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Mathematics
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Mathematics in Advanced Reliability and Maintenance Modeling
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Mathematics in Advanced Reliability and Maintenance Modeling

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 2124

Special Issue Editors

Prof. Dr. Tadashi Dohi

E-Mail Website
Guest Editor
Graduate School of Advanced Science and Engineering, School of Informatics and Data Sciences, Hiroshima University, 1-4-1 Kagamiyama, Higashihiroshima 7398527, Japan
Interests: stochastic model; reliability and maintenance; performance evaluation
Special Issues, Collections and Topics in MDPI journals
Dr. Junjun Zheng

E-Mail Website
Guest Editor
Graduate School of Advanced Science and Engineering, School of Informatics and Data Sciences, Hiroshima University, 1-4-1 Kagamiyama, Higashihiroshima 7398527, Japan
Interests: software reliability; dependable computing; performance evaluation; computer security
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Xufeng Zhao

E-Mail Website
Guest Editor
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Interests: probability theory; stochastic process; reliability and maintenance theory; applications in computer and industrial systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As technological advancements like cloud computing and AI evolve, they bring new challenges to maintaining and ensuring the reliability, security, and availability of these systems. Especially mathematical aspects play a central role in the development of reliability and maintenance modelling and spread to several areas such as optimization algorithms, stochastic processes, statistical inference, and machine learning, among others. This Special Issue, “Mathematics in Advanced Reliability and Maintenance Modeling”, aims to highlight innovative research, practical challenges, and advanced methodologies in terms of applied mathematics. Our purpose is to share advanced knowledge and information related to reliability and maintenance. In fact, reliability and maintenance are the fundamental technologies required in various fields, such as power systems, communication networks, transportation, cloud computing, electronic systems, buildings and infrastructure, medical and healthcare, and aviation and railway systems. We hope that this Special Issue will provide and explore solutions to the various reliability challenges facing society.

Topics of interest include (but are not limited to) the following: manufacturing system reliability; software reliability and testing communication systems; reliability modeling human reliability; Bayesian reliability; fuzzy reliability network reliability and optimization; safety and risk assessment; cyber security; security issues; internet reliability engineering; service and reliability; estimation and statistical testing; survival analysis; warranty analysis; resilience; computer system dependability; design for six sigma; fault-tolerant computing; maintenance optimization; maintainability and availability; reliability physics; accelerated degradation testing; accelerated life testing; big data; data mining and analytics; diagnostics; condition monitoring; engineering asset management; machine health assessment; and dynamic reliability analysis.

We expect the high-quality submissions that were presented at the 11th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM2024) held in Nagoya, Japan, on August 26–30, 2024, but the presentation at the symposium is not mandatory for the submission to this Special Issue. If the paper is accepted, then the authors are requested to cover the APC in MDPI. For the best-quality papers evaluated by the Guest Editors, MDPI will give a token of a 100% discount for the top 10 high-quality papers. The submission deadline is November 30, 2024.

Prof. Dr. Tadashi Dohi
Dr. Junjun Zheng
Prof. Dr. Xufeng Zhao
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • manufacturing system reliability
  • software reliability and testing
  • communication systems
  • reliability modeling human reliability
  • Bayesian reliability
  • fuzzy reliability
  • network reliability and optimization
  • safety and risk assessment
  • cybersecurity
  • security issues
  • internet reliability engineering
  • service and reliability
  • estimation and statistical testing
  • survival analysis
  • warranty analysis
  • resilience
  • computer systems dependability
  • design for six sigma
  • fault-tolerant computing
  • maintenance optimization
  • maintainability and availability
  • reliability physics
  • accelerated degradation testing
  • accelerated life testing
  • big data
  • data mining and analytics
  • diagnostics
  • condition monitoring
  • engineering asset management
  • machine health assessment
  • dynamic reliability analysis.

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Published Papers (3 papers)

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Research

23 pages, 1229 KiB  
Article
Structural Properties of Optimal Maintenance Policies for k-out-of-n Systems with Interdependence Between Internal Deterioration and External Shocks
by Mizuki Kasuya and Lu Jin
Mathematics 2025, 13(5), 716; https://doi.org/10.3390/math13050716 - 23 Feb 2025
Cited by 1 | Viewed by 331
Abstract
Many modern engineering systems, such as offshore wind turbines, rely on k-out-of-n configurations to ensure reliability. These systems are exposed to both internal deterioration and external shocks, which can significantly impact operational efficiency and maintenance costs, necessitating optimal maintenance policies. This [...] Read more.
Many modern engineering systems, such as offshore wind turbines, rely on k-out-of-n configurations to ensure reliability. These systems are exposed to both internal deterioration and external shocks, which can significantly impact operational efficiency and maintenance costs, necessitating optimal maintenance policies. This study investigates an optimal condition-based maintenance policy for a k-out-of-n system, where each unit deteriorates independently following a gamma process and is subject to random external shocks that cause sudden jumps in deterioration. This study considers (1) stochastic dependencies among units, where shock-induced cumulative deterioration in one unit affects others, and (2) interdependencies between external shocks and internal deterioration, where internal deterioration influences external factors and vice versa. Using a Markov decision process framework, we derive an optimal maintenance policy that minimizes expected maintenance costs while incorporating these interdependencies. Under reasonable assumptions, we establish key structural properties of the optimal policy, enabling its efficient identification. A case study on offshore wind turbines demonstrates the effectiveness of the proposed approach, achieving up to a 9.9% reduction in maintenance costs compared to alternative policies. This cost reduction is achieved by optimizing the timing of preventive maintenance while incorporating the two aforementioned types of dependence into the decision-making process. Sensitivity analyses further explore the effects of cost parameters, deterioration rates, and shock characteristics, offering valuable insights into designing maintenance strategies for systems influenced by shocks and interdependent deterioration. Full article
(This article belongs to the Special Issue Mathematics in Advanced Reliability and Maintenance Modeling)
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18 pages, 947 KiB  
Article
Joint Optimal Policy for Maintenance, Spare Unit Selection and Inventory Control Under a Partially Observable Markov Decision Process
by Nozomu Ogura, Mizuki Kasuya and Lu Jin
Mathematics 2025, 13(3), 406; https://doi.org/10.3390/math13030406 - 26 Jan 2025
Cited by 1 | Viewed by 562
Abstract
This research investigates the joint optimization of maintenance and spare unit management for series systems composed of multiple heterogeneous units. With advancements in communication and sensing technologies, condition-based maintenance has gained attention as an integral aspect of spare unit management. Furthermore, the inherent [...] Read more.
This research investigates the joint optimization of maintenance and spare unit management for series systems composed of multiple heterogeneous units. With advancements in communication and sensing technologies, condition-based maintenance has gained attention as an integral aspect of spare unit management. Furthermore, the inherent interaction between maintenance activities and spare unit management underscores the necessity of their simultaneous optimization to enhance overall system performance. Based on uncertain information about the system’s deterioration state and spare unit inventory, decision-makers determine actions related to spare units and maintenance, such as replacements, selection of spare units for corresponding units, order quantities and inventory levels. Within the framework of a partially observable Markov decision process, this research proposes an optimal joint policy for maintenance and spare unit management with the objective of minimizing total expected costs. The proposed policy is demonstrated through a three-state, two-unit series system. Sensitivity analyses and comparisons with benchmark policies are also conducted to evaluate the performance of the proposed policy and to investigate the impact of various cost parameters on the proposed decisions. Full article
(This article belongs to the Special Issue Mathematics in Advanced Reliability and Maintenance Modeling)
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28 pages, 1423 KiB  
Article
Directional Handover Analysis with Stochastic Petri Net and Poisson Point Process in Heterogeneous Networks
by Zhiyi Zhu, Junjun Zheng, Eiji Takimoto, Patrick Finnerty and Chikara Ohta
Mathematics 2025, 13(3), 349; https://doi.org/10.3390/math13030349 - 22 Jan 2025
Viewed by 757
Abstract
Handover is crucial for ensuring seamless connectivity in heterogeneous networks (HetNet) by enabling user equipment (UE) to switch its connection link between cells based on signal conditions. However, conventional analytical approaches ignored the distinctions between macro-cell to small-cell (M2S) and small-cell to macro-cell [...] Read more.
Handover is crucial for ensuring seamless connectivity in heterogeneous networks (HetNet) by enabling user equipment (UE) to switch its connection link between cells based on signal conditions. However, conventional analytical approaches ignored the distinctions between macro-cell to small-cell (M2S) and small-cell to macro-cell (S2M) scenarios during a handover decision-making process, which resulted in handover failures (HoF) or ping-pong handovers. Therefore, this paper proposes a novel framework, Do-SPN-PPP, that combines stochastic Petri net (SPN) and the Poisson point process (PPP) to quantitatively analyze M2S and S2M handover performance differences. The proposed framework also reveals and predicts how handover parameters affect UE residence time in a cell within the HetNet, and it exhibits a higher predictive accuracy compared with the traditional conventional analytical approach. In addition, the Monte Carlo simulation verified the Do-SPN-PPP framework, and the proposed framework exhibits a 96% reduction in computation time while maintaining a 95% confidence interval and 0.5% error tolerance compared with the simulation. Full article
(This article belongs to the Special Issue Mathematics in Advanced Reliability and Maintenance Modeling)
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