Lifecycle operational reliability assessment of water distribution networks based on the probability density evolution method

In this study, a lifecycle operational reliability assessment framework for water distribution networks (WDNs) is proposed on the basis of the probability density evolution method (PDEM). The occurrence models of daily accidents are fitted using the maintenance data provided by a local water administration sector. For a given accident, two types of accidents (e.g., leaks and bursts) are distinguished in different occurrence probabilities and simulated in various ways. The pipe deterioration process in the lifecycle is reflected by incorporating the time-dependent pipe roughness model. Considering various randomness in the model, PDEM, a newly proposed and developed method for a stochastic system, is used to evaluate the lifecycle operational reliability of WDNs. The framework is demonstrated using an actual WDN, and the nodal reliabilities in the lifecycle are obtained. Comparisons of the operational reliabilities of all nodes calculated via the PDEM and Monte Carlo simulations prove that PDEM is an accurate and highly efficient method.     

A study of the exponential smoothing technique in software reliability growth prediction

Software reliability models can provide quantitative measures of the reliability of software systems which are of growing importance today. Most of the models are parametric ones which rely on the modelling of the software failure process as a Markov or non-homogeneous Poisson process. It has been noticed that many of them do not give a very accurate prediction of future software failures as the focus is on the fitting of past data. In this paper we study the use of the double exponential smoothing technique to predict software failures. The proposed approach is a non-parametric one and has the ability of providing more accurate prediction compared with traditional parametric models because it gives a higher weight to the most recent failure data for a better prediction of future behaviour. The method is very easy to use and requires a very limited amount of data storage and computational effort. It can be updated instantly without much calculation. Hence it is a tool that should be more commonly used in practice. Numerical examples are shown to highlight the applicability. Comparisons with other commonly used software reliability growth models are also presented. © 1997 John Wiley & Sons, Ltd.     

An approach for assessing human decision reliability

This paper presents a method to study human reliability in decision situations related to nuclear power plant disturbances. Decisions often play a significant role in handling of emergency situations. The method may be applied to probabilistic safety assessments (PSAs) in cases where decision making is an important dimension of an accident sequence. Such situations are frequent e.g. in accident management. In this paper, a modelling approach for decision reliability studies is first proposed. Then, a case study with two decision situations with relatively different characteristics is presented. Qualitative and quantitative findings of the study are discussed. In very simple decision cases with time pressure, time reliability correlation proved out to be a feasible reliability modelling method. In all other decision situations, more advanced probabilistic decision models have to be used. Finally, decision probability assessment by using simulator run results and expert judgement is presented.     

The robustness of markov reliability models

Markov models are an established part of current systems reliability and availability analysis. They are extensively used in various applications, including, in particular, electrical power supply systems. One of their advantages is that they considerably simplify availability evaluation so that the availability of very large and complex systems can be computed. It is generally assumed, with some justification, that the results obtained from such Markov reliability models are relatively robust. It has, however, been known for some time, that practical time to failure distributions are frequently non-exponential, particular attention being given in much reliability work to the Weibull family. Morover, recently additional doubt has been case on the validity of the Markov approach, both because of the work of Professor Kline and others on the non-exponentiality of practical repair time distribution, and because of the advantages to be obtained in terms of modelling visibility of the alternative simulation approach. In this paper we employ results on the ability of the k-out-of-n systems to span the coherent set to investigate the robustness of Markov reliability models based upon a simulation investigation of coherent systems of up to 10 identical components. We treat the case where adequate repair facilities are available for all components. The effects upon the conventional transient and steady-state measures of Weibull departures from exponentiality are considered. In general, the Markov models are found to be relatively robust, with alterations to failure distributions being more important than those to repair distributions, and decreasing hazard rates more critical than increasing hazard rates. Of the measures studied, the mean time to failure is most sensitive to variations in distributional shape.     

Dynamic response and reliability analysis of structures with uncertain parameters

An original approach for dynamic response and reliability analysis of stochastic structures is proposed. The probability density evolution equation is established which implies that incremental rate of the probability density function is related to the structural response velocity. Therefore, the response analysis of stochastic structures becomes an initial‐value partial differential equation problem. For the dynamic reliability problem, the solution can be derived through solving the probability density evolution equation with an initial value condition and an absorbing boundary condition corresponding to specified failure criterion. The numerical algorithm for the proposed method is suggested by combining the precise time integration method and the finite difference method with TVD scheme. To verify and validate the proposed method, a SDOF system and an 8‐storey frame with random parameters are investigated in detail. In the SDOF system, the response obtained by the proposed method is compared with the counterparts by the exact solution. The responses and the reliabilities of a frame with random stiffness, subject to deterministic excitation or random excitation, are evaluated by the proposed method as well. The mean, the standard deviation and the reliabilities are compared, respectively, with the Monte Carlo simulation. The numerical examples verify that the proposed method is of high accuracy and efficiency. Moreover, it is found that the probability transition of structural responses is like water flowing in a river with many whirlpools, showing complexity of probability transition process of the stochastic dynamic responses. Copyright © 2004 John Wiley & Sons, Ltd.     

Reliability Modelling of Multiple Repairable Units

This paper proposes a model selection framework for analysing the failure data of multiple repairable units when they are working in different operational and environmental conditions. The paper provides an approach for splitting the non‐homogeneous failure data set into homogeneous groups, based on their failure patterns and statistical trend tests. In addition, when the population includes units with an inadequate amount of failure data, the analysts tend to exclude those units from the analysis. A procedure is presented for modelling the reliability of a multiple repairable units under the influence of such a group to prevent parameter estimation error. We illustrate the implementation of the proposed model by applying it on 12 frequency converters in the Swedish railway system. The results of the case study show that the reliability model of multiple repairable units within a large fleet may consist of a mixture of different stochastic models, that is, the homogeneous Poisson process/renewal process, trend renewal process, non‐homogeneous Poisson process and branching Poisson processes. Therefore, relying only on a single model to represent the behaviour of the whole fleet may not be valid and may lead to wrong parameter estimation. Copyright © 2015 John Wiley & Sons, Ltd.     

信息融合多传感器可信度的确定方法及应用

借鉴层次分析法相对比较的思想,提出一种确定多传感器可信度的方法．该方法基于传感器提供的信息的相对可信度,对不同目标分别建立多传感器可信度判断矩阵,求得各传感器对该目标的可信度,进而求得各传感器的综合可信度．给出了一个数值算例．根据传感器的可信度,改变径向基函数神经网络的样本空间的大小,分析了训练时间和网络融合性能,验证了方法的有效性和实用性．     

2D C/SiC复合材料的可靠性评价

采用概率论和数理统计方法, 以研究分析2D C/SiC复合材料的弯曲强度分布规律为切入点, 比较了失效概率预测值与实验值, 用可靠度、 风险函数和可靠强度评价了该材料可靠性。通过线性回归分析和拟合优度检验得到正态、 对数正态和三参数Weibull分布模型均可表征其弯曲强度分布规律; 确定了该材料弯曲强度失效概率、 可靠度函数、 风险函数和可靠强度的数学模型中的参数, 可以预测给定强度条件和许用可靠度条件下的多种可靠性指标; 材料弯曲强度均值的三种模型预测值与实测值最大相对误差仅0.07%, 计算得到的失效概率曲线与实验弯曲强度的失效分布均符合很好。      

Integrated system identification and reliability evaluation of stochastic building structures

System identification and reliability evaluation play a significant role in structural health monitoring to ensure the serviceability and safety of existing structures. Although the development of system identification methods has attained much attention and some degree of maturity, reliability evaluation of existing structures still remains a challenging problem especially when uncertainties in measurement data and inherent randomness, which are inevitably involved in civil structures, are considered. In this regard, this paper presents a framework for integrated system identification and reliability evaluation of stochastic building structures. Two algorithms are proposed to respectively evaluate component reliability and system reliability of stochastic building structures by combining a statistical moment-based system identification method and a probability density evolution equation-based reliability evaluation method. System identification is embedded in the procedure of reliability evaluation of a stochastic building structure. The uncertainties in both the structure and the external excitation are considered. Numerical examples show that the structural component and system reliabilities of a three-story shear building structure with three damage scenarios can be effectively evaluated by the proposed methods.     

引入不确定参数的汽车盘式制动器振动稳定性分析

针对汽车制动器的噪声抑制问题,基于可靠性分析理论,将蒙特卡洛法与响应面法相结合,提出了一种汽车盘式制动器系统振动稳定性的可靠性分析方法。该方法针对制动噪声产生具有不确定性的特点,引入随机和区间不确定性参数对制动器系统进行描述,建立包含随机参数和区间参数的制动器不稳定特征值的响应面近似模型,进而采用Sobol′全局灵敏度分析法和蒙特卡洛法分别对不确定参数的全局灵敏度和系统稳定性的可靠度进行分析。用该方法对某车的浮钳盘式制动器系统进行研究,分析了系统稳定性的可靠度和不确定参数的全局灵敏度,甄别了不确定性参数对系统稳定性的影响,并从可靠性角度提出了改善制动器系统振动稳定性的工程措施。     

Joint layout,pipe size and hydraulic reliability optimization of water distribution systems

A multicriteria maximum-entropy approach to the joint layout, pipe size and reliability optimization of water distribution systems is presented. The capital cost of the system is taken as the principal criterion, and so the trade-offs between cost, entropy, reliability and redundancy are examined sequentially in a large population of optimal solutions. The novelty of the method stems from the use of the maximum-entropy value as a preliminary filter, which screens out a large proportion of the candidate layouts at an early stage of the process before the designs and their reliability values are actually obtained. This technique, which is based on the notion that the entropy is potentially a robust hydraulic reliability measure, contributes greatly to the efficiency of the proposed method. The use of head-dependent modelling for simulating pipe failure conditions in the reliability calculations also complements the method in locating the Pareto-optimal front. The computational efficiency, robustness, accuracy and other advantages of the proposed method are demonstrated by application to a sample network.     

Efficient surrogate models for reliability analysis of systems with multiple failure modes

Despite many advances in the field of computational reliability analysis, the efficient estimation of the reliability of a system with multiple failure modes remains a persistent challenge. Various sampling and analytical methods are available, but they typically require accepting a tradeoff between accuracy and computational efficiency. In this work, a surrogate-based approach is presented that simultaneously addresses the issues of accuracy, efficiency, and unimportant failure modes. The method is based on the creation of Gaussian process surrogate models that are required to be locally accurate only in the regions of the component limit states that contribute to system failure. This approach to constructing surrogate models is demonstrated to be both an efficient and accurate method for system-level reliability analysis.     

Bayesian updating of reliability of civil infrastructure facilities based on condition-state data and fault-tree model

This paper considers a difficult but practical circumstance of civil infrastructure management—deterioration/failure data of the infrastructure system are absent while only condition-state data of its components are available. The goal is to develop a framework for estimating time-varying reliabilities of civil infrastructure facilities under such a circumstance. A novel method of analyzing time-varying condition-state data that only reports operational/non-operational status of the components is proposed to update the reliabilities of civil infrastructure facilities. The proposed method assumes that the degradation arrivals can be modeled as a Poisson process with unknown time-varying arrival rate and damage impact and that the target system can be represented as a fault-tree model. To accommodate large uncertainties, a Bayesian algorithm is proposed, and the reliability of the infrastructure system can be quickly updated based on the condition-state data. Use of the new method is demonstrated with a real-world example of hydraulic spillway gate system.     

The Bayes linear approach to inference and decision-making for a reliability programme

In reliability modelling it is conventional to build sophisticated models of the probabilistic behaviour of the component lifetimes in a system in order to deduce information about the probabilistic behaviour of the system lifetime. Decision modelling of the reliability programme requires a priori, therefore, an even more sophisticated set of models in order to capture the evidence the decision maker believes may be obtained from different types of data acquisition.Bayes linear analysis is a methodology that uses expectation rather than probability as the fundamental expression of uncertainty. By working only with expected values, a simpler level of modelling is needed as compared to full probability models.In this paper we shall consider the Bayes linear approach to the estimation of a mean time to failure MTTF of a component. The model built will take account of the variance in our estimate of the MTTF, based on a variety of sources of information.     

The set-theory method for systems reliability of structures with degrading components

The times and frequencies of inspection, maintenance and replacement in structural systems are complicated by uncertain degradation rates of structural characteristics. Although degradation work at the component, or single failure mode level, is ongoing, this paper presents a method for assessing systems reliability where failure events may be described by time-variant parallel and/or series systems. Herein the models for the degradation rates contain random variables and time. For multiple failure modes and a sequence of discrete times, set theory establishes the true incremental failure region that emerges from a safe region. Probabilities via Monte-Carlo simulation require only time-invariant calculations. The cumulative failure distribution is the summation of the incremental failure probabilities. A practical implementation of the theory requires only two contiguous times. Error analysis suggests ways to predict and minimize errors so the method appears sufficiently accurate for engineering applications. Two structures with elastic-brittle material and time-invariant loads show the details of the method and the potential of the approach. It is shown that the proposed method provides a more realistic and efficient way to predict systems reliability than path-tracing methods that are available in the open literature.     

A multi-mode failure boundary exploration and exploitation framework using adaptive kriging model for system reliability assessment

Various adaptive reliability analysis methods based on surrogate models have recently been developed. A multi-mode failure boundary exploration and exploitation framework (MFBEEF) was proposed for system reliability assessment using the adaptive kriging model based on sample space partitioning to reduce computational cost and use the characteristics of the failure boundary in multiple failure mode systems. The efficiency of the adaptive construction of kriging model can be improved by using the characteristics of the center sample of the small space to represent the characteristics of all samples in the small space. This method proposes a failure boundary exploration and exploitation strategy and a convergence criterion based on the maximum failure probability error for a system with multiple failure modes to adaptively approximate the failure boundary of a system with multiple failure modes. A multiple-failure-mode learning function was used to identify the optimal training sample to gradually update the kriging model during the failure boundary exploration and exploitation stages. In addition, a complex failure boundary-oriented adaptive hybrid importance sampling method was developed to improve the applicability of the MFBEEF method to small failure probability assessments. Finally, the MFBEEF method was proven to be effective using five system reliability analysis examples: a series system, a parallel system, a series–parallel hybrid system, a multi-dimensional series system with multiple failure modes, and an engineering problem with multiple implicit performance functions.     

Component lifetime modelling

There are two approaches to component lifetime modelling. The first one uses a reliability prediction method as described in the (military) handbooks with the appropriate models and parameters. The advantages are:

• (a) It takes into account all possible failure mechanisms.
• (b) It is easy to use.

The disadvantages are:

• (a) It assumes a constant failure rate which is often not the case (infant mortality).
• (b) It contains no designable parameters and therefore it cannot be used for built-in reliability.

The second approach is to model the different degradation mechanisms and to incorporate this into an (existing) circuit simulator. Here we have also advantages and disadvantages which are mostly complementary to those of the first method.     

Reliability based design optimization using response surfaces in application to multidisciplinary systems

Traditionally, reliability based design optimization (RBDO) is formulated as a nested optimization problem. For these problems the objective is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure corresponding to each of the failure modes or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large scale multidisciplinary systems which are likewise computationally intensive. In this research, a framework for performing reliability based multidisciplinary design optimization using approximations is developed. Response surface approximations (RSA) of the limit state functions are used to estimate the probability of failure. An outer loop is incorporated to ensure that the approximate RBDO converges to the actual most probable point of failure. The framework is compared with the exact RBDO procedure. In the proposed methodology, RSAs are employed to significantly reduce the computational expense associated with traditional RBDO. The proposed approach is implemented in application to multidisciplinary test problems, and the computational savings and benefits are discussed.     

A Bayesian framework for accelerated reliability growth testing with multiple sources of uncertainty

Reliability growth tests are often used for achieving a target reliability for complex systems via multiple test‐fix stages with limited testing resources. Such tests can be sped up via accelerated life testing (ALT) where test units are exposed to harsher‐than‐normal conditions. In this paper, a Bayesian framework is proposed to analyze ALT data in reliability growth. In particular, a complex system with components that have multiple competing failure modes is considered, and the time to failure of each failure mode is assumed to follow a Weibull distribution. We also assume that the accelerated condition has a fixed time scaling effect on each of the failure modes. In addition, a corrective action with fixed ineffectiveness can be performed at the end of each stage to reduce the occurrence of each failure mode. Under the Bayesian framework, a general model is developed to handle uncertainty on all model parameters, and several special cases with some parameters being known are also studied. A simulation study is conducted to assess the performance of the proposed models in estimating the final reliability of the system and to study the effects of unbiased and biased prior knowledge on the system‐level reliability estimates.     

A study of software reliability growth from the perspective of learning effects

For the last three decades, reliability growth has been studied to predict software reliability in the testing/debugging phase. Most of the models developed were based on the non-homogeneous Poisson process (NHPP), and S-shaped type or exponential-shaped type of behavior is usually assumed. Unfortunately, such models may be suitable only for particular software failure data, thus narrowing the scope of applications. Therefore, from the perspective of learning effects that can influence the process of software reliability growth, we considered that efficiency in testing/debugging concerned not only the ability of the testing staff but also the learning effect that comes from inspecting the testing/debugging codes. The proposed approach can reasonably describe the S-shaped and exponential-shaped types of behaviors simultaneously, and the results in the experiment show good fit. A comparative analysis to evaluate the effectiveness for the proposed model and other software failure models was also performed. Finally, an optimal software release policy is suggested.