Validation of reliability computational models using Bayes networks

This paper proposes a methodology based on Bayesian statistics to assess the validity of reliability computational models when full-scale testing is not possible. Sub-module validation results are used to derive a validation measure for the overall reliability estimate. Bayes networks are used for the propagation and updating of validation information from the sub-modules to the overall model prediction. The methodology includes uncertainty in the experimental measurement, and the posterior and prior distributions of the model output are used to compute a validation metric based on Bayesian hypothesis testing. Validation of a reliability prediction model for an engine blade under high-cycle fatigue is illustrated using the proposed methodology.     

Validation and error estimation of computational models

This paper develops a Bayesian methodology for assessing the confidence in model prediction by comparing the model output with experimental data when both are stochastic. The prior distribution of the response is first computed, which is then updated based on experimental observation using Bayesian analysis to compute a validation metric. A model error estimation methodology is then developed to include model form error, discretization error, stochastic analysis error (UQ error), input data error and output measurement error. Sensitivity of the validation metric to various error components and model parameters is discussed. A numerical example is presented to illustrate the proposed methodology.     

Bayesian belief network-based framework for sourcing risk analysis during supplier selection

Increasing trend in global business integration and movement of material around the world has caused supply chain system susceptible to disruption involving higher risks. This paper presents a methodology for supplier selection in a global sourcing environment by considering multiple cost and risk factors. Failure modes and effects analysis technique from reliability engineering field and Bayesian belief networks are used to quantify the risk posed by each factor. The probability and the cost of each risk are then incorporated into a decision tree model to compute the total expected costs for each supply option. The supplier selection decision is made based on the total purchasing costs including both deterministic costs (such as product and transportation costs) and the risk-associated costs. The proposed approach is demonstrated using an example of a US-based Chemical distributor. This framework provides a visual tool for supply chain managers to see how cost and risks are distributed across the different alternatives. Lastly, managers can calculate expected value of perfect information to avoid a certain risk.     

Assessing high reliability via Bayesian approach and accelerated tests

Sometimes the assessment of very high reliability levels is difficult for the following main reasons:

the high reliability level of each item makes it impossible to obtain, in a reasonably short time, a sufficient number of failures;

the high cost of the high reliability items to submit to life tests makes it unfeasible to collect enough data for ‘classical’ statistical analyses.

In the above context, this paper presents a Bayesian solution to the problem of estimation of the parameters of the Weibull–inverse power law model, on the basis of a limited number (say six) of life tests, carried out at different stress levels, all higher than the normal one.The over-stressed (i.e. accelerated) tests allow the use of experimental data obtained in a reasonably short time. The Bayesian approach enables one to reduce the required number of failures adding to the failure information the available a priori engineers' knowledge. This engineers' involvement conforms to the most advanced management policy that aims at involving everyone's commitment in order to obtain total quality.A Monte Carlo study of the non-asymptotic properties of the proposed estimators and a comparison with the properties of maximum likelihood estimators closes the work.     

Towards Bayesian network methodology for predicting the equipment health factor of complex semiconductor systems

This paper presents a general methodology to improve risk assessment in the specific workshops of semiconductor manufacturers. We are concerned, in this case, with the problem of equipment failures and drifts. These failures are generally observed, with delay, during the product metrology phase. To improve the reactivity of the control system, we propose a predictive approach based on the Bayesian technique. Increased use of these techniques is the result of the advantages obtained. This approach allows early action to maintain, for example, the equipment before it can drift. Also, our contribution consists in proposing a generic model to predict the equipment health factor (EHF), which will define decision support strategies on preventive maintenance to avoid unscheduled equipment downtime. Following the proposed methodology, a data extraction and processing prototype is also designed to identify the real failure modes which will instantiate the Bayesian model. EHF results are decision support elements. They can be further used to improve production performance: reduced cycle time, improved yield and enhanced equipment effectiveness.     

Bayesian structural equation modeling method for hierarchical model validation

A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.     

A novel Bayesian approach to reliability modeling: The benefits of uncertainty evaluation in the model selection procedure

This paper proposes a different likelihood formulation within the Bayesian paradigm for parameter estimation of reliability models. Moreover, the assessment of the uncertainties associated with parameters, the goodness of fit, and the model prediction of reliability are included in a systematic framework for better aiding the model selection procedure. Two case studies are appraised to highlight the contributions of the proposed method and demonstrate the differences between the proposed Bayesian formulation and an existing Bayesian formulation.     

Application of Bayesian network to the probabilistic risk assessment of nuclear waste disposal

The scenario in a risk analysis can be defined as the propagating feature of specific initiating event which can go to a wide range of undesirable consequences. If we take various scenarios into consideration, the risk analysis becomes more complex than do without them. A lot of risk analyses have been performed to actually estimate a risk profile under both uncertain future states of hazard sources and undesirable scenarios. Unfortunately, in case of considering specific systems such as a radioactive waste disposal facility, since the behaviour of future scenarios is hardly predicted without special reasoning process, we cannot estimate their risk only with a traditional risk analysis methodology. Moreover, we believe that the sources of uncertainty at future states can be reduced pertinently by setting up dependency relationships interrelating geological, hydrological, and ecological aspects of the site with all the scenarios. It is then required current methodology of uncertainty analysis of the waste disposal facility be revisited under this belief.In order to consider the effects predicting from an evolution of environmental conditions of waste disposal facilities, this paper proposes a quantitative assessment framework integrating the inference process of Bayesian network to the traditional probabilistic risk analysis. We developed and verified an approximate probabilistic inference program for the specific Bayesian network using a bounded-variance likelihood weighting algorithm. Ultimately, specific models, including a model for uncertainty propagation of relevant parameters were developed with a comparison of variable-specific effects due to the occurrence of diverse altered evolution scenarios (AESs). After providing supporting information to get a variety of quantitative expectations about the dependency relationship between domain variables and AESs, we could connect the results of probabilistic inference from the Bayesian network with the consequence evaluation model addressed. We got a number of practical results to improve current knowledge base for the prioritization of future risk-dominant variables in an actual site.     

Combining the cost of reducing uncertainty with the selection of risk assessment models for remediation decision of site contamination

The decision as to whether a contaminated site poses a threat to human health and should be cleaned up relies increasingly upon the use of risk assessment models. However, the more sophisticated risk assessment models become, the greater the concern with the uncertainty in, and thus the credibility of, risk assessment. In particular, when there are several equally plausible models, decision makers are confused by model uncertainty and perplexed as to which model should be chosen for making decisions objectively. When the correctness of different models is not easily judged after objective analysis has been conducted, the cost incurred during the processes of risk assessment has to be considered in order to make an efficient decision. In order to support an efficient and objective remediation decision, this study develops a methodology to cost the least required reduction of uncertainty and to use the cost measure in the selection of candidate models. The focus is on identifying the efforts involved in reducing the input uncertainty to the point at which the uncertainty would not hinder the decision in each equally plausible model. First, this methodology combines a nested Monte Carlo simulation, rank correlation coefficients, and explicit decision criteria to identify key uncertain inputs that would influence the decision in order to reduce input uncertainty. This methodology then calculates the cost of required reduction of input uncertainty in each model by convergence ratio, which measures the needed convergence level of each key input's spread. Finally, the most appropriate model can be selected based on the convergence ratio and cost. A case of a contaminated site is used to demonstrate the methodology.     

Probabilistic reliability assessment of a heritage structure under horizontal loads

This paper proposes a methodology for the probabilistic reliability assessment of heritage buildings. The procedure addresses investigation and tests on the structure and it considers the implementation of Bayesian updating techniques for a rational use of the collected information. After having described the peculiarities of ancient buildings, it is shown how probabilistic methods can be adapted to evaluate their safety. A practical application of the methodology to a relevant case study is presented, namely a historic aqueduct in Italy. The main goal is to demonstrate the effectiveness of a probabilistic approach to the reliability assessment of heritage structures.     

Determining the optimal maintenance action for a deteriorating repairable system

This paper develops a decision model for risk management of the deterioration of a repairable system. When a failure occurs in a deteriorating system, an optimal maintenance decision that includes the possibility of system replacement, as compared to mere deterioration reduction, should be made. There are many uncertainties associated with deterioration, however, so the decision may require a probabilistic analysis. Here, a well-known nonhomogeneous Poisson process with a power law intensity function is used to model the uncertain behavior of the deteriorating system. A Bayesian statistical approach is adopted to allow for the uncertainty of the parameters of the power law intensity function, which imposes a conjugate prior distribution of the parameters. A power law maintenance cost function and the failure cost are analyzed to determine the magnitude of failure risk reduction by minimizing the expected cost incurred from the maintenance action and future failures. A numerical example is given.     

Component reliability assessment using quantitative and qualitative data

The estimation of a component failure rate depends on the availability of plant specific numerical data. The purpose of this study was development of a new method that explicitly includes numerical and linguistic information into the assessment of a specific failure rate. The basis of the method is the Bayesian updating approach. A prior distribution is selected from a generic database, whereas likelihood is assessed using the principles of fuzzy set theory. The influence of component operating conditions on component failure rate is modeled using a fuzzy inference system. Results of fuzzy reasoning are then used for building an appropriate likelihood function for the Bayesian inference.The method was applied on a high voltage transformer. Results show that with the proposed method, one can estimate the specific failure rate and analyze possible measures to improve component reliability. The method can be used for specific applications including components for which there is not enough numerical data for specific evaluation.     

Model validation under epistemic uncertainty

This paper develops a methodology to assess the validity of computational models when some quantities may be affected by epistemic uncertainty. Three types of epistemic uncertainty regarding input random variables - interval data, sparse point data, and probability distributions with parameter uncertainty - are considered. When the model inputs are described using sparse point data and/or interval data, a likelihood-based methodology is used to represent these variables as probability distributions. Two approaches - a parametric approach and a non-parametric approach - are pursued for this purpose. While the parametric approach leads to a family of distributions due to distribution parameter uncertainty, the principles of conditional probability and total probability can be used to integrate the family of distributions into a single distribution. The non-parametric approach directly yields a single probability distribution. The probabilistic model predictions are compared against experimental observations, which may again be point data or interval data. A generalized likelihood function is constructed for Bayesian updating, and the posterior distribution of the model output is estimated. The Bayes factor metric is extended to assess the validity of the model under both aleatory and epistemic uncertainty and to estimate the confidence in the model prediction. The proposed method is illustrated using a numerical example.     

Validation of models with multivariate output

This paper develops metrics for validating computational models with experimental data, considering uncertainties in both. A computational model may generate multiple response quantities and the validation experiment might yield corresponding measured values. Alternatively, a single response quantity may be predicted and observed at different spatial and temporal points. Model validation in such cases involves comparison of multiple correlated quantities. Multiple univariate comparisons may give conflicting inferences. Therefore, aggregate validation metrics are developed in this paper. Both classical and Bayesian hypothesis testing are investigated for this purpose, using multivariate analysis. Since, commonly used statistical significance tests are based on normality assumptions, appropriate transformations are investigated in the case of non-normal data. The methodology is implemented to validate an empirical model for energy dissipation in lap joints under dynamic loading.     

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.     

数据驱动下孪生贝叶斯理论非齐次泊松过程的结构损伤评估方法

以结构件裂纹扩展过程中的损伤状态评估为研究对象,提出了一种孪生贝叶斯理论非齐次泊松过程的结构损伤评估方法.首先,结合基于裂尖场能量的可靠度序化策略与非齐次泊松过程,运用贝叶斯理论对试验信息及总体过程参数的渐进关系进行组合,获得过程参数先验分布.同时,基于裂尖场能量递进因子与似然函数的概念,通过先验信息、序化策略及后验信...     

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.     

Bayesian calculation of optimal burn‐in time using the joint criteria of cost and delivered reliability

Burn‐in is a quality control process used to minimize the warranty cost of a product by screening out defective products through prior operation for a period of time before sale. Two decision criteria used to determine the optimal burn‐in time are the maximization of the reliability of the delivered product and the minimization of the total cost, which are composed of the cost of burn‐in process and the cost of warranty claims. Because of uncertainty regarding the underlying lifetime distribution of the product, both the product reliability and the total cost are random variables. In this paper, the uncertainty in reliability and cost is quantified by use of Bayesian analysis. The joint distribution of reliability and cost is inferred from the uncertainty distribution of the parameters of the product lifetime distribution. To incorporate the uncertainty in reliability and cost as well as the tradeoff between them into the selection of optimal burn‐in time, the joint utility function of reliability and cost is constructed using the joint distribution of reliability and cost. The optimal burn‐in time is selected as the time that maximizes the joint utility function. Copyright © 2010 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.     

Reliability-based assessment of ageing bridges using risk ranking and life cycle cost decision analyses

Information about present and anticipated bridge reliabilities, in conjunction with decision models, provides a rational and powerful decision-making tool for the structural assessment of bridges. For assessment purposes, an updated reliability (after an inspection) may be used for comparative or relative risk purposes. This may include the prioritisation of risk management measures (risk ranking) for inspection, maintenance, repair or replacement. A life-cycle cost analysis may also be used to quantify the expected cost of a decision. The present paper will present a broad overview of the concepts, methodology and immediate applications of risk-based assessments of bridges. In particular, two practical applications of reliability-based bridge assessment are considered — risk ranking and life-cycle cost analysis.