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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.

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.

The reliability function of a specific individual system can be dynamically updated by utilizing inspection data collected over time. However, due to limited inspection resources, such as time, budget, and manpower, it is oftentimes impossible to collect all the inspection data for all the components, subsystems, and the entire system simultaneously. There is an urgent need to optimally allot the limited inspection resources across multiple physical levels of a system, so as to identify the health status of a system and/or its subset of components of interest as accurately as possible to facilitate the ensuing system health management. To address the above research question, a metric is put forth in this paper to quantify the effectiveness of a particular multilevel inspection strategy for multistate systems (MSSs). Based on the proposed metric, an optimization problem is formulated to seek the optimal multilevel inspection strategy which possesses the maximum effectiveness of revealing the true state of a system and/or its subset of components of interest under limited inspection resources. The resulting optimization problem is resolved by a tailored ant colony optimization algorithm. The findings from our illustrative examples are 1) the proposed metric is capable of quantifying the effectiveness of various multilevel inspection strategies; 2) the analytical solution of the proposed metric is exactly the same with the simulation results, but much more computationally efficient; and 3) the optimal inspection strategy varies with respect to the operation time of a specific individual system.

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.

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.