A combined physics of failure and Bayesian network reliability analysis method for complex electronic systems

Summary & ConclusionsAs part of a UK DTI collaborative funded project developing a holistic methodology and assessment model for the enhancement of electronics reliability, a study into the use of Physics of Failure (PoF) methods was undertaken. It was conducted by reviewing the use made of PoF techniques by the partners and specifically by undertaking of a number of case studies. It is concluded that PoF methods, and particularly life modelling, are an essential tool in design for reliability. PoF analysis can also be used in establishing reliability enhancement testing (RET) and environmental stress screening (ESS) conditions. A guide for the effective use and inclusion of the PoF methods into product design and development process has been developed and described. The techniques offer benefits in getting a design right first time, thereby avoiding redesign and retest cycles, with consequent cost savings and reduced product development times. The PoF method has limitations associated with the fact that it is essentially a bottom up approach assessing time to failure due to known failure mechanisms. It is consequently difficult to apply to full systems, has limitations in assessing failure rate prior to the onset of life limiting wear out, and is dependent on identifying, and having a validated model, for all potential failure mechanisms.

This paper proposes a quantitative reliability analysis method for power systems with multi-level standby structure based on GO method. First, the GO model used to describe the multi-level standby structure is proposed. Then, the reliability analysis process for such systems based on GO method is formulated. Finally, the proposed GO method is applied in reliability analysis of AC power system for single unit with 100% capacity divisions in nuclear power plant. In order to verify the feasibility, advantage and reasonable of the proposed GO method, its analysis result compared with the analysis result of GO method without considering standby correlations among the multi-level standby structure. All in all, this study provides guidance of reliability analysis for power systems with multi-level standby structure.

This paper presents a robust reliability analysis method for systems of multimodular redundant (MMR) controllers using the method of partitioning and parallel processing of a Markov chain (PPMC). A Markov chain is formulated to represent the N distinct states of the MMR controllers. Such a Markov chain has N2 directed edges, and each edge corresponds to a transition probability between a pair of start and end states. Because N can be easily increased substantially, the system reliability analysis may require large computational resources, such as the central processing unit usage and memory occupation. By the PPMC, a Markov chain's transition probability matrix can be partitioned and reordered, such that the system reliability can be evaluated through only the diagonal submatrices of the transition probability matrix. In addition, calculations regarding the submatrices are independent of each other and thus can be conducted in parallel to assure the efficiency. The simulation results show that, compared with the sequential method applied to an intact Markov chain, the proposed PPMC can improve the performance and produce allowable accuracy for the reliability analysis on large-scale systems of MMR controllers.

For T/R module failure caused by heat, random and statistical characteristics of temperature load and other influence factors are considered. Based on stress-strength interference model, functional function method is used. On the basis of T/R module thermal simulation model and thermal simulation analysis, a reliability modeling method based on physics of failure method realized by multi-simulation software cooperation is proposed to establish a parametric thermal reliability simulation model, thermal reliability analysis is performed, reliability sensitivity is calculated, and major influence factors of T/R module and key components are found, and then for the weak points, corresponding improvement suggestions for T/R module are proposed.

In recent years, there often exist multiple priors from experienced experts or historical experiments with the rapid development of system structure in engineering fields. Bayesian Melding Method is commonly used for integrating multiple priors, which is based on the deterministic system structure. However, if the system model cannot be described by an explicit expression, the traditional Bayesian Melding Method is not feasible for system reliability analysis anymore. In order to describe the structure relationship clearly, Bayesian Network is applied in this paper to construct the complex system structure model and the system reliability is calculated by node probability tables rather than explicit expressions. Combining the advantages of the Bayesian Melding Method and Bayesian Network, a multi-prior integration and updating algorithm is developed for the system reliability analysis of complex system structures. Finally, a satellite attitude control system is used to demonstrate the proposed method. The system is established by the Bayesian Network and the comparison between natural prior and updated prior is discussed at length.

It is now widely accepted that intelligent problem solving requires access to a source of domain‐specific knowledge, and the existence of a control system to constrain the manner in which domain knowledge is searched. An example of a domain which has been intensively investigated is problem solving in physics. A number of researchers have proposed mutually incompatible theories to explain the search control strategies used in this area. This paper looks at backward inference, schema‐guided forward inference, and planstacking (a form of meta‐level backward inference followed by forward inference at the object level). It also considers a proposal to introduce neural network modelling into the short‐term memory component of a production rule‐based problem solver.One widely reported finding (Larkin, McDermott, Simon & Simon, 1980), is that novice problem solvers in the domain of physics use backward inference as a search control technique, while experts use forward inference. The backward‐to‐forward inference shift has indeed become so entrenched that attention has already shifted from whether to how it occurs. In spite of its widespread acceptance, the empirical basis for this claim is somewhat fragile, and a major aim of the present study was to re‐examine it using much larger samples of experts and novices than have been employed in the past, and a methodology which does not depend upon protocol analysis.Our data show that both experts and novices exhibit a forward inference rather than a backward inference order of equation generation. Experts were more likely to be able to plan their solutions at a descriptive meta‐level than novices. While existing theories are able to account for some of these findings, none of them is completely satisfactory in explaining the full range of data.

The relationship between the reliability probabilities of the component and the system is hard to get. If this relationship can be obtained easily, the reliability of the system can be calculated by using the reliability structures of the components. The common method to express this relationship is using the linear correlation index, which only shows the linear correlation between the components failure rather than the relationship between high nonlinear functions. In order to describe this relationship accurately and calculate the system reliability using the component reliability structures, a Uniform Design (UD)-Saddlepoint Approximation (SA)-based system reliability analysis method is proposed. The system reliability analysis method is decomposed to three simple steps: (1) calculating the weight coefficient which represents the contribution rate of each component to system reliability, (2) approximating Cumulant Generation Function (CGF) of each component, (3) calculating CGF of the system and approximating the system reliability with SA method. The weight coefficient of each component is derived from UD method, and a variable interval selection method is developed to decrease the required number of samples and increase the accuracy of the weight coefficients. First-Order Saddlepoint Approximation (FOSA) method or Mean-Value First-Order Saddlepoint Approximation (MVFOSA) method is used to analyze the CGF of a component performance function. Then the CGF of the system can be obtained by the weighted addition law by combining the CGFs of components performance functions with the weight coefficients. Finally, the system reliability can be approximated by SA method. Four examples are employed to demonstrate that the new method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

In order to ensure high reliability of complex engineered systems against deterioration or natural and man-made hazards, it is essential to have an efficient and accurate method for estimating the probability of system failure regardless of different system configurations (series, parallel, and mixed systems). Since system reliability prediction is of great importance in civil, aerospace, mechanical, and electrical engineering fields, its technical development will have an immediate and major impact on engineered system designs. To this end, this chapter presents a comprehensive review of advanced numerical methods for system reliability analysis under uncertainty. Offering excellent in-depth knowledge for readers, the chapter provides insights on the application of system reliability analysis methods to engineered systems and gives guidance on how we can predict system reliability for series, parallel, and mixed systems. Written for the professionals and researchers, the chapter is designed to awaken readers to the need and usefulness of advanced numerical methods for system reliability analysis.

A novel approach for software reliability analysis of digital instrumentation and control systems in nuclear power plants

A self-anchored suspension bridge contains many interrelated and acting components. The damage of any component under load may affect the service function of the bridge. The reliability index of a single element often overestimates the safety state of the bridge. To evaluate the overall reliability of a self-anchored suspension bridge, a reliability analysis method for a self-anchored suspension bridge system based on the integral dimension reduction (IDR) method is established, which avoids the calculation of high-dimensional integral and greatly improves the analysis efficiency. Firstly, the reliability indexes and checkpoints of each potential failure element are analyzed. Secondly, the sensitivity of random variable reliability is analyzed and the corresponding safety margin equation is established. Finally, the IDR method is used to reduce the dimension of high-dimensional integral and transform it into the product of equivalent linear failure mode failure probability, which improves the analysis efficiency. Using this analysis method, the static system reliability of a three-tower self-anchored suspension bridge is analyzed, which provides a method of system reliability analysis of this kind of bridge.

Bayesian networks (BNs) are being studied in recent years for system diagnosis, reliability analysis, and design of complex engineered systems. In several practical applications, BNs need to be learned from available data before being used for design or other purposes. Current BN learning algorithms are mainly developed for networks with only discrete variables. Engineering design problems often consist of both discrete and continuous variables. This paper develops a framework to handle continuous variables in BN learning by integrating learning algorithms of discrete BNs with Gaussian mixture models (GMMs). We first make the topology learning more robust by optimizing the number of Gaussian components in the univariate GMMs currently available in the literature. Based on the BN topology learning, a new multivariate Gaussian mixture (MGM) strategy is developed to improve the accuracy of conditional probability learning in the BN. A method is proposed to address this difficulty of MGM modeling with data of mixed discrete and continuous variables by mapping the data for discrete variables into data for a standard normal variable. The proposed framework is capable of learning BNs without discretizing the continuous variables or making assumptions about their conditional probability densities (CPDs). The applications of the learned BN to uncertainty quantification and model calibration are also investigated. The results of a mathematical example and an engineering application example demonstrate the effectiveness of the proposed framework.

The intermittence and fluctuation of renewable energy bring significant uncertainty to the power system, which enormously increases the operational risks of the power system. The development of efficient interval prediction models can provide data support for decision making and help improve the economy and reliability of energy interconnection operation. The performance of Bayesian deep learning models and Bayesian shallow neural networks in short-term interval prediction of photovoltaic power is compared in this study. Specifically, an LSTM Approximate Bayesian Neural Network model (ABNN-I) is built on the basis of the deep learning and Monte Carlo Dropout method. Meanwhile, a Feedforward Bayesian Neural Network (ABNN-II) model is introduced by Feedforward Neural Network and the Markov Chain Monte Carlo method. To better compare and verify the interval prediction capability of the ABNN models, a novel clustering method with three-dimensional features which include the number of peaks and valleys, the average power value, and the non-stationary measurement coefficient is proposed for generating sunny and non-sunny clustering sets, respectively. Results show that the ABNN-I model has an excellent performance in the field of photovoltaic short-term interval forecasting. At a 95% confidence level, the interval coverage from ABNN-I to ABNN-II can be increased by up to 3.1% and the average width of the interval can be reduced by 56%. Therefore, with the help of the high computational capacity of deep learning and the inherent ability to quantify uncertainty of the interval forecast from Bayesian methods, this research provides high-quality interval prediction results for photovoltaic power prediction and solves the problem of difficult modeling for over-fitting that exists in the training process, especially on the non-sunny clustering sets.

The command and control network is the center of information collection and command release in modern information warfare, and its reliability will directly affect the outcome of the war. In this paper, the equipment and environmental factors in the command and control network are comprehensively considered, and Bayes-GO method is used to analyze the two-terminal reliability of the artillery command vehicle to command the howitzer to strike the target. According to its command and control path, the GO model is established, and the GO graph is transformed into the corresponding Bayesian network on the basis of the mapping rules between models. In accordance with the forward and backward inference calculation rules of the Bayesian network, the quantitative analysis results of the two-terminal reliability of the command and control network can be obtained, and the weak links of the system are diagnosed.

Bayesian approaches have been demonstrated as effective methods for reliability analysis of complex systems with small-amount data, which integrate prior information and sample data using Bayes’ theorem. However, there is an assumption that precise prior probability distributions are available for unknown parameters, yet these prior distributions are sometimes unavailable in practical engineering. A possible way to avoiding this assumption is to generalize Bayesian reliability analysis approach by using imprecise probability theory. In this paper, we adopt a set of imprecise Dirichlet distributions as priors to quantify uncertainty of unknown parameters and extend traditional Bayesian reliability analysis approach by introducing an imprecise Dirichlet model (IDM). When the prior information is rare, the result of imprecise Bayesian analysis method is too rough to support engineering decision-making, so we proposed an optimization model to reduce the imprecision of the new method. Spindles are crucial for machine tools and reliability data related to spindles of new-developed machine tools are often rare. We can then use the imprecise Bayesian reliability analysis method to assess its reliability. In this paper, we mainly investigate the reliability assessment of a motorized spindle to illustrate the effectiveness of the proposed method.

Efficient system reliability analysis illustrated for a retaining wall and a soil slope