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.     

Reliability assessment for systems suffering common cause failure based on Bayesian networks and proportional hazards model

The Bayesian network (BN) is an efficient tool for probabilistic modeling and causal inference, and it has gained considerable attentions in the field of reliability assessment. The common cause failure (CCF) is simultaneous failure of multiple elements in a system under a common cause, and it is a common phenomenon in engineering systems with dependent elements. Several models and methods have been proposed for modeling and assessment of complex systems with CCF. In this paper, a new reliability assessment method is proposed for the systems suffering from CCF in a dynamic environment. The CCF among components is characterized by a BN, which allows for bidirectional reasoning. A proportional hazards model is applied to capture the dynamic working environment of components and then the reliability function of the system is obtained. The proposed method is validated through an illustrative example, and some comparative studies are also presented.     

A generic method for estimating system reliability using Bayesian networks

This study presents a holistic method for constructing a Bayesian network (BN) model for estimating system reliability. BN is a probabilistic approach that is used to model and predict the behavior of a system based on observed stochastic events. The BN model is a directed acyclic graph (DAG) where the nodes represent system components and arcs represent relationships among them. Although recent studies on using BN for estimating system reliability have been proposed, they are based on the assumption that a pre-built BN has been designed to represent the system. In these studies, the task of building the BN is typically left to a group of specialists who are BN and domain experts. The BN experts should learn about the domain before building the BN, which is generally very time consuming and may lead to incorrect deductions. As there are no existing studies to eliminate the need for a human expert in the process of system reliability estimation, this paper introduces a method that uses historical data about the system to be modeled as a BN and provides efficient techniques for automated construction of the BN model, and hence estimation of the system reliability. In this respect K2, a data mining algorithm, is used for finding associations between system components, and thus building the BN model. This algorithm uses a heuristic to provide efficient and accurate results while searching for associations. Moreover, no human intervention is necessary during the process of BN construction and reliability estimation. The paper provides a step-by-step illustration of the method and evaluation of the approach with literature case examples.     

Reliability assessment for failure-dependent and uncertain systems: A Bayesian network based on copula method and probability-box

Managing failure dependence of complex systems with hybrid uncertainty is one of the hot problems in reliability assessment. Epistemic uncertainty is attributed to complex working environment, system structure, human factors, imperfect knowledge, etc. Probability-box has powerful characteristics for uncertainty analysis and can be effectively adopted to represent epistemic uncertainty. However, arithmetic rules on probability-box structures are mostly used among structures representing independent random variables. In most practical engineering applications, failure dependence is always introduced in system reliability analysis. Therefore, this paper proposes a developed Bayesian network combining copula method with probability-box for system reliability assessment. There are four main steps involved in the reliability computation process: marginal distribution identification and estimation, copula function selection and parameter estimation, reliability analysis of components with correlations and Bayesian forward analysis. The benefits derived from the proposed approach are used to overcome the computational limitations of n-dimensional integral operation, and the advantages of useful properties of copula function in reliability analysis of systems with correlations are adopted. To demonstrate the effectiveness of the developed Bayesian network, the proposed method is applied to a real large piston compressor.     

Integrated predictive maintenance strategy for manufacturing systems by combining quality control and mission reliability analysis

Predictive maintenance (PdM) is an effective means to eliminate potential failures, ensure stable equipment operation and improve the mission reliability of manufacturing systems and the quality of products, which is the premise of intelligent manufacturing. Therefore, an integrated PdM strategy considering product quality level and mission reliability state is proposed regarding the intelligent manufacturing philosophy of ‘prediction and manufacturing’. First, the key process variables are identified and integrated into the evaluation of the equipment degradation state. Second, the quality deviation index is defined to describe the quality of the product quantitatively according to the co-effect of manufacturing system component reliability and product quality in the quality–reliability chain. Third, to achieve changeable production task demands, mission reliability is defined to characterise the equipment production states comprehensively. The optimal integrated PdM strategy, which combines quality control and mission reliability analysis, is obtained by minimising the total cost. Finally, a case study on decision-making with the integrated PdM strategy for a cylinder head manufacturing system is presented to validate the effectiveness of the proposed method. The final results shows that proposed method achieves approximately 26.02 and 20.54% cost improvement over periodic preventive maintenance and conventional condition-based maintenance respectively.     

Improving the analysis of dependable systems by mapping fault trees into Bayesian networks

Bayesian Networks (BN) provide a robust probabilistic method of reasoning under uncertainty. They have been successfully applied in a variety of real-world tasks but they have received little attention in the area of dependability. The present paper is aimed at exploring the capabilities of the BN formalism in the analysis of dependable systems. To this end, the paper compares BN with one of the most popular techniques for dependability analysis of large, safety critical systems, namely Fault Trees (FT). The paper shows that any FT can be directly mapped into a BN and that basic inference techniques on the latter may be used to obtain classical parameters computed from the former (i.e. reliability of the Top Event or of any sub-system, criticality of components, etc). Moreover, by using BN, some additional power can be obtained, both at the modeling and at the analysis level. At the modeling level, several restrictive assumptions implicit in the FT methodology can be removed and various kinds of dependencies among components can be accommodated. At the analysis level, a general diagnostic analysis can be performed. The comparison of the two methodologies is carried out by means of a running example, taken from the literature, that consists of a redundant multiprocessor system.     

An algorithm of discrete-time Bayesian network for reliability analysis of multilevel system with warm spare gate

Discrete-time Bayesian network (DTBN) is a popular tool for the reliability analysis of dynamic systems, which, however, is insufficient in analyzing the reliability of multilevel system (MLS) with warm spare (WSP) gates. Additionally, conventional DTBNs are not able to consider the situation that dormant components and primary components may fail during the same time interval. To this end, this paper analyzes the dynamic reliability characteristics of dormant systems with WSP gates by utilizing DTBNs. Moreover, an algorithm of modeling the conditional probability table (CPT) for WSP gates together with a new schedule of constructing dynamic Bayesian networks is put forward. The validation of the proposed techniques is implemented by Monte Carlo simulation (MCS) and reliability analysis of an actual communication station system.     

Bayesian network approach to change propagation analysis

The prediction of change propagation is one of the important issues in engineering change management. The aim of this article is to explore the capability of Bayesian network (BN), which is an emerging tool for a wide range of risk management, in modeling and analysis of change propagation. To this end, we compare the BN with change prediction method (CPM), which is the most established probabilistic methods for predicting change propagation. This paper shows that a CPM-based model can be converted into an equivalent BN, and the probabilistic inference technique on the latter results in the same change prediction result obtained from the former. Then, this paper shows that several improvements can be obtained at various levels using the BN. At the modeling level, complex relationship between components such as combined effect of simultaneous changes or multistate relationship can be naturally represented with the BN. At the analysis level, various change propagation scenarios can be analyzed using probabilistic inference on the BN. Finally, BN provides a robust framework for learning change propagation probabilities from empirical data. The case study is conducted to show the feasibility of the model.     

Developing a factory-wide intelligent predictive maintenance system based on Industry 4.0

Abstract

The main purpose of predictive maintenance (PdM) is to reduce unscheduled downtime and consequently improve productivity and reduce production cost. PdM has been featured as a key theme of Industry 4.0. However, the traditional PdM system was only designed for a single tool; as such, the resources allocation will become extremely complicated when hundreds of tools are working together in a factory. A manageable hierarchy and various health indexes are required for factory-wide equipment maintenance. To solve the problem mentioned above, this paper proposes a factory-wide intelligent predictive maintenance system by applying the so-called cyber-physical agent and advanced manufacturing cloud of Things to fulfill the requirements of Industry 4.0, the baseline predictive maintenance scheme to accomplish the PdM functions, and the newly proposed health index hierarchy to supervise factory-wide equipment maintenance.     

源于工业生产事故溯因的复杂人机系统可靠性分析流程研究

目的 探索和研究复杂人机系统可靠性的分析流程.方法 首先从特征的角度建立简单人机系统结构模型.在此基础上结合社会技术系统理论建立复杂人机系统结构模型,接着结合轨迹交叉理论和功能共振思想进一步构建S-F网络图.在具体分析一起实际发生过的生产安全事故的过程中,融合S-F网络图、功能共振分析方法和贝叶斯网络理论进行改进,最后...     

A framework to practical predictive maintenance modeling for multi-state systems

A simple practical framework for predictive maintenance (PdM)-based scheduling of multi-state systems (MSS) is developed. The maintenance schedules are derived from a system-perspective using the failure times of the overall system as estimated from its performance degradation trends.

The system analyzed in this work is a flow transmission water pipe system. The various factors influencing PdM-based scheduling are identified and their impact on the system reliability and performance are quantitatively studied. The estimated times to replacement of the MSS may also be derived from the developed model.

The results of the model simulation demonstrate the significant impact of maintenance quality and the criteria for the call for maintenance (user demand) on the system reliability and mean performance characteristics. A slight improvement in maintenance quality is found to postpone the system replacement time by manifold. The consistency in the quality of maintenance work with minimal variance is also identified as a very important factor that enhances the system's future operational and downtime event predictability.

The studies also reveal that in order to reduce the frequency of maintenance actions, it is necessary to lower the minimum user demand from the system if possible, ensuring at the same time that the system still performs its intended function effectively.

The model proposed can be utilized to implement a PdM program in the industry with a few modifications to suit the individual industrial systems’ needs.     

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.     

Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis

This paper deals with the use of Bayesian networks to compute system reliability. The reliability analysis problem is described and the usual methods for quantitative reliability analysis are presented within a case study. Some drawbacks that justify the use of Bayesian networks are identified. The basic concepts of the Bayesian networks application to reliability analysis are introduced and a model to compute the reliability for the case study is presented. Dempster Shafer theory to treat epistemic uncertainty in reliability analysis is then discussed and its basic concepts that can be applied thanks to the Bayesian network inference algorithm are introduced. Finally, it is shown, with a numerical example, how Bayesian networks’ inference algorithms compute complex system reliability and what the Dempster Shafer theory can provide to reliability analysis.     

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.     

Analysis of correlated multivariate degradation data in accelerated reliability growth

Modern engineering systems have become increasingly complex and at the same time are expected to be developed faster. To shorten the product development time, organizations commonly conduct accelerated testing on a small number of units to help identify failure modes and assess reliability. Many times design changes are made to mitigate or reduce the likelihood of such failure modes. Since failure-time data are often scarce in reliability growth programs, existing statistical approaches used for predicting the reliability of a system about to enter the field are faced with significant challenges. In this work, a statistical model is proposed to utilize degradation data for system reliability prediction in an accelerated reliability growth program. The model allows the components in the system to have multiple failure modes, each associated with a monotone stochastic degradation process. To take into account unit-to-unit variation, the random effects of degradation parameters are explicitly modeled. Moreover, a mean-degradation-stress relationship is introduced to quantify the effects of different accelerating variables on the degradation processes, and a copula function is utilized to model the dependency among different degradation processes. Both a maximum likelihood (ML) procedure and a Bayesian alternative are developed for parameter estimation in a two-stage process. A numerical study illustrates the use of the proposed model and identifies the cases where the Bayesian method is preferred and where it is better to use the ML alternative.     

Methodology for the optimal component selection of electronic devices under reliability and cost constraints

The objective of this paper is to present an efficient computational methodology for the reliability optimization of electronic devices under cost constraints. The system modeling for calculating the reliability indices of the electronic devices is based on Bayesian networks using the fault tree approach, in order to overcome the limitations of the series–parallel topology of the reliability block diagrams. Furthermore, the Bayesian network modeling for the reliability analysis provides greater flexibility for representing multiple failure modes and dependent failure events, and simplifies fault diagnosis and reliability allocation. The optimal selection of components is obtained using the simulated annealing algorithm, which has proved to be highly efficient in complex optimization problems where gradient‐based methods can not be applied. The reliability modeling and optimization methodology was implemented into a computer program in Matlab using a Bayesian network toolbox. The methodology was applied for the optimal selection of components for an electrical switch of power installations under reliability and cost constraints. The full enumeration of the solution space was calculated in order to demonstrate the efficiency of the proposed optimization algorithm. The results obtained are excellent since a near optimum solution was found in a small fraction of the time needed for the complete enumeration (3%). All the optimum solutions found during consecutive runs of the optimization algorithm lay in the top 0.3% of the solutions that satisfy the reliability and cost constraints. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of operational system structures based on reliability data

Systems of components have a structure that plays an important role in determining how the reliability of the individual components relates to the reliability of the system. The system reliability can be computed from component reliabilities using results from basic probability theory in the simplest case with all of the components assumed to act independently of one another. However, in the case of dependence, such calculations can be much more involved. When reliability data have been independently collected on both the system and each component in the system, it can be difficult to model any possible dependence between components. Established methods use the known structure of a system, along with these data, to assess whether the reliability of the individual components are mutually independent. In this paper, we expand this methodology to include an assessment of the type of dependence that may exist between the components. This is based on finding the system structure that would most likely produce the observed reliability data, under independence. In the frequentist setting, the likelihood approach is used to find these structures and an observed confidence measure is used to assess the strength of the statistical evidence in favor of each possible structure. In the Bayesian setting, posterior probabilities along with Bayes factors are used. An example demonstrates how these methods can be used in an applied setting.     

Optimal structure of fault-tolerant software systems

This paper considers software systems consisting of fault-tolerant components. These components are built from functionally equivalent but independently developed versions characterized by different reliability and execution time. Because of hardware resource constraints, the number of versions that can run simultaneously is limited. The expected system execution time and its reliability (defined as probability of obtaining the correct output within a specified time) strictly depend on parameters of software versions and sequence of their execution. The system structure optimization problem is formulated in which one has to choose software versions for each component and find the sequence of their execution in order to achieve the greatest system reliability subject to cost constraints. The versions are to be chosen from a list of available products. Each version is characterized by its reliability, execution time and cost.The suggested optimization procedure is based on an algorithm for determining system execution time distribution that uses the moment generating function approach and on the genetic algorithm. Both N-version programming and the recovery block scheme are considered within a universal model. Illustrated example is presented.     

Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

Most maintenance optimization models of gear systems have considered single failure mode. There have been very few papers dealing with multiple failure modes, considering mostly independent failure modes. In this paper, we present an optimal Bayesian control scheme for early fault detection of the gear system with dependent competing risks. The system failures include degradation failure and catastrophic failure. A three‐state continuous‐time–homogeneous hidden Markov model (HMM), namely the model with unobservable healthy and unhealthy states, and an observable failure state, describes the deterioration process of the gear system. The condition monitoring information as well as the age of the system are considered in the proposed optimal Bayesian maintenance policy. The objective is to maximize the long‐run expected average system availability per unit time. The maintenance optimization model is formulated and solved in a semi‐Markov decision process (SMDP) framework. The posterior probability that the system is in the warning state is used for the residual life estimation and Bayesian control chart development. The prediction results show that the mean residual lives obtained in this paper are much closer to the actual values than previously published results. A comparison with the Bayesian control chart based on the previously published HMM and the age‐based replacement policy is given to illustrate the superiority of the proposed approach. The results demonstrate that the Bayesian control scheme with two dependent failure modes can detect the gear fault earlier and improve the availability of the system.