Modelling dependable systems using hybrid Bayesian networks

A hybrid Bayesian network (BN) is one that incorporates both discrete and continuous nodes. In our extensive applications of BNs for system dependability assessment, the models are invariably hybrid and the need for efficient and accurate computation is paramount. We apply a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction tree structures to perform inference in hybrid BNs. We illustrate its use in the field of dependability with two example of reliability estimation. Firstly we estimate the reliability of a simple single system and next we implement a hierarchical Bayesian model. In the hierarchical model we compute the reliability of two unknown subsystems from data collected on historically similar subsystems and then input the result into a reliability block model to compute system level reliability. We conclude that dynamic discretisation can be used as an alternative to analytical or Monte Carlo methods with high precision and can be applied to a wide range of dependability problems.     

Fuzzy belief propagation in constrained Bayesian networks with application to maintenance decisions

Bayesian networks have been widely applied to domains such as medical diagnosis, fault analysis, and preventative maintenance. In some applications, because of insufficient data and the complexity of the system, fuzzy parameters and additional constraints derived from expert knowledge can be used to enhance the Bayesian reasoning process. However, very few methods are capable of handling the belief propagation in constrained fuzzy Bayesian networks (CFBNs). This paper therefore develops an improved approach which addresses the inference problem through a max-min programming model. The proposed approach yields more reasonable inference results and with less computational effort. By integrating the probabilistic inference drawn from diverse sources of information with decision analysis considering a decision-maker's risk preference, a CFBN-based decision framework is presented for seeking optimal maintenance decisions in a risk-based environment. The effectiveness of the proposed framework is validated based on an application to a gas compressor maintenance decision problem.     

Decision support in early development phases—A case study from machine engineering

In the case study presented in this paper we consider early development phases of a mechanical product. We want to evaluate different concepts and decide which one(s) to pursue. A problem in early phases is that usually no test runs are available. In our case study, based on a standard, there are ways to compute the lifetime distributions of the components of the different concepts. Some parameters needed for these computations are not known precisely. Unfortunately, the lifetime distributions of the components are highly sensitive to these parameters. Our approach is to equip these parameters with distributions. These distributions would be called prior distributions in Bayesian terminology, but no update is possible since no test runs are available. Our approach implies that the distribution of the system lifetime for each concept is random, i.e. we get random elements in the space of lifetime distributions. Using Monte-Carlo simulations, we demonstrate several ways to compare the random lifetime distributions of the concepts. Some of these comparisons use stochastic orderings. We also introduce a new stochastic ordering which is particularly suitable for reliability purposes. Our case study, consisting of three scenarios, allows us to demonstrate some conclusions that can be reached.     

Radyban: A tool for reliability analysis of dynamic fault trees through conversion into dynamic Bayesian networks

In this paper, we present Radyban (Reliability Analysis with DYnamic BAyesian Networks), a software tool which allows to analyze a dynamic fault tree relying on its conversion into a dynamic Bayesian network. The tool implements a modular algorithm for automatically translating a dynamic fault tree into the corresponding dynamic Bayesian network and exploits classical algorithms for the inference on dynamic Bayesian networks, in order to compute reliability measures. After having described the basic features of the tool, we show how it operates on a real world example and we compare the unreliability results it generates with those returned by other methodologies, in order to verify the correctness and the consistency of the results obtained.     

The Diagnosis of Reciprocating Machinery by Bayesian Networks

A Bayesian Network is a reasoning tool based on probability theory and has many advantages that other reasoning tools do not have,This paper discusses the basic theory of Bayesian networks and studies the problems in constructing Bayesian networks.The paper also consturcts a Bayesian diagnosis network of a reciprocating compressor.The example helps us to draw a conclusion that Bayesian diagnosis networks can diagnose reciprocating machinery effectively.     

Inference in hybrid Bayesian networks

Since the 1980s, Bayesian networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability techniques (like fault trees and reliability block diagrams). However, limitations in the BNs’ calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (the so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability.     

Reliability and validity of risk analysis

In this paper we investigate to what extent risk analysis meets the scientific quality requirements of reliability and validity. We distinguish between two types of approaches within risk analysis, relative frequency-based approaches and Bayesian approaches. The former category includes both traditional statistical inference methods and the so-called probability of frequency approach. Depending on the risk analysis approach, the aim of the analysis is different, the results are presented in different ways and consequently the meaning of the concepts reliability and validity are not the same.     

Failure mode and effect analysis using multi-linguistic terms and Dempster–Shafer evidence theory

Failure mode and effect analysis (FMEA) is a useful technique to identify and quantify potential failures. FMEA determines a potential failure mode by evaluating risk factors. In recent years, there are many works improving FMEA by allowing multiple experts to use linguistic term sets to evaluate risk factors. However, it is important to design a framework that can consider both the weight of risk factors and the weight of the experts. In addition, managing conflicts among experts is also an urgent problem to be addressed. In this paper, we proposed an FMEA model based on multi-granularity linguistic terms and the Dempster–Shafer evidence theory. On the other hand, the weights for both experts and risk factors are taken into consideration. The weights are computed objectively and subjectively to ensure the reasonability. Further, we apply our method to an emergency department case, which shows the effectiveness of the method.     

An imprecise Dirichlet model for Bayesian analysis of failure data including right-censored observations

This paper is intended to make researchers in reliability theory aware of a recently introduced Bayesian model with imprecise prior distributions for statistical inference on failure data, that can also be considered as a robust Bayesian model. The model consists of a multinomial distribution with Dirichlet priors, making the approach basically nonparametric. New results for the model are presented, related to right-censored observations, where estimation based on this model is closely related to the product-limit estimator, which is an important statistical method to deal with reliability or survival data including right-censored observations. As for the product-limit estimator, the model considered in this paper aims at not using any information other than that provided by observed data, but our model fits into the robust Bayesian context which has the advantage that all inferences can be based on probabilities or expectations, or bounds for probabilities or expectations. The model uses a finite partition of the time-axis, and as such it is also related to life-tables.     

基于动态贝叶斯网络与DS证据理论的轧机颤振监测方法

提出了基于动态贝叶斯网络和DS(Dempster/Shafer)证据理论的轧机颤振实时监测方法,该方法预选多个时域和频域的特征参数表征轧机不同工况下振动信号的不同特征,利用稳定判别率方法筛选敏感度高的特征参数;使用动态贝叶斯网络与DS证据理论实时监测模型建立轧机颤振状态实时监测系统,构建连续的速度载荷时间片,将3个连续的速度载荷时间片作为DS证据理论的证据体,给出了优化基本概率分配的信任度方法,解决了DS证据理论的证据体间冲突问题;最后在轧机实验平台进行实验,诊断结果表明：该方法对轧机颤振不同状态的识别率达到99.05%。     

Sensibility of Bayesian inference methods for reliability prediction of ageing systems,case of Diesel locomotives

This paper addresses the problem of reliability analysis of in-service identical systems when a limited number of lifetime data is available compared to censored ones. Lifetime (resp. censored) data characterise the life of failed (resp. non-failed) systems in the sample. Because, censored data induce biassed estimators of reliability model parameters, a methodology approach is proposed to overcome this inconvenience and improve the accuracy of the parameter estimation based on Bayesian inference methods. These methods combine, in an effective way, system’s life data and expert opinions learned from failure diagnosis of similar systems. Three Bayesian inference methods are considered: Classical Bayesian, Extended Bayesian and Bayesian Restoration Maximisation methods. Given a sample of lifetime data, simulated according to prior opinions of maintenance expert, a sensibility analysis of each Bayesian method is performed. Reliability analysis of critical subsystems of Diesel locomotives is established under the proposed methodology approach. The relevance of each Bayesian inference methods with respect to collected reliability data of critical subsystems and expert opinions is discussed.     

Footprint of knowledge acquisition improvement in failure diagnosis analysis

Fault tree analysis (FTA) as an effective and efficient risk assessment tool are widely used to analyze the reliability of a complex system. In this context, FTA can properly improve the safety performance of the system by preventing an event which may lead to occurrence of a catastrophic accident. However, traditional FTA is still suffering from dynamic structure demonstration and importantly epistemic uncertainty processing. In this study, a novel methodology is introduced using Bayesian updating mechanism to deal with dynamic structure and 2‐tuple fuzzy set named as intuitionistic fuzzy numbers are employed to cope with subjectivity of uncertainty processing. Accordingly, the most critical system components which affect the system reliability are recognized by using an appropriate sensitivity analysis method. The proposed methodology is then applied on a real case study application (a brake fluid filling system) in order to examine the effectiveness and feasibility of the approach. The results illustrated that the new methodology can have enough benefits for diagnosing the systems' faults compared with listing approaches of safety and reliability analysis. In terms of empirical case study, “electromotor failure” was evaluated as the second most critical basic event in conventional‐based approaches, whereas in the novel methodology “high pressure liquefied material” was recognized as the second one.     

Bayesian networks for multilevel system reliability

Bayesian networks have recently found many applications in systems reliability; however, the focus has been on binary outcomes. In this paper we extend their use to multilevel discrete data and discuss how to make joint inference about all of the nodes in the network. These methods are applicable when system structures are too complex to be represented by fault trees. The methods are illustrated through four examples that are structured to clarify the scope of the problem.     

多重模糊假设检验的贝叶斯方法

应用统计推断和统计决策问题中,常常需要处理模糊概念,模糊假设检验是其中非常重要的一种情形。本文将模糊性引入到多重假设中,从贝叶斯决策的角度,分样本为清晰数据和模糊信息两种情形,研究了多重模糊假设的贝叶斯方法,并给出了数值例。     

Imperfect Preventive Maintenance Policy for Complex Systems Based on Bayesian Networks

The main challenge in maintenance planning lies in the realistic modeling of the maintenance policy. This paper is focused on the maintenance optimization of complex repairable systems using Bayesian networks. A new policy is developed for periodic imperfect preventive maintenance policy with minimal repair at failure; this policy allows us to take into consideration several types of preventive maintenance with different efficiency levels. The Bayesian networks are used for complex system modeling, allowing the evaluation of the model parameters. The Weibull parameters and the maintenance efficiency are evaluated thanks to the proposed methodology using Bayesian inference. The approach developed in this paper is applied on a real system, to determine the optimal maintenance plan for a turbo‐pump in oil industry. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian estimation of location parameters in life distributions

For some distributions commonly used in reliability analysis the likelihood function has a singularity at the smallest observation. The use of grouped likelihood in Bayesian inference is discussed. It is shown that the product of spacings can be used in place of the likelihood. Similarities with and differences from a standard Bayesian approach are illustrated by means of examples. In particular some computational advantages are pointed out.     

An improved failure mode and effects analysis method based on uncertainty measure in the evidence theory

mode and effects analysis (FMEA) is an effective tool to assess the risk of a system or process under uncertain environment. However, how to handle the uncertainty in the subjective assessment is an open issue. In this paper, a novel method to deal with the uncertainty coming from subjective assessments of FMEA experts is proposed in the framework of Dempster–Shafer evidence theory. First, the uncertain degree of the assessment is measured by the ambiguity measure. Then, the uncertainty is transformed to the reliability of each FMEA expert and the relative importance of each risk factor. After that, the assessments from FMEA team will be fused with a discounting-based combination rule to address the potential conflict. Moreover, to avoid the situation that different risk priorities of failure modes may have the same ranking based on classical risk priority number method, the gray relational projection method (GRPM) is adopted for ranking risk priorities of failure modes. Finally, an application of the improved FMEA model in sheet steel production process verifies the reliability and validity of the proposed method.     

基于贝叶斯网络的核电站应急电力系统安全评价

在故障树分析法(FTA)基础上提出了一种基于贝叶斯网络(BN)的核电站应急电力系统安全评价方法,比较了FTA和BN在建立安全评价模型和评价能力上的不同.该方法在应对众多影响因素上有很大优势,能进行更多有意义的分析:既能进行前向的预测推理,又能进行后向的诊断推理,可以找出影响故障的组合模式,从而能够找出系统的薄弱环节.同时采用基于Matlab的BNT软件包,大大简化了计算过程.通过对10MW高温气冷堆(HTR-10)应急电力系统的安全评价实例的分析,证明该方法是对传统的基于故障树分析的安全评价方法的有益改进.     

A discrete-time Bayesian network reliability modeling and analysis framework

Dependability tools are becoming an indispensable tool for modeling and analyzing (critical) systems. However the growing complexity of such systems calls for increasing sophistication of these tools. Dependability tools need to not only capture the complex dynamic behavior of the system components, but they must be also easy to use, intuitive, and computationally efficient. In general, current tools have a number of shortcomings including lack of modeling power, incapacity to efficiently handle general component failure distributions, and ineffectiveness in solving large models that exhibit complex dependencies between their components. We propose a novel reliability modeling and analysis framework based on the Bayesian network (BN) formalism. The overall approach is to investigate timed Bayesian networks and to find a suitable reliability framework for dynamic systems. We have applied our methodology to two example systems and preliminary results are promising. We have defined a discrete-time BN reliability formalism and demonstrated its capabilities from a modeling and analysis point of view. This research shows that a BN based reliability formalism is a powerful potential solution to modeling and analyzing various kinds of system components behaviors and interactions. Moreover, being based on the BN formalism, the framework is easy to use and intuitive for non-experts, and provides a basis for more advanced and useful analyses such as system diagnosis.     

一种可行的不确定性演绎推理模型

本文简述Ｄｅｍｐｓｔｅｒ／ｓｈａｆｅｒ的证据理论和Ｚａｄｅｈ的可能性和模糊集理论．指出这两种理论模型在实际应用中存在的不足之处，并就此提出一个统一的表示方法。最后．根据这个统一的表示方法．阐述一种简单可行的演绎推理模型。