Failure-Frequency Evaluation of Complex Systems Using Cut-Set Approach

The paper develops a new method for evaluating failure frequency of complex systems with 2-state components, from corresponding cut sets. The method is derived by direct application of cut-set techniques to the failure frequency formula obtained by Buzacott and Singh. The method is suitable for computer implementation and can be used for cut-set diagrams with overlapping and non minimal cut-sets. Two examples are presented and the results are compared with those obtained by a common approximate approach.     

A new technique for active minimal cut set selection used in substation reliability evaluation

This paper presents a new technique for the selection of active minimal cut sets in substation reliability evaluation. This technique is presented in this paper using a simple substation configuration. The developed technique can be used in the development of computer programs for substation reliability evaluation. This developed technique is further illustrated by application to other practical system examples.     

A Heuristic Algorithm for System Failure Frequency

For reliability analysis, the choice between tie-sets and cut-sets is not a matter of convenience but depends on assessment of computational effort. The system configuration alone determines the preference of the approach. The present paper offers a faster algorithm for evaluating system failure frequency using both approaches. An expression for system failure frequency between two specified nodes is derived using either tie-sets or cut-sets. The expression is in terms of failure frequency, availability, and unavailability of the system elements. A heuristic algorithm to obtain the expression can be programmed for a computer. The algorithm is illustrated through an example. The manner in which Abraham's algorithm can be used to determine system probability of failure using cut-sets is suggested. The algorithms are also useful for evaluating sensitivity coefficients.     

Graph Theory Concepts in Frequency and Availability Analysis

Steady-state availability and failure frequency are two key indices in a repairable system. They are generally evaluated from Markov models with constant transition rates. Numerical solutions can be found for relatively large systems using computer programs. It is more difficult to obtain general equations for a specific system using transition rate symbols. The determination of these equations usually involves linear simultaneous equations, either directly or using Cramer's Rule. This paper describes a general purpose graphical approach for obtaining steady-state availability and frequency expressions from a flow graph based on the Markov model. A set of generalised formulae is developed and applied to several configurations. This technique avoids the need to use matrices for developing general purpose equations. Its direct approach is useful to practising engineers and students of reliability concepts.     

ADS-B系统运行可靠性评价方法

为实现ADS-B系统运行可靠性的综合评价,提出了一种基于T-S模糊神经网络的方法。以平均首次故障时间、平均故障间隔时间、平均维修时间、平均可用度和维修时间率5项可靠性评价指标作为输入向量。利用T-S模糊系统构建可靠性综合评价的非线性映射关系,经神经网络的自适应训练,调整模糊规则和隶属度函数,建立ADS-B系统运行可靠性的综合评价模型。实验仿真与应用情况表明,该方法可行、有效,并具有较高的计算稳定性、精确性和良好的泛化能力,且评价结果客观、准确可靠,可作为提高ADS-B系统运行可靠性的决策依据。     

Bayesian Confidence Limits for the Reliability of Cascade Exponential Subsystems

The problem treated here is that of deriving exact Bayesian confidence intervals for the reliability of a cascade system consisting of N independent subsystems each having an exponential distribution of life with a failure rate which is estimated from life test data. The posterior probability density function of the system reliability is derived in closed form, using the method of the Mellin integral transform. The posterior distribution function is obtained, yielding Bayesian confidence limits on the total system reliability. These results, which are believed to be new for N > 3, have an immediate application to problems of reliability evaluation and test planning.     

Fractional duration before first failure—A useful index and an analytical tool

This paper defines a new index, fractional duration before first failure and describes the methodology for its calculation. The relationship of this index to the mean time to first failure is also presented. The fractional duration before first failure is, therefore, not only a useful measure of system reliability but also provides an alternative approach to calculate mean time to first failure. The concepts and techniques are illustrated with suitable examples.     

Qualitative Analysis in Reliability & Safety Studies

The qualitative evaluation of system logic models is described as it pertains to assessing the reliability and safety characteristics of nuclear systems. Qualitative analysis of system logic models, i.e., models couched in an event (Boolean) algebra, is defined, and the advantages inherent in qualitative analysis are explained. Certain qualitative procedures that were developed as a part of fault-tree analysis are presented for illustration. Five fault-tree analysis computer-programs that contain a qualitative procedure for determining minimal cut sets are surveyed. For each program (SETS, MOCUS, PREP, MICSUP, ELRAFT), the minimal cut-set algorithm and limitations on its use are described. The recently developed common-cause analysis for studying the effect of common-causes of failure on system behavior is explained. This qualitative procedure does not require altering the fault tree, but does use minimal cut sets from the fault tree as part of its input. The method is applied using two different computer programs, COMCAN and SETS.     

Reliability prediction models to support conceptual design

During the early stages of conceptual design, the ability to predict reliability is very limited. Without a prototype to test in a lab environment or without field data, component failure rates and system reliability performance are usually unknown. A popular method for early reliability prediction is to develop a computer model for the system. However, most of these models are extremely specific to an individual system or industry. This paper presents three general procedures (using both simulation and analytic solution techniques) for predicting system reliability and average mission cost. The procedures consider both known and unknown failure rates and component-level and subsystem-level analyzes. The estimates are based on the number of series subsystems and redundant (active or stand-by) components for each subsystem. The result is a set of approaches that engineers can use to predict system reliability early in the system-design process. Software was developed (and is discussed in this paper) that facilitates the application of the simulation-based techniques. For the specific type of system and mission addressed in this paper, the analytic approach is superior to the simulation-based prediction models. However, all three approaches are presented for two reasons: (1) to convey the development process involved with building these prediction tools; and (2) the simulation-based approaches are of greater value as the research is extended to consider more complex systems and scenarios     

Parametric Representation of Probability in Two Dimensions?A New Approach in System Reliability Evaluation

The evaluation of system reliability becomes very diffilcult when the number of components in a system is large or the system configuration is complex. This note presents a straightforward method for system reliability evaluation. Probability is treated as a point in a Cartesian frame and formulas are derived to evaluate the reliability of series, parallel, series-parallel, and bridge networks. The values obtained by the classical method agree closely with those obtained by this parametric method.     

Calculating the failure frequency of a repairable system

Failure frequency is an important parameter of a repairable system. Combining the techniques of cut set, tie set and exclusive manipulation, a general formula has been derived in this paper. It can give the exact result at any point of time for systems whose component failure and repair times are arbitrarily distributed.     

基于故障树分析法的水洞可靠性研究

通过分析暂冲式水洞的系统结构,建立了系统的故障树;利用最小割集法对故障树进行定性分析,找到了系统所有可能的故障模式,得到了系统的34个一阶、34个二阶最小割集;总结出各种设备故障和人为因素所造成的故障,是造成本系统故障的两个主要因素;以控制系统故障树的定量分析为例,得到了计算系统可靠度及各底事件的重要度的方法,进而分析出一阶最小割集中的故障是整个系统的最薄弱环节;并提出了提高系统可靠性的相应措施.     

Fault Tree Synthesis From a Directed Graph Model for a Power Distribution Network

The Lapp-Powers fault tree synthesis algorithm is applied to an electrical power distribution network and the cut sets are derived for a sustained loss of power on one busbar. This algorithm is based on a directed graph (digraph) representation of the system, in contrast with the method of Camarda, et al. which is based on a reliability graph. The digraph model forces an explicit evaluation of the corrective actions (negative feedback and negative feed forward) that are taken to counteract disturbances which enter the network. The presentation is tutorial and shows the disciplined application of fault-tree synthesis operators.     

Bayesian Confidence Limits for the Reliability of Mixed Cascade and Parallel Independent Exponential Subsystems

This paper deals with the theoretical problem of derving Bayesian confidence intervals for the reliability of a system consisting of both cascade and parallel subsystems where each subsystem is independent and has an exponential failure probability density function (pdf). This approach is applicable when test data are available for each individual subsystem and not for the enfire system. The Mellin integral transform is used to analyze the system in a step-by-step procedure until the posterior pdf of the system reliability is obtained. The posterior cumulative distribution function is then obtained in the usual manner by integrating the pdf, which serves the dual purpose of yielding system reliability confidence limits while at the same time providing a check on the accuracy of the derived pdf. A computer program has been written in FORTRAN IV to evaluate the confidence limits. An example is presented which uses the computer program.     

系统可靠性的IMML法

提出一种对修正极大似然（modification of maximum likelihood）法的改进方法,记为IMML法。用于系统可靠性综合时进行系统等效成败型数据的折算,其准确度与CMSR法相同。既克服了L－M法的保守,又防止了MML法的冒进,并且消除了CMSR法在使用上的限制,对高可靠零故障系统的可靠性评估具有重要意义。     

容错计算机系统的可靠性建模和分布式仿真

对容错计算机系统的可靠性进行评估是一项重要而困难的工作。为容错计算机系统的各个组成部件建立了部件级故障模型,并以此为基础建立了整个容错计算机系统的可靠性测评模型。基于所建立模型,我们提出了分布式仿真的思想,它把系统的各个部件仿真为网络上的一个站点,并增设一台服务器来对整个系统的可靠性性能进行统计和分析。仿真结果验证了建立模型的正确性和方法的有效性。     

Analysis of a two-unit warm standby system subject to degradation

This paper deals with the reliability analysis and the mean time to system recovery of a single server, two-unit (priority and ordinary) warm standby subject to degradation. Initially the priority unit is operative and the ordinary unit is kept as a warm standby. The priority unit passes through three different operative stages (excellent, good and satisfactory) before it fails. The priority unit enters into the total failure mode only from the satisfactory stage, and after repair it enters into the normal mode with any of the ‘excellent’, ‘good’ and ‘satisfactory’ stages with different probabilities. The failure, repair and degradation time distributions are assumed to be general and arbitrary. The system is observed at suitable regenerative epochs in order to carry out the expected first passage time analysis. Moreover, three special cases have been considered. The results of Gupta [Int. J. Systems Sci.22 (11) 2329–2338 (1991)] are derived from the present results as a special case. A computer program for calculating the mean time to system failure and the mean time to system recovery is made.     

Closed form expressions for resonant frequency of rectangular patchantennas with multidielectric layers

The conformal mapping approach combined with a generalized transmission line model has been developed to predict the resonant frequency of rectangular patch antennas with multidielectric layers. A set of closed form expressions is derived, which is suitable for direct application in CAD programs. Numerical results are presented to validate this method     

Design for diagnosis using a diagnostic evaluation measure

The results demonstrated by the SAN system show how a real fault tolerant system can have more than one configuration with almost the same reliability. However, from a diagnosis perspective, the designs can have different costs of diagnosis at failure time. A method for measuring the cost of diagnosing diagnosis decision trees (DDT) was demonstrated, which is a specialized weighted mean depth of traversing the DDT. This evaluation method incorporates the qualitative (structure) and quantitative (reliability analysis) into one measure for predicting diagnosis cost. DDTs incorporate the same qualitative and quantitative data as the diagnosis cost measure, which makes this measure suitable for evaluating these decision trees. Evaluating and comparing alternative system designs using the diagnosis cost function as we demonstrated is an efficient and simple method for pursuing the design for diagnosis objective.     

A Cut Set Method for Reliability Evaluation of Systems Having s-Dependent Components

The cut set method presently assumes components to be s-independent. This paper presents a method called MCS approach for extending the cut set approach to systems involving s-dependencies. The method is based on MCS theorem and consists in decomposing the system by cut sets and using the Markov processes for calculating terms in the cut set equations. The Markov process associated with only the members of one cut set need be considered at a time and the transition rate matrix of the entire system need not be generated. The MCS approach is feasible when Pr{C?i} and F(S) can be calculated from the transition rate matrix of the members of Ci. This is possible when the MCS theorem applies and the MP of the entire system can be merged to obtain the MP of Ci. However, in many situations where the MCS theorem does not rigorously apply, approximate results may still be possible by the MCS method. The judgment in such cases is based on how approximately does the MCS theorem apply.