Two formulas for computing the reliability of incompletek-out-of-n:G systems

Reliability computation of highly redundant systems most commonly uses approximate methods. Except for k-out-of-n:G systems or consecutive k-out-of-n:G systems, exact reliability formulas offering a broader range of applicability are rare. This paper gives two new formulas for this purpose: the first handles k-out-of-n:G systems of which some paths are not present; the second allows for the reliability calculation of a coherent binary system in general. Both formulas express system reliability in terms of the reliabilities of k-out-of-n:G systems. In practice, these new formulas cope with highly redundant systems with certain similarities to k-out-of-n:G systems. For example, a reliability of the control-rod system of a nuclear reactor is computed. Although the paper is directed to system reliability, the results can be used for computing the failure probability of a system which in practical applications is sometimes more convenient. In which case, the formulas are to be changed such that a system is given by its minimal cut-sets instead of minimal path-sets, and p should be a component unreliability instead of its reliability. The first proof of formula uses domination theory and, in thus contributes to the state of the art in this field     

Reliability analysis for redundancy of industrial power distribution systems

Redundancy in design of industrial power distribution system reflects the goals of service continuity and improvement of service reliability. However, this results in higher initial cost.A possible means of analyzing costs vs reliability may be reliability analysis which may offer a cost-reliability trade off decision affecting design.In this paper, a set of general equations developed at The Ralph M. Parsons Company is presented for use of computing the failure rate of a redundant system with any given number of identical units, some of which are necessary for successful operation. The remainder are redundant. From the obtained system failure rate, system reliability and system availability can be determined.     

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

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Two unit repairable redundant standby system

The Laplace-Stieltjes (LS) transform for the distribution of time to first system failure (TFSF), transition probability, availability and mean time to system failure have been derived for two unit repairable redundant standby system with perfect as well as imperfect switchover condition. General expressions for computing various reliability performance indices have been obtained by using Markov Renewal techniques considering general distributions for time to failure and time to repair for the units.     

一个计算无圈有向网络可靠度的新算法

本文对无圈有向网络的可靠度计算进行了研究。提出了加权有序根树的概念，给出了路径集合的一种特殊排序方法，导出一个计算无圈有向网络可靠度的拓扑公式。在该公式的基础上提出了一个新的计算无圈有向网络可靠度的不交积和算法，算法可以生成简洁的可靠度表达式，从而可以有效地计算无圈有向网络的可靠度。同时验证了算法的有效性。     

An O(n·(log2(n))2) algorithm forcomputing the reliability of k-out-of-n:G and k-to-l-out-of-n:G systems

This paper presents the RAFFT-GFP (Recursively Applied Fast Fourier Transform for Generator Function Products) algorithm as a computationally superior algorithm for expressing and computing the reliability of k-out-of-n:G and k-to-l-out-of-n:G systems using the fast Fourier transform. Originally suggested by Barlow and Heidtmann (1984), generating functions provide a clear, concise method for computing the reliabilities of such systems. By recursively applying the FFT to computing generator function products, the RAFFT-GFP achieves an overall asymptotic computational complexity of O(n·(log₂(n)) ²) for computing system reliability. Algebraic manipulations suggested by Upadhyaya and Pham (1993) are reformulated in the context of generator functions to reduce the number of computations. The number of computations and the CPU time are used to compare the performance of the RAFFT-GFP algorithm to the best found in the literature. Due to larger overheads required, the RAFFT-GFP algorithm is superior for problem sizes larger than about 4000 components, in terms of both computation and CPU time for the examples studied in this paper. Lastly, studies of very large systems with unequal reliabilities indicate that the binomial distribution gives a good approximation for generating function coefficients, allowing algebraic solutions for system reliability     

Reliability of a dynamic n-unit shared load parallel system under different failure times

A generalized formula is derived for the reliability of a dynamic parallel system of n-components with equally shared load failing at different failure times. This formula is obtained using success modes analysis (SMA) and the same is completely verified for exponential distribution.     

现代电力通信网可靠性研究

电力通信网可靠性在电力系统安全稳定运行中起着至关重要的作用。通过从网络自身和网络运行2个方面对电力通信网可靠性影响因素、评价指标等内容做了分析,归纳出了可靠度、平均故障间隔时间、平均修复时间和生存性4个可靠性参数并分别给出了计算公式。最后,探讨了电力通信网的可靠性研究方法,为今后电力通信网的发展研究奠定了一定的基础。     

Closed-form solution for lifetime distribution of single-component failure delay systems

In this note an explicit formula for computing lifetime distribution of single-component failure delay systems is given, along with a program computing it, and comparison is made with an approximate solution.     

(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。     

Reliability and MTTF evaluation of a repairable complex system under waiting

This paper deals with the reliability and mean time to failure (MTTF) evaluation of a complex system under waiting incorporating the concept of hardware failure and human error. Failure rates of the complex system follow exponential time distributions, whereas repair follows a general repair time distribution. Laplace transforms of various state probabilities have been evaluated and then reliability is obtained by the inversion process. A formula for variance of time to failure has also been developed. A particular case is also given to highlight some important results. Moreover, various plots have been sketched at the end.     

基于故障树分析法的配电终端失效研究

配电终端的可靠性对配电自动化有效运维至关重要,文章结合故障树分析法与比例分摊原则,提出了适用于配电终端失效研究的一种方法。该方法通过分析各配电终端各模块工作与失效机理,建立配电终端的故障树分析模型,采用故障树分析法推导顶端事件失效计算公式;根据失效分摊法计算出各模块对系统失效的贡献比例,并据此识别配电终端的薄弱环节。最后以重庆某地区配电终端现场运行数据为样本,验证了该方法的有效性。     

A failure-distance based method to bound the reliability ofnonrepairable fault-tolerant systems without the knowledge of minimalcuts

CTMC (continuous-time Markov chains) are a commonly used formalism for modeling fault-tolerant systems. One of the major drawbacks of CTMC is the well-known state-space explosion problem. This paper develops and analyzes a method (SC-BM) to compute bounds for the reliability of nonrepairable fault-tolerant systems in which only a portion of the state space of the CTMC is generated. SC-BM uses the failure distance concept as the method described previously by the authors (1997) but, unlike that method, which is based on the computation of exact failure distances, SC-BM uses lower bounds for failure distances, which are computed on the system fault-tree, avoiding the computation and holding of all minimal cuts as required in the earlier work. This is important because computation of all minimal cuts is NP-hard and the number of minimal cuts can be very large. In some cases SC-BM gives exactly the same bounds as the previous method; in other cases it gives less tight bounds. SC-BM computes tight bounds for the reliability of quite complex systems with an affordable number of generated states for short to quite large mission times. The analysis of several examples seems to show that the bounds obtained by SC-BM appreciably outperform those obtained by simpler methods, and, when they are not equal, are only slightly worse than the bounds obtained by the previous method. In addition, the overhead in CPU time due to computing lower bounds for failure distances seems to be reasonable     

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     

Microelectronic System Reliability Prediction

The paper reviews the US MIL-HDBK-217 (MH-217) method of part stress-analysis failure-rate prediction for microelectronic systems and investigates the extent to which the MH-217 failure-rate formula is compatible with the physics of actual failure modes. A new formula is proposed which takes account separately of the reliability of the microelectronic devices in a system and of the system-level determinants of reliability. It is simpler than the current MH-217 formula, and more useful. It enables the system level aspects such as reliability program activities to be taken into account in the prediction, and allows better correlation to be made between part test and system test data. An example applies the new formula to a typical microelectronic system. By considering separately the failure physics of parts and the system level determinants, reliability prediction can be made a more useful tool both for part stress analysis and for reliability program management. The model would enable better correlations to be made between part and system test results. More work needs to be done to refine and validate the parameters. For high-reliability programs with closely controlled maintenance or with no maintenance, the use of a decreasing failure rate model for part failures should be considered. The failure rate formulae for other electronic parts used in microelectronic systems would also need to be reviewed, but apart from removal of the environmental factor and reduction in the failure rate values proportionate to that proposed for microelectronic parts, no changes should be necessary.     

Human error analysis of a standby redundant system with arbitrarily distributed repair times

This paper presents human error analysis of a (two units working and one on standby) system with arbitrarily distributed repair times. The supplementary vairables method is used to develop the system availability expressions. A general formula for the system steady-state availability is developed when the failed system repair times are gamma distributed. Time-dependent availability, system reliability with repair, mean time to failure and variance of time to failure formulae are developed for some particular cases. Selective plots are shown to demonstrate the impact of critical human error on system availability and reliability.     

A reliability model for real-time rule-based expert systems

This paper uses two modeling tools to analyze the reliability of real-time expert systems: (1) a stochastic Petri net (SPN) for computing the conditional response time distribution given that a fixed number of expert system match-select-act cycles are executed, and (2) a simulation search tree for computing the distribution of expert system match-select-act cycles for formulating a control strategy in response to external events. By modeling the intrinsic match-select-act cycle of expert systems and associating rewards rates with markings of the SPN, the response time distribution for the expert system to reach a decision can be computed as a function of design parameters, thereby facilitating the assessment of reliability of expert systems in the presence of real-time constraints. The utility of the reliability model is illustrated with an expert system characterized by a set of design conditions under a real-time constraint. This reliability model allows the system designers to: (1) experiment with a range of selected parameter values; and (2) observe their effects on system reliability     

Distributed-program reliability analysis: complexity and efficientalgorithms

This paper investigates the problem of distributed-program reliability in various classes of distributed computing systems. This problem is computationally intractable for arbitrary distributed computing systems, even when it is restricted to the class of star distributed computing systems. One solvable case for star distributed computing systems is identified, in which data files are distributed with respective to a consecutive property; a polynomial-time algorithm is developed for this case. A linear-time algorithm is developed to test whether or not an arbitrary star distributed computing system has this consecutive file distribution property. Efficient algorithms may still be sought for computing lower and upper bounds on the distributed program reliability for arbitrary distributed computing systems     

Interval Reliability for Initiating and Enabling Events

This paper describes generation and evaluation of logic models such as fault trees for interval reliability. Interval reliability assesses the ability of a system to operate over a specific time interval without failure. The analysis requires that the sequence of events leading to system failure be identified. Two types of events are described: 1) initiating events (cause disturbances or perturbations in system variables) that cause system failure and 2) enabling events (permit initiating events to cause system failure). Control-system failures are treated. The engineering and mathematical concepts are described in terms of a simplified example of a pressure-tank system. Later these same concepts are used in an actual industrial application in which an existing chlorine vaporizer system was modified to improve safety without compromising system availability. Computer codes that are capable of performing the calculations, and pitfalls in computing accident frequency in fault tree analysis, are discussed.     

Reliability of a large consecutive-k-out-of-r-from-n:F system withunequal component-reliability

For a consecutive-k-out-of-r-from-n:F system with unequal component reliability: (1) upper and lower reliability bounds are obtained; and (2) a limit formula and a life distribution for the reliability of a large system are derived under certain conditions. Many previous results on the reliability of the consecutive-k-out-of-n:F system are special cases of this paper