ordered linear sequence of n i.i.d. components fails iff there are at least m non-overlapping runs of at least k consecutive failed components. We call such a system an m-consecutive-at least-k-out-of-n:F system. This paper presents a graphical evaluation and review technique (GERT) analysis of both types of systems providing closed form explicit formulae for reliability evaluation in a unified manner. GERT, besides providing a visual picture of the system, helps to analyse the system in a less inductive manner. Numerical examples for each system are studied in detail by computing the reliability for various combinations of sets of values of the parameters involved. It is observed that m-consecutive-at least-k-out-of-n:F systems are more reliable than m-consecutive-k-out-of-n:F systems as the number of possible state combinations leading to system's failure are larger in the latter. Mathematica is used for systematic computations. Numerical investigations illustrate the efficiency of GERT in reliability analysis of such systems. In comparison with the existing formulae of m-consecutive-k-out-of-n:F systems for i.i.d. components, the formula obtained by GERT analysis, to be referred to as GERT-F, is much more efficient owing to its significantly low computational time, and easy implementation     

(n,F,k)系统可靠性

(n,F,k)系统由n个单元组成,当且仅当大于F个单元发生故障,或者k个或k个以上相邻单元发生故障,则系统失效本文提出了(n,F,k)系统可靠性的一般计算公式,并给出该系统可靠性的上下界。     

An explicit closed-form formula for profit-maximizing k-out-of-n systems subject to two kinds of failures

This paper derives and analyzes an explicit closed-form formula for the optimal k in k-out-of-n systems consisting of i.i.d. components. The system can be in one of two possible modes with a pre-specified probability. The components are subject to failure in each of the two modes. The costs of the two kinds of system failures are generally not identical. Since the formula is explicit, it permits a calculation of the optimal k directly in terms of the parameters of the system. In addition, it yields many results concerning both the bounds of the optimal k and the effects of a change in parameters on the optimal k and on the optimized value of the system's expected profit.     

Exact Reliability Formulas for Linear & Circular Consecutive-k-out-of-n:F Systems

A consecutive-k-out-of-n:F system, with n linearly or circularly arranged i.i.d. components is examined. The system reliability has an exact formula which is straight forward and more effective than those given elsewhere; the two formulas are given.     

An Efficient Algorithm for Computing the Reliability of Consecutive-$k$-Out-Of-$n$:F Systems

Many algorithms for computing the reliability of linear or circular consecutive-k-out-of-n:F systems appeared in this Transactions. The best complexity estimate obtained for solving this problem is O(k³ log(n/k)) operations in the case of i.i.d. components. Using fast algorithms for computing a selected term of a linear recurrence with constant coefficients, we provide an algorithm having arithmetic complexity O(k log (k) log(log(k)) log(n)+k^omega) where 2相似文献   

Efficient algorithms for k-out-of-n andconsecutive-weighted-k-out-of-n:F system

A new reliability model, consecutive-weighted-k-out-of-n:F system, is proposed and an O(n) algorithm is provided to evaluate its reliability. An O(n·min(n,k)) algorithm is also presented for the circular case of this model. The authors design an O(n) parallel algorithm using k processors to compute the reliability of k-out-of-n systems, that achieves linear speedup     

An O(k/sup 2//spl middot/log(n)) algorithm for computing the reliability of consecutive-k-out-of-n: F systems

This study presents an O(k/sup 2//spl middot/log(n)) algorithm for computing the reliability of a linear as well as a circular consecutive-k-out-of-n: F system. The proposed algorithm is more efficient and much simpler than the O(k/sup 3//spl middot/log(n/k)) algorithm of Hwang & Wright.     

n中取k表决系统的可靠性评估

文章主要以2/3[G]系统为例对k/n[G]系统的可靠性进行评估,并同单系统进行比较,为选取k/n[G]作为系统模型提供依据。最后讨论了k/n[G]系统的表决器可靠性要求。     

计算无圈有向网络ST可靠性的一个新方法

本文考虑计算无圈有向网络的ＳＴ可靠性问题（至少存在一条从源点ｓ到汇点ｔ的正常运行道路的概率）。文章引进了深度优先搜索（Ｄｅｐｔｈ－ＦｉｒｓｔＳｅａｒｃｈ）有序根树的概念并提出一个新的计算无圈有向网络ＳＴ可靠性的拓扑公式。以该公式为基础,我们利用ＤＦＳ方法提出一个新的计算无圈有向网络ＳＴ可靠性算法,它能生成简洁的可靠性表达式,进而有效地计算无圈有向网络的ＳＴ可靠性。两个例子例证了我们的结论     

Computing consecutive-type reliabilities nonrecursively

The reliability of consecutive-type systems has been approached from various angles. A new method is presented for deriving exact expressions for the generating functions and the reliabilities of various consecutive-type systems. This method, based on Feller's run theory, is easy to implement, and leads to both recursive and nonrecursive formulas for the reliability. The nonrecursive expression is especially advantageous for systems with numerous components. In comparison to the n (number of components) computations that the recursive formulas require, the nonrecursive formula only requires the computation of the roots of a polynomial of order k. The method is extended for computing generating functions and reliabilities of systems with multi-state components as well as systems with s-dependent components.     

An Algorithm for Evaluating Overall Reliability of Special Tree-Networks

The overall reliability of networks composed of trees, cycles and semi-cycles is determined using a computer algorithm. An n-node cycle contains n nodes and links forming a single loop; an n-node semi-cycle has more than one loop, but reduces to a cycle upon the removal of one link. The algorithm identifies all cycles and semi-cycles and determines iteratively the overall reliability using a simple formula and Bayesian decomposition.     

A Generalized Reliability Function for Systems of Parallel Components

In systems of parallel components, the system reliability function Rp(t) is usually defined as the probability that not all the parallel components fail in a time interval t, given that all the components are operating at the beginning of the interval. This definition implies that if there is one component which operates throughout the whole interval in question, then the system reliability is perfect. Consider the system S which always requires M > 1 components to do its job. It is obvious that the system is not reliable if there are only k, 1 ? k < M, components working in the time interval t. The conventional reliability function Rp(t) is then insufficient for studying the reliability of the system S. A generalized reliability function Rr,n(t) is presented in this paper, and it is shown that the conventional reliability function Rp(t) is a special case of the generalized reliability function Rr,n(t). The practical application of this generalized reliability function is also discussed.     

On the Consecutive-k-of-n:F System

The linear (circular) k-of-n:F system has n linearly (circularly) ordered components. Each component either functions or fails. The system fails i.f.f.k consecutive components fail. This paper provides, in the i.i.d. case, recursive formulas and bounds for computing system reliability. It considers properties of system life distributions and, in the non i.i.d. case, questions of optimal system design.     

OBS网络中的数据信道调度算法性能的理论分析和仿真

在光突发交换(OBS)网络的数据信道调度算法的性能分析中,人们多采用一种近似理论模型Erlang B公式.但该模型与OBS的实际情况有很大差距.文章以M/M/k/k模型为基础,对这些算法性能的理论分析作了一些修正,并给出了各类典型算法的理论性能模型.最后,分别对这些算法从理论性能和仿真性能上进行比较,结果表明:各种算法的性能在理论分析和实际仿真上都偏离Erlang B公式的推导结果.     

可靠性与维修性在雷达系统效能评估中的应用

可靠性与维修性指标是影响武器系统效能的重要因素.文中对雷达系统效能评估中的可靠性和维修性进行研究,给出了可靠性与维修性试验数据的处理方法.通过对系统的分析在建立效能评估WSEIAC模型的基础上,把可靠性与维修性数据应用到系统效能评估中.最后,分析了可靠性与维修性对系统效能的影响.     

The Reliability of Repairable Complex Systems Part B: The Dissimilar Machine Case

A generalization of the reliability model given in Part A of this reliability study is made. The failure and repair rates are assumed to be exponential as in Part A, but the model equations are changed so that the following ramifications are possible. 1) The label case: it is necessary to know which of the similar machines are broken down in order to decide if a system failure has occurred. 2) The parameter case: the values of the failure and repair rates are not the same on each machine. 3) The type of failure case: the system goes from state i to i + j after a failure, j ? 1, and to i - k after a repair, k ? 1, whereas in Part A j = k = 1 only. A procedure for finding dissimilar machine model equations with time delays before failure and time restoration constraints after repair are given.     

System availability with non-exponentially distributed outages

This paper studies the steady-state availability of systems with times to outages and recoveries that are generally distributed. Availability bounds are derived for systems with limited information about the distributions. Also investigated are the applicability of convenient exponential models in evaluating availability for systems that have two-sided bounded distributions of times to planned outages. A general closed-form formula is derived for the steady-state availability of a system with multiple outage types of arbitrary distributions. The formula shows that only the mean values of times to repair (TTR_i , i = 1, 2,..., n) affect the steady-state availability; i.e., distributions of TTR_i with the same mean value have the same effect in determining the steady-state system availability. However, the distributions of times to outages, (TTO_i, i = 1, 2,..., n), have an important impact on the steady-state system availability. Bounds are provided for the steady-state availability for a system subject to unplanned outages, for which times-to-outages are exponentially distributed and planned outages for which times-to-outages have bounded distributions. In practice, the distribution of time to planned outages is generally bounded due to economic constraints and industrial competition. The bounds derived here are good estimates of the system's steady-state availability, if the only known information of time-to-planned-outage is its two-sided bounds. Popular all-exponential models that assume that all times to outages and recoveries are exponentially distributed can under-estimate or over-estimate system availability if used for a system with generally distributed times to outages, of which limited information is known. Therefore explicit criteria are presented for determining when an all-exponential model, if applied to systems with outages of two-sided bounded general distributions, is a good approximation     

Consecutive k-out-of-r-from-n system with multiple failure criteria

This paper proposes a new model which generalizes the linear consecutive k-out-of-r-from-n system to the case of multiple failure criteria. In this model, the system consists of n linearly ordered elements, and fails iff in any group of r/sub 1/,...,r/sub H/ consecutive elements less than k/sub 1/,...,k/sub H/ elements respectively are in a working state. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of system reliability evaluation are presented.     

A New Real-Time Reliability Prediction Method for Dynamic Systems Based on On-Line Fault Prediction

While a specific system is in use, its reliability will decrease gradually after the infant mortality period because of the components' degradation, or external attacks. Thus, reliability is a natural characteristic of a system's health, and can be used for condition monitoring & predictive maintenance. This paper introduces a new real-time reliability prediction method for dynamic systems which incorporates an on-line fault prediction algorithm. The factors that may reduce a system's reliability are modeled as an additive fault input to the system, and the fault is assumed to be varying linearly with time, approximately. The time-varying fault is roughly estimated based on a modified particle filtering algorithm at first. Then, as a time series, the fault estimate sequence is smoothed, and predicted by an exponential smoothing method. Mathematical analysis shows that the effects of the system, and measurement noises on the fault estimates are greatly reduced by exponential smoothing, which indicates that the comparatively high accuracy of the fault estimates & predictions is guaranteed. Based on the particle filtering & fault prediction results, the whole system's predictive reliability is computed through a Monte Carlo simulation strategy. The effectiveness of the proposed real-time reliability prediction method is validated by a computer simulation of a three-vessel water tank system.     

Designing a Reliable Power System: Hydro-Quebec's Integrated Approach

Hydro-Que/spl acute/bec's transmission system is among the most extensive and complex transmission networks in North America. The system's design was improved over the last few years using an optimization process based on acquired experience as well as customers' expectations. Hydro-Que/spl acute/bec's transmission system is currently designed in accordance with four major guiding principles based on a successive line of defense concept designed to counter events that are increasingly more severe but also increasingly more rare. These major guiding principles are a direct reflection of the level of risk that society accepts to tolerate in relation to the costs involved by higher reliability requirements. Que/spl acute/bec's specific context, which is characterized by long transmission lines, harsh weather, and customers' heavy reliance on electricity for their heating needs, means that very high security standards must be used in the system design. To obtain a level of reliability on par with that of our neighbors' systems, however, requires more stringent criteria and standards. This paper will describe the design philosophy of Hydro-Que/spl acute/bec's power system, the underlying major guiding principles, and the defense plans designed to ensure its reliability.