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Improving reliability and eliminating the potential design risk are crucial for product design. Failure mode and effect analysis (FMEA), as an effective reliability assurance tool, has been extensively used in product design. However, causalities among failure modes, interactions among risk factors, and correlations among risk evaluations were not jointly considered in existing FMEA methods. On the other hand, the cost and time caused by the occurrence of failure modes were seldom incorporated into risk factors. Due to the lack of accurate values and/or information loss of customers and experts, these risk factors inevitably contain uncertainty that cannot be overlooked in product design. In this article, a novel FMEA-based approach is proposed to facilitate risk analysis of product design under uncertainty. In this approach, the stable grey causality vector state and the grey interaction vector are respectively established to characterize causalities and interactions. To reduce the uncertainty contained in cost and time, the extended information axiom is put forth, and then, their grey information contents can be obtained and are to be incorporated into the design. Subsequently, we extend Choquet integral to prioritize the potential failure modes and identify the optimal design scheme while coping with correlations. The proposed approach is validated by an example of a substrate design.

Fast recognition of integrated circuits markings is an essential but challenging task in electronic device manufacturing lines. This article develops an adaptive deep learning framework to facilitate the fast marking recognition of IC chips. The proposed framework contains four deep learning components, namely chip segmentation, orientation correction, character extraction, and character recognition. The four components utilize different convolutional neural network structures to guarantee excellent adaptivity to a wide range of IC types, and mitigate the influence of the low-quality chip images. In particular, the character extraction model is comprised of two improved label generation strategies and a proposed border correction method, so as to accommodate tiny scale chips and compactly printed markings. Experiments for a set of chip images from a real laptop manufacturing line demonstrate the superiority of the proposed framework to the state-of-the-art models and the effectiveness of handling a great diversity of chips.

As multistate system (MSS) reliability models can characterize the multistate deteriorating nature of engineering systems, they have received considerable attention in the past decade. The states of a multistate system/component can be distinguished by its performance capacity, which deteriorates over time and can be restored by maintenance activities. On the other hand, the deterioration of a system/component is, oftentimes, controllable by setting a loading strategy. In this article, a dynamic load optimization problem for repairable MSSs is investigated to achieve the maximum expected cumulative performance within a finite time horizon and limited maintenance resources. The degraded components in a system are dynamically maintained to recover to their better conditions, whereas the performance rate of each component can also be dynamically specified. The resulting sequential decision problem is formulated as a Markov decision process with a continuous action space and a mixed integer discrete continuous state space. The deep deterministic policy gradient algorithm, which is a specific deep reinforcement learning algorithm in the actor−critic framework, is customized to overcome the “curse of dimensionality” and mitigate the uncountable state and action spaces. The effectiveness of the proposed method is examined by two illustrative examples, and a set of comparative studies are conducted to demonstrate the advantage of the proposed dynamic loading strategy.

Wind power has been widely used in the past decade because of its safety and cleanness. Double fed induction generator (DFIG), as one of the most popular wind turbine generators, suffers from degradation. Therefore, reliability assessment for this type of generator is of great significance. The DFIG can be characterized as a multi-state system (MSS) whose components have more than two states. However, due to the limited data and/or vague judgments from experts, it is difficult to obtain the accurate values of the states and thus it inevitably contains epistemic uncertainty. In this paper, the fuzzy universal generating function (FUGF) method is utilized to conduct the reliability assessment of the DFIG by describing the states using fuzzy numbers. First, the fuzzy states of the DFIG system’s components are defined and the entire system state is calculated based the system structure function. Second, all components’ states are determined as triangular fuzzy numbers (TFN) according to experts’ experiences. Finally, the reliability assessment of the DFIG based on the FUGF is conducted.

It is crucial to evaluate reliability measures of a system over time, so that reliability-related decisions, such as maintenance planning and warranty policy, can be appropriately made for the syst...

In this article, we develop a mixture of Gaussians-evidential hidden Markov model (MoG-EHMM) to fuse expert knowledge and condition monitoring information for remaining useful life (RUL) prediction under the belief function theory framework. The evidential expectation–maximization algorithm is implemented in the offline phase to train the MoG-EHMM based on historical data. In the online phase, the trained model is used to recursively update the health state and reliability of a particular individual system. The predicted RUL is, then, represented in the form of its probability mass function. A numerical metric is defined based on the Bhattacharyya distance to measure the RUL prediction accuracy of the developed methods. We applied the developed methods on a simulation experiment and a real-world dataset from a bearing degradation test. The results demonstrate that despite imprecisions in expert knowledge, the performance of RUL prediction can be substantially improved by fusing expert knowledge with condition monitoring information.

In engineering scenarios, expert judgments play an essential role in reliability assessment, especially for those systems with few historical data. To achieve a rational result, experts from different areas should be involved, and the uncertainties in their assessments should be properly addressed. Such information is often referred to as multisource imprecise information (MSII) and might contain high degree of conflicts, as different experts usually have different expertise and knowledge. Properly quantifying the conflicts among the MSII, then, becomes a critical issue, as the subsequent processing of MSII (e.g., combination and calibration), depends on the degree of conflict in the MSII. To this end, a new conflict measure is put forth based on the Dempster–Shafer theory (DST) to quantify and visualize the conflict in the MSII from a group of experts. In the first place, the MSII from each expert is used to construct the basic belief assignment (BBA) of the reliability estimates for the corresponding expert under the DST. A 2-D conflict measure, which combines the conflict factor and Jousselme distance in DST, is, then, proposed to measure the conflict between the experts’ BBAs. The conflict is quantified from two perspectives, viz., mutual conflict and total conflict. Finally, a Bhattacharyya distance-based method is developed to further quantify the informativeness of each expert's MSII to the system reliability estimate. A numerical example along with an engineering case is used to validate the effectiveness of the proposed approach.

Multi-state is a typical characteristic of engineered systems. Most existing studies of redundancy allocation problems (RAPs) for multi-state system (MSS) design assume that the state probabilities of redundant components are precisely known. However, due to lack of knowledge and/or ambiguous judgements from engineers/experts, the epistemic uncertainty associated with component states cannot be completely avoided and it is befitting to be represented as belief quantities. In this paper, a multi-objective RAP is developed for MSS design under the belief function theory. To address the epistemic uncertainty propagation from components to system reliability evaluation, an evidential network (EN) model is introduced to evaluate the reliability bounds of an MSS. The resulting multi-objective design optimization problem is resolved via a modified non-dominated sorting genetic algorithm II (NSGA-II), in which a set of new Pareto dominance criteria is put forth to compare any pair of feasible solutions under the belief function theory. A numerical case along with a SCADA system design is exemplified to demonstrate the efficiency of the EN model and the modified NSGA-II. As observed in our study, the EN model can properly handle the uncertainty propagation and achieve narrower reliability bounds than that of the existing methods. More importantly, the original nested design optimization formulation can be simplified into a one-stage optimization model by the proposed method.

Importance measures of multi-state systems have been intensively investigated from different perspectives in the past few years as the results are able to provide a valuable guidance for effective reliability improvement and enhancement. The state assignment is oftentimes conducted to identify the state of a multi-state system when features and/or knowledge related to the health condition of the particular system are collected. However, due to the scarcity of sensor data, limited accuracy of sensing techniques, and vague/conflicting judgments from experts, conducting the state assignment is imprecise and inevitably produces epistemic uncertainty. In this paper, some composite importance measures of multi-state systems are extended by considering the epistemic uncertainty associated with component state assignment. To take account of such epistemic uncertainty, the proposed method contains three basic steps: (1) propagate the epistemic uncertainty associated with component state assignment to the reliability function of a multi-state system by dynamic evidential network models, (2) evaluate the intervals of the conditional reliability by inputting hard evidences and/or vacuous evidence into the tailored dynamic evidential network models, and (3) compute the extended composite importance measures by constructing a pair of optimization problems and properly handling the dependency among input intervals. A numerical example of a multi-state bridge system together with an engineering example of a feeding control system of CNC lathes is exemplified to demonstrate the impact of the epistemic uncertainty on the importance measures of components and their rankings.

The fault tree analysis has been extensively implemented in failure analysis of engineered systems. In most cases, the probabilities of basic events, e.g. components’ failures, are represented by crisp values in the fault tree analyses. However, due to lack of knowledge, scarcity of failure data, or vague judgments from experts, it may produce parameter uncertainty associated with degradation models of components/systems, and such model parameter uncertainty can be quantified by the epistemic uncertainty. In addition, the common cause failure, related to the simultaneous failures of two or more components caused by physical interactions or shared environments, often exists in advanced engineered systems and computing systems. In this paper, by considering both the common cause failure and the epistemic uncertainty associated with model parameters, an evidential network model embedded with common cause failure is proposed to facilitate system failure analysis. The detailed transformations from some logic gates of a fault tree to an evidential network model are given. Moreover, the conditional belief mass tables are constructed to quantify the dependency between the states of components and the entire system. An engineering case of an aero-engine oil system, together with comparative results, is presented to demonstrate the effectiveness of the proposed evidential network model.

Structure function, which quantitatively represents the relation between system states and unit states, is essential for system reliability assessment and oftentimes may not be known in advance due to complicated interactions among units. In this article, a dynamic Bayesian network (DBN) model is put forth to leverage incomplete observation sequences of hierarchical multi-state systems for structure function learning. To achieve a consistent structure function at different time instants, a customized Expectation-Maximization (EM) algorithm with parameter modularization is proposed and executed by two steps: (1) filling the missing values in the incomplete observation sequences with their expectations to break the dependencies among nodes; (2) decomposing the graphical network into V-shape structures, and then integrating the identical V-shape structures at different time slices to learn the parameters in the DBN model. Based on the learned DBN model, system state distribution and reliability function over time can be readily assessed. Two illustrative examples are presented and the results demonstrate that the structure function of a hierarchical multi-state system can be accurately learned despite the incompleteness of observation sequences.

Reliability assessment is a crucial activity for engineered systems as the results are able to provide valuable information for reliability-related decisions, such as maintenance planning and warranty policy. Nevertheless, accurately assessing the system reliability is challenging if only some pieces of reliability-related data can be collected from experts. Such data may be, however, imprecise, heterogeneous, and from multiple physical levels of a system. In this paper, a constrained optimization model is put forth to assess the system reliability by fusing multi-source of imprecise reliability data. Firstly, a set of constraints is constructed for a resulting optimization model by representing various imprecise reliability data as functions of unknown parameters associated with degradation models of components. Secondly, by maximizing and minimizing system reliability function, the upper and lower bounds of system reliability can be evaluated. Finally, a model selection approach is developed to identify component degradation model which matches up with all the imprecise reliability data to the maximum extent. An illustrative example shows that system reliability over time can be effectively evaluated by fusing imprecise reliability data. The conflicts among multi-source of imprecise reliability data can be properly avoided by identifying the feasible region of all the unknown parameters in which all the constraints can be satisfied.

By utilizing inspection data, reliability of a particular individual system can be dynamically updated. In view of the hierarchical structure of engineering systems, inspection data can be collected from multiple physical levels of a system. Nevertheless, due to the limited inspection resources, such as time, budget, and manpower, simultaneously inspecting all the components, subsystems, and the entire system is unaffordable. It, therefore, raises a natural question: how to identify the optimal inspection strategy under limited resources to reveal the health states of a system and its components to the maximum extent. To address the above question, a new metric is proposed in this paper to quantify the effectiveness of a particular inspection strategy in terms of revealing the states of components in a multi-state system. The optimal multi-level inspection strategy for the system is, thereby, determined by maximizing the proposed metric under limited inspection resources. An illustrative example shows that the proposed method can optimally allocate the limited inspection resources, so as to maximally reveal the states of components of interest and facilitate dynamic reliability assessment of a system.

Sustainable product design has captured considerable attention over recent years due to the growing customer demands of sustainability. To improve the environmental performance of products at the early stage of product design, a variety of economic, social, and environmental factors, such as manufacturing cost and time, product yield, capacity, customer preferences, and pollutant emissions, have to be taken into account jointly. However, due to the lack of knowledge and ambiguity of customers and experts, some of these factors may contain epistemic uncertainties, overlooking them may lead to an infeasible design. To fill the gap, we propose a new multi-objective optimization-based technique for order preference by similarity to ideal solution (TOPSIS) method to facilitate sustainable product design under epistemic uncertainty. In the proposed method, we develop a fuzzy Mahalanobis–Taguchisystem method to address the epistemic uncertainty of customer preferences on optimization objectives. Meanwhile, we introduce the Me measure to manipulate the epistemic uncertainty of experts’ judgments on process parameters and variables during the manufacturing process. Subsequently, we implement the new TOPSIS method to obtain the optimal design scheme. We provide an example of sustainable substrate design, along with sensitivity analysis scenarios and comparative studies, to elaborate on the performance of the proposed method.

Disruptive events such as natural disasters and human errors can have widespread adverse impacts on several networked infrastructures, affecting their functionalities and possibly resulting in large economic losses. It is, therefore, of great significance for these networks to exhibit resilience, defined as the ability of a network to recover from a disruptive event. Inspired by the measures of component importance used in reliability communities, this paper proposes a new resilience-based component importance ranking measure for multi-state networks from the perspective of a post-disaster restoration process. Considering the stochastic nature of disruptive events, the importance measure of each component is evaluated by finding the minimal recovery paths for various disruptive events, and it can be represented by a probability distribution. A stochastic ranking approach is implemented to identify the importance rank of each component in a network. Compared to existing methods, the proposed importance measure not only takes the multi-state characteristics of a network and its components into account but also quantifies the impact of both capacity improvement and recovery time of a component on network resilience. The proposed importance measure is exemplified through case studies in the Seervada Park road network.