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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 October 2024) | Viewed by 13800

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Special Issue Editors

Dr. Meilin Wen

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Guest Editor

School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Interests: belief reliability theory; reliability optimization; uncertainty theory; uncertain programming; data envelopment analysis

Prof. Dr. Xiaoyang Li

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Guest Editor

School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Interests: belief reliability theory; reliability experiment theory; reliability and resilience modeling; accelerated degradation testing theory
Special Issues, Collections and Topics in MDPI journals

Dr. Qingyuan Zhang

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Guest Editor

School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
Interests: belief reliability theory; uncertainty quantification and analysis; reliability modeling; function-oriented reliability design

Dr. Tianpei Zu

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Guest Editor

School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
Interests: belief reliability theory; reliability evaluation; uncertainty quantification method

Special Issue Information

Dear Colleagues,

Reliability and system engineering, as important approaches used to fight against product failure and risk, have been challenged by various problems, especially the epistemic uncertainty of information and data caused by the increase in complexity. In recent years, uncertainty theory has been widely used to cope with uncertainty issues in reliability and systems engineering, including the epistemic uncertainty quantification of the failure process, reliability and resilience modelling, risk assessment, reliability-based design optimization, and degradation testing modelling.

This planned Special Issue in Symmetry aims to provide a platform for researchers and industrial engineers to exchange the latest research results on the application of uncertainty theory in reliability and system engineering. The papers accepted in this Special Issue are expected to employ symmetry or asymmetry concepts in their methods to cope with uncertainty quantification, modelling, and analysis regarding system failure and reliability. Topics of interest for submission include, but are not limited to, the following:

Uncertainty quantification in reliability and systems engineering;
Reliability optimization with uncertainty;
Reliability evaluation method with limited information;
Reliability and resilience for complex systems with uncertainty;
Prognostics and health management using uncertainty theory;
Uncertain decision making in reliability and systems engineering.

When submitting your paper, please select the Journal “Symmetry” and the Special Issue “Advances in and Applications of Uncertainty Theory in Reliability and Systems Engineering” via MDPI’s submission system. Our papers will be published on a rolling basis. We look forward to receiving your submissions.

Dr. Meilin Wen
Prof. Dr. Xiaoyang Li
Dr. Qingyuan Zhang
Dr. Tianpei Zu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

reliability and systems engineering
uncertainty theory
reliability optimization with uncertainty
reliability evaluation with limited information
reliability and resilience for complex systems with uncertainty
uncertain decision making

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Published Papers (10 papers)

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Research

18 pages, 2232 KiB

Open AccessArticle

The Reliability and Availability Analysis of a Single-Unit System under the Influence of Random Shocks and the Variation in Demand from Production with Erlang Distribution

by Zienab M. Hussien and Mohamed S. El-Sherbeny

Symmetry 2024, 16(7), 815; https://doi.org/10.3390/sym16070815 - 28 Jun 2024

Viewed by 590

Abstract

This study evaluates the reliability measures for a system consisting of a single unit that is subject to random shocks at random times with mismatches between demand and production. The system may sometimes be subject to random shocks leading to a system failure with probability p. The system may also fail completely for various reasons other than shocks. The unit is serviced by a technician if it is affected by a shock. However, the system may fail during operation for various other reasons, such as a programming error, human error, operational continuity and stress, and weather conditions. A single technician immediately repairs or maintains the failed unit. The system is in an operational state when there is demand or in an idle state when there is no demand. The distributions of all times in this system follow a negative exponential, while the time to repair follows a two-stage Erlang distribution. The expressions for the reliability metrics are obtained as functions of time using the Laplace transform and the supplementary variables technique. Sensitivity and relative sensitivity analyses were also performed for the system parameters. Finally, the efficiency of the system is illustrated using numerical examples. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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20 pages, 3749 KiB

Open AccessArticle

Belief Reliability Modeling Method for Wind Farms Considering Two-Directional Rotor Equivalent Wind Speed

by Shuyu Li, Rui Kang, Meilin Wen and Tianpei Zu

Symmetry 2024, 16(5), 614; https://doi.org/10.3390/sym16050614 - 15 May 2024

Viewed by 763

Abstract

Compared to conventional energy sources, wind power is a clean energy source with high intermittence and uncertainty. As a system that converts wind energy into electricity, wind farms inevitably face severe reliability issues. In this paper, based on reliability theory, a new reliability modeling method for wind farms is proposed. Firstly, a belief reliability model for wind farms is constructed. Then, a power generation model based on two-directional rotor equivalent wind speed is established to represent the wind farm performance in the belief reliability model. Finally, several numerical studies are conducted to verify the power generation model under different wind speeds and directions, to demonstrate the belief reliability model with different levels of uncertainty, and to compare the belief reliability considering two-directional rotor equivalent wind speed with other methods. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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30 pages, 3174 KiB

Open AccessArticle

Modeling Renewable Warranties and Post-Warranty Replacements for Self-Announcing Failure Products Subject to Mission Cycles

by Lijun Shang, Jianhui Chen, Baoliang Liu, Cong Lin and Li Yang

Symmetry 2024, 16(5), 603; https://doi.org/10.3390/sym16050603 - 13 May 2024

Cited by 1 | Viewed by 747

Abstract

The number of failures serves as a critical indicator that dynamically impacts the reliability of self-announcing failure products, making it highly practical to incorporate the failure count into reliability management throughout the entire product life cycle. This paper investigates comprehensive methodologies for effectively managing the reliability of self-announcing failure products throughout both the warranty and post-warranty stages, taking into account factors such as the failure count, mission cycles, and limited time duration. Three renewable warranty strategies are introduced alongside proposed models for post-warranty replacements. By analyzing variables like the failure number, mission cycles, and time constraints, these proposed warranties provide practical frameworks for efficient reliability management during the warranty stage. Additionally, the introduced warranties utilize cost and time metrics to extract valuable insights that inform decision making and enable effective reliability management during the warranty stage. Moreover, this study establishes cost and time metrics for key post-warranty replacements, facilitating the development of individual cost rates and model applications in other post-warranty scenarios. Analyses of the renewable free-repair–replacement warranties demonstrate that establishing an appropriate number of failures as the replacement threshold can effectively reduce warranty-servicing costs and extend the coverage duration. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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17 pages, 2412 KiB

Open AccessArticle

Cascading Failure Modeling for Circuit Systems Considering Continuous Degradation and Random Shocks Using an Impedance Network

by Yi Jin and Qingyuan Zhang

Symmetry 2024, 16(4), 488; https://doi.org/10.3390/sym16040488 - 17 Apr 2024

Cited by 1 | Viewed by 863

Abstract

The reliability of circuit systems is primarily affected by cascading failures due to their complex structural and functional coupling. Causes of cascading failure during circuit operation include the continuous degradation process of components and external random shocks. Circuit systems can exhibit asymmetric structural changes and functional loss during cascading failure propagation due to the coupling of degradation and shock and their uncertainty effects. To tackle this issue, this paper abstracts the circuit into an impedance network and constructs a component failure behavior model that considers the correlation between degradation and shock. The interactions between soft and hard failure processes among different components are discussed. Two types of cascading failure propagation processes are described: slow propagation associated with continuous degradation and damage shock, and fast propagation due to fatal shock. Based on this, a cascading failure simulation algorithm is developed. This article presents a case study to demonstrate the proposed models and to analyze the reliability of a typical circuit system. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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23 pages, 1354 KiB

Open AccessArticle

Based Copula Reliability Estimation with Stress-Strength Model for Bivariate Stress under Progressive Type II Censoring

by Junrui Wang and Rongfang Yan

Symmetry 2024, 16(3), 265; https://doi.org/10.3390/sym16030265 - 21 Feb 2024

Viewed by 1806

Abstract

This study investigates the dependence between stress and component strength in a stress–strength model with bivariate stresses by incorporating a specialized Archimedean copula, specifically the 3-dimensional Clayton copula. Diverging from prior research, we consider a scenario where two stresses simultaneously influence the component strength, enhancing the realism of our model. Initially, dependent parameter estimates were obtained through moment estimation. Subsequently, maximum likelihood estimation and Bayesian estimation were employed to acquire point and interval estimates for the model parameters. Finally, numerical simulations and real-world data analysis were conducted to validate the accuracy and practicality of our proposed model. This research establishes a foundation for further exploration of general dependence structures and multi-component stress–strength correlation issues. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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16 pages, 1976 KiB

Open AccessArticle

Uncertainly Analysis of Prior Distribution in Accelerated Degradation Testing Bayesian Evaluation Method Based on Deviance Information Criterion

by Tianji Zou, Kai Liu, Wenbo Wu, Ke Wang and Congmin Lv

Symmetry 2024, 16(2), 160; https://doi.org/10.3390/sym16020160 - 30 Jan 2024

Viewed by 977

Abstract

The accelerated degradation testing (ADT) Bayesian evaluation method comprehensively utilizes product degradation data under accelerated stress levels collected over a short period of time and multiple sources of prior information, such as historical information, similar product information, simulation information, etc., to conduct life and reliability evaluation. Through the prior distribution, prior information affects the ADT Bayesian evaluation results ultimately. However, different evaluators may obtain different prior distributions based on the same prior information due to varying experiences or rules, which may lead to differences in the ADT Bayesian evaluation results. Therefore, it is necessary to analyze and study the impact of prior distribution uncertainty on the ADT Bayesian evaluation results while also finding criteria to judge the quality of prior distributions. This paper focuses on the ADT Bayesian evaluation method based on the Wiener process and the Arrhenius relation, studying the influence of different prior distributions on the robustness of ADT Bayesian evaluation results. Additionally, based on the deviance information criterion (DIC), a criterion for selecting prior distributions in the ADT Bayesian evaluation method is proposed. Through carrying out uncertainty analysis of prior distribution in the ADT Bayesian evaluation method, a theoretical system and framework for analyzing prior uncertainty in ADT Bayesian evaluation based on DIC are established, providing a better foundation for the practical application of the ADT Bayesian evaluation method in engineering. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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12 pages, 3114 KiB

Open AccessArticle

Reliability-Centered Preventive Maintenance Optimization for a Single-Component Mechanical Equipment

by Yaojun Liu, Yuhua Tang, Ping Wang, Xiaolin Song and Meilin Wen

Symmetry 2024, 16(1), 16; https://doi.org/10.3390/sym16010016 - 21 Dec 2023

Viewed by 2641

Abstract

Due to the high failure rates of mechanical equipment with complex structures and numerous moving parts, devising an effective preventive maintenance (PM) plan and avoiding the influence brought by failure is crucial. However, some PM efforts are disorganized, unpractical, and unscientific, leading to prolonged downtime and significant cost losses. The challenge in creating PM plans is exacerbated by the asymmetry between maintenance and failure data. Therefore, focusing on single-unit mechanical equipment, the reliability-centered maintenance (RCM) idea is put forward to find out the key parts to implement preventive maintenance, and PM models are built to draw up a more reasonable PM plan. Such strategies aim to lower maintenance costs and enhance economic performance. Data on past maintenance and failures are analyzed to determine the life distribution and maintenance effect functions, helping to quantify the uncertainty caused by data asymmetry. Two PM optimization models considering time-varying failure rates are proposed: one focuses on minimizing costs, while the other aims to maximize availability. A PM plan example is demonstrated using a component from a tire-building machine including six parts, which proves the validity of the models. The availability results of two parts corresponding to the maintenance strategy obtained by the availability maximization model are above 0.99, and the results of total costs per unit time of the remaining four parts obtained by the cost minimization model are under 5.69. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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15 pages, 330 KiB

Open AccessArticle

Rényi Entropy for Past Lifetime Distributions with Application in Inactive Coherent Systems

by Mohamed Kayid and Mansour Shrahili

Symmetry 2023, 15(7), 1310; https://doi.org/10.3390/sym15071310 - 26 Jun 2023

Cited by 5 | Viewed by 1172

Abstract

In parallel with the concept of Rényi entropy for residual lifetime distributions, the Rényi entropy of inactivity time of lifetime distributions belonging to asymmetric distributions is a useful measure of independent interest. For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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14 pages, 6046 KiB

Open AccessArticle

Fault Diagnosis for China Space Station Circulating Pumps: Prototypical Network with Uncertainty Theory

by Wenbo Wu, Tianji Zou, Dong Guo, Lu Zhang, Ke Wang and Xuzhi Li

Symmetry 2023, 15(4), 903; https://doi.org/10.3390/sym15040903 - 13 Apr 2023

Cited by 2 | Viewed by 1413

Abstract

Methods for fault diagnosis based on metric learning, in which a query sample is classified by picking the closest prototype from the support set based on their feature similarities, have been the subject of many studies. In real-world applications of in-orbit products, such as circulating pumps, the computation of similarity between different pairs is prone to different degrees of inaccuracy, especially epistemic uncertainty. Knowing and considering the uncertainty of similarity may improve fault detection accuracy. This article provides a unique approach to fault diagnosis based on Prototypical Network (Pro-Net) and Uncertainty Theory. In particular, we use epistemic uncertainty by altering the representation of prototypes from a deterministic scalar to an uncertain representation. To assess the similarity between a query and the prototypes in a support set, we calculate the uncertain distance between the pairs using cross-entropy. Experiments with symmetrical structures reveal that our proposed method significantly enhances classification precision and achieves state-of-the-art performance. It improves the reliability of fault diagnosis and reduces the risk of making erroneous judgments in safety-critical systems, decreasing the possibility of adverse consequences. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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14 pages, 2832 KiB

Open AccessArticle

A Novel Safe Life Extension Method for Aircraft Main Landing Gear Based on Statistical Inference of Test Life Data and Outfield Life Data

by Yueshuai Fu, Huimin Fu and Sheng Zhang

Symmetry 2023, 15(4), 880; https://doi.org/10.3390/sym15040880 - 7 Apr 2023

Cited by 4 | Viewed by 1834

Abstract

Safe life extension work is demanded on an aircraft’s main landing gear (MLG) when the outfield MLG reaches the predetermined safe life. Traditional methods generally require costly and time-consuming fatigue tests, whereas they ignore the outfield data containing abundant life information. Thus, this paper proposes a novel life extension method based on statistical inference of test and outfield life data. In this method, the MLG’s fatigue life is assumed to follow a right-skewed lognormal distribution with an asymmetric probability density function. In addition, the MLG’s new safe life can be inferred through the Bayesian approach in which the test life data and outfield life data are used for prior information acquisition and Bayesian update, respectively. The results indicated that the MLG’s safe life was significantly extended, illustrating the effectiveness of the proposed method. Numerous simulations also demonstrated that the extended safe life can meet the requirements of reliability and confidence and thus is applicable in engineering practice. Full article

(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)

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