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.     

A comparison of reliability estimation methods for binary systems

This paper uses a simulation-based approach to compare the predictive accuracy of five different methods for estimating the risk of failure for binary failure/no failure systems such as US strategic missiles, space launch vehicles, and security systems based on the results of a number of tests. This paper tests two Bayesian approaches, two classical (frequentist) approaches, and the method currently used the US Air Force Strategic Command (STRATCOM) to estimate the reliability of strategic nuclear missiles. First, test results are simulated based on an assumed underlying reliability profile. Then the system's reliability is estimated by each of the approaches using the simulated test results, and these estimates are compared with the assumed underlying reliability. Statistical procedures are used to compare the errors from the different methods. The results of this study show that the STRATCOM approach and a classical approach using only the test data from the current period are significantly less accurate than the other three methods and that the accuracy of the Bayesian methods depend on the prior density functions used. The results in this paper provide a quantitative assessment of the accuracy of the tested methods.     

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.     

A model for Bayesian software reliability analysis

Two problems which are of great interest in relation to software reliability are the prediction of future times to failure and the calculation of the optimal release time. An important assumption in software reliability analysis is that the reliability grows whenever bugs are found and removed. In this paper we present a model for software reliability analysis using the Bayesian statistical approach in order to incorporate in the analysis prior assumptions such as the (decreasing) ordering in the assumed constant failure rates of prescribed intervals. We use as prior model the product of gamma functions for each pair of subsequent interval constant failure rates, considering as the location parameter of the first interval the failure rate of the following interval. In this way we include the failure rate ordering information. Using this approach sequentially, we predict the time to failure for the next failure using the previous information obtained. Using also the relevant predictive distributions obtained, we calculate the optimal release time for two different requirements of interest: (a) the probability of an in‐service failure in a prescribed time t; (b) the cost associated with a single or more failures in a prescribed time t. Finally a numerical example is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Modelling the reliability of search and rescue operations with Bayesian Belief Networks

This paper uses a Bayesian Belief Networks (BBN) methodology to model the reliability of Search And Rescue (SAR) operations within UK Coastguard (Maritime Rescue) coordination centres. This is an extension of earlier work, which investigated the rationale of the government's decision to close a number of coordination centres. The previous study made use of secondary data sources and employed a binary logistic regression methodology to support the analysis. This study focused on the collection of primary data through a structured elicitation process, which resulted in the construction of a BBN. The main findings of the study are that statistical analysis of secondary data can be used to complement BBNs. The former provided a more objective assessment of associations between variables, but was restricted in the level of detail that could be explicitly expressed within the model due to a lack of available data. The latter method provided a much more detailed model, but the validity of the numeric assessments was more questionable. Each method can be used to inform and defend the development of the other. The paper describes in detail the elicitation process employed to construct the BBN and reflects on the potential for bias.     

Workload prediction for improved design and reliability of complex systems

This paper describes a method and a tool for analysing and predicting workload for the design and reliability of complex socio-technical systems. It concentrates on the need to assess workload early in the design phase to prevent systems failures. This is a continuation of our previous work on workload assessment. The method is supported by a tool that enables scenario-based validation of prospective socio-technical systems designs such as command and control rooms of military vessels. The approach combines probabilistic measures of human performance with subjective estimates of workload. The causal relationships of performance shaping factors (PSF) are modelled in a Bayesian belief network (BBN) and used to assess the agent's operational performance and reliability. Workload for each agent is calculated based on demand placed upon agents in terms of behavioural response to tasks, communications and interactions between humans and technology. The approach uses scenarios to stress test prospective system designs, where each scenario is modelled as a sequence of events. Reliability is expressed in terms of human error and is dynamically assessed throughout test scenario executions using BBN technology. The innovation beyond traditional reliability analysis relies to the use of dynamic and static estimates of reliability inputs for better informed assessment. This method enables identification of performance bottlenecks to be addressed by the designer early in the design phase. A case study is presented that demonstrates the use of the method and tool for the design of the command and control room of a military vessel.     

Safety analysis of safety-critical systems for their applicability on NPP systems: A state-of-the-art review

Since any risk in the safety-critical systems (SCSs) might lead to a terrible disaster, the utmost quality attribute of these systems is safety. Researchers are putting their efforts to ensure the safety of such systems. This paper summarizes the state-of-the-art in the area of the safety attribute of such critical systems. The in depth literature survey is performed to explore the several methods/models used for safety analysis of the SCS. The limitations of such methods are also shown regarding their applicability in SCS of the nuclear power plant (NPP). We also propose a framework to perform safety analysis, which can deal with these limitations and demonstrated the approach on a case study of NPP. Further, the direction for future work is advised to extend the further scope of research based on the case study.     

Multi-scale reliability analysis and updating of complex systems by use of linear programming

Complex systems are characterized by large numbers of components, cut sets or link sets, or by statistical dependence between the component states. These measures of complexity render the computation of system reliability a challenging task. In this paper, a decomposition approach is described, which, together with a linear programming formulation, allows determination of bounds on the reliability of complex systems with manageable computational effort. The approach also facilitates multi-scale modeling and analysis of a system, whereby varying degrees of detail can be considered in the decomposed system. The paper also describes a method for computing bounds on conditional probabilities by use of linear programming, which can be used to update the system reliability for any given event. Applications to a power network demonstrate the methodology.     

A study of service reliability and availability for distributed systems

Distributed systems are usually designed and developed to provide certain important services such as in computing and communication systems. In this paper, a general model is presented for a centralized heterogeneous distributed system, which is widely used in distributed system design. Based on this model, the distributed service reliability which is defined as the probability of successfully providing the service in a distributed environment, an important performance measure for this type of systems, is investigated. An application example is used to illustrate the procedure. Furthermore, with the help of the model, various issues such as the release time to achieve a service reliability requirement, and the sensitivity of model parameters are studied. This type of analysis is important in the application of this type of models.     

Application of the fault tree analysis for assessment of power system reliability

A new method for power system reliability analysis using the fault tree analysis approach is developed. The method is based on fault trees generated for each load point of the power system. The fault trees are related to disruption of energy delivery from generators to the specific load points. Quantitative evaluation of the fault trees, which represents a standpoint for assessment of reliability of power delivery, enables identification of the most important elements in the power system. The algorithm of the computer code, which facilitates the application of the method, has been applied to the IEEE test system. The power system reliability was assessed and the main contributors to power system reliability have been identified, both qualitatively and quantitatively.     

Bayesian reliability analysis of a products of probabilities model for parallel systems with dependent components

In a Bayesian reliability analysis of a system with dependent components, an aggregate analysis (i.e. system-level analysis) or a simplified disaggregate analysis with independence assumptions may be preferable if the estimations obtained from employing these two approaches do not deviate substantially from those derived through a disaggregate analysis, which is generally considered the most accurate method. This study was conducted to identify the key factors and their range of values that lead to estimation errors of great magnitude. In particular, a copula-based Bayesian reliability model was developed to formulate the dependence structure for a products of probabilities model of a simple parallel system. Monte Carlo simulation, regionalised sensitivity analysis and classification tree learning were employed to investigate the key factors. The resulting classification tree achieved favourable predictive accuracy. Several decision rules suggesting the optimal approach under different combinations of conditions were also extracted. This study has made a methodological contribution in laying the groundwork for investigating systems with dependent components using copula-based Bayesian reliability models. With regard to practical implications, this study also derived useful guidelines for selecting the most appropriate analysis approach under different scenarios with different magnitude of dependence.     

Citation-related reliability analysis for a pilot sample of underground coal mines

The scrutiny of underground coal mine safety was heightened because of the disasters that occurred in 2006–2007, and more recently in 2010. In the aftermath of the 2006 incidents, the U.S. Congress passed the Mine Improvement and New Emergency Response Act of 2006 (MINER Act), which strengthened the existing regulations and mandated new laws to address various issues related to emergency preparedness and response, escape from an emergency situation, and protection of miners. The National Mining Association-sponsored Mine Safety Technology and Training Commission study highlighted the role of risk management in identifying and controlling major hazards, which are elements that could come together and cause a mine disaster. In 2007 MSHA revised its approach to the “Pattern of Violations” (POV) process in order to target unsafe mines and then force them to remediate conditions in their mines. The POV approach has certain limitations that make it difficult for it to be enforced. One very understandable way to focus on removing threats from major-hazard conditions is to use citation-related reliability analysis. The citation reliability approach, which focuses on the probability of not getting a citation on a given inspector day, is considered an analogue to the maintenance reliability approach, which many mine operators understand and use. In this study, the citation reliability approach was applied to a stratified random sample of 31 underground coal mines to examine its potential for broader application. The results clearly show the best-performing and worst-performing mines for compliance with mine safety standards, and they highlight differences among different mine sizes.     

Collaborative optimization with inverse reliability for multidisciplinary systems uncertainty analysis

This article introduces a method which combines the collaborative optimization framework and the inverse reliability strategy to assess the uncertainty encountered in the multidisciplinary design process. This method conducts the sub-system analysis and optimization concurrently and then improves the process of searching for the most probable point (MPP). It reduces the load of the system-level optimizer significantly. This advantage is specifically more prominent for large-scale engineering system design. Meanwhile, because the disciplinary analyses are treated as the equality constraints in the disciplinary optimization, the computation load can be further reduced. Examples are used to illustrate the accuracy and efficiency of the proposed method.     

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.     

Human reliability analysis for manned submersible diving process based on CREAM and Bayesian network

The diving mission of manned submersibles is a long‐term, high‐intensity work that is affected by many factors and is in a narrow confined space. In order to improve the reliability of oceanauts' safe operations, this paper is based on the cognitive reliability and error analysis method (CREAM) and the Bayesian network method to study the human errors of the diving mission. First, we construct a Bayesian network framework of the diving process by analyzing the diving steps. Second, the CREAM is applied to calculate the prior probability of each root node's error. Then, the backward reasoning ability of the Bayesian network is used to calculate the posterior probabilities and identify the top few risk nodes. Finally, we obtained the top few risk factors. Among them, we find that the light distribution design in the risk nodes is the more influential risk factor, so a brief design is made on them.     

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.     

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.     

An algorithm for reliability analysis of phased-mission systems

The purpose of this paper is to describe an efficient Boolean algebraic algorithm that provides exact solution to the unreliability of a multi-phase mission system where the configurations are described through fault trees. The algorithm extends and improves the Boolean method originally proposed by Somani and Trivedi. By using the Boolean algebraic method, we provide an efficient modeling approach which avoids the state space explosion and the mapping problems that are encountered by the Markov chain approach. To calculate the exact solution of the phased-mission system with deterministic phase durations, we introduce the sum of disjoint phase products (SDPP) formula, which is a phased-extension of the sum of disjoint products (SDP) formula. Computationally, the algorithm is quite efficient because it calls an SDP generation algorithm in the early stage of the SDPP computation. In this way, the phase products generated in the early stage of the SDPP formula are guaranteed to be disjoint. Consequently, the number of the intermediate phase products is greatly reduced. In this paper, we also consider the transient analysis of the phased-mission system. Special care is needed to account for the possible latent failures at the mission phase change times. If there are more stringent success criteria just after a mission phase change time, an unreliability jump would occur at that time. Finally, the algorithm has been implemented in the software package . With , the complexities of the phased-mission system is made transparent to the potential users. The user can conveniently specify a phased-mission model at a high level (through fault trees) and analyze the system quantitatively.