IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i9p1414-d1389163.html
   My bibliography  Save this article

A Statistical Evaluation Method Based on Fuzzy Failure Data for Multi-State Equipment Reliability

Author

Listed:
  • Jingjing Xu

    (Institute of Advanced Manufacturing and Intelligent Technology, Beijing University of Technology, Beijing 100124, China)

  • Qiaobin Yan

    (Institute of Advanced Manufacturing and Intelligent Technology, Beijing University of Technology, Beijing 100124, China)

  • Yanhu Pei

    (China National Machine Tool Quality Supervision Testing Center, Beijing 101312, China)

  • Zhifeng Liu

    (Institute of Advanced Manufacturing and Intelligent Technology, Beijing University of Technology, Beijing 100124, China
    Key Laboratory of CNC Equipment Reliability, Ministry of Education, Jilin University, Changchun 130025, China
    Key Laboratory of Advanced Manufacturing and Intelligent Technology for High-End CNC Equipment, Changchun 130025, China)

  • Qiang Cheng

    (Institute of Advanced Manufacturing and Intelligent Technology, Beijing University of Technology, Beijing 100124, China)

  • Hongyan Chu

    (Institute of Advanced Manufacturing and Intelligent Technology, Beijing University of Technology, Beijing 100124, China)

  • Tao Zhang

    (Institute of Advanced Manufacturing and Intelligent Technology, Beijing University of Technology, Beijing 100124, China)

Abstract

For complex equipment, it is easy to over-evaluate the impact of failure on production by estimating the reliability level only through failure probability. To remedy this problem, this paper proposes a statistical evaluation method based on fuzzy failure data considering the multi-state characteristics of equipment failures. In this method, the new reliability-evaluation scheme is firstly presented based on the traditional statistical analysis method using the Weibull distribution function. For this scheme, the failure-grade index is defined, and a fuzzy-evaluation method is also proposed by comprehensively considering failure severity, failure maintenance, time, and cost; this is then combined with the time between failures to characterize the failure state. Based on the fuzzy failure data, an improved adaptive-failure small-sample-expansion method is proposed based on the classical bootstrap method and the deviation judgment between distributions of the original and newborn samples. Finally, a novel reliability-evaluation model, related to the failure grade and its membership degree, is established to quantify the reliability level of equipment more realistically. Example cases for three methods of the scheme (the failure-grade fuzzy-evaluation method, the sample-expansion method, and the reliability-evaluation modeling method) are presented, respectively, to validate the effectiveness and significance of the proposed reliability-evaluation technology.

Suggested Citation

  • Jingjing Xu & Qiaobin Yan & Yanhu Pei & Zhifeng Liu & Qiang Cheng & Hongyan Chu & Tao Zhang, 2024. "A Statistical Evaluation Method Based on Fuzzy Failure Data for Multi-State Equipment Reliability," Mathematics, MDPI, vol. 12(9), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1414-:d:1389163
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/9/1414/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/9/1414/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ping-Chen Chang, 2022. "Reliability evaluation and big data analytics architecture for a stochastic flow network with time attribute," Annals of Operations Research, Springer, vol. 311(1), pages 3-18, April.
    2. Honggang Zhang & Jingyong Su & Linlin Tang & Anuj Srivastava, 2023. "Elastic statistical analysis of interval-valued time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 50(1), pages 60-85, January.
    3. Luo, Chunling & Shen, Lijuan & Xu, Ancha, 2022. "Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Amel Abd-El-Monem & Mohamed S. Eliwa & Mahmoud El-Morshedy & Afrah Al-Bossly & Rashad M. EL-Sagheer, 2023. "Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    2. Xiaoyu Shi & Hanyu Zhang & Guanjie Wang, 2024. "ANOVA-GP Modeling for High-Dimensional Bayesian Inverse Problems," Mathematics, MDPI, vol. 12(2), pages 1-18, January.
    3. Kowal, Karol, 2022. "Lifetime reliability and availability simulation for the electrical system of HTTR coupled to the electricity-hydrogen cogeneration plant," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    4. Liang Wang & Sanku Dey & Yogesh Mani Tripathi, 2022. "Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    5. Wang, Jiaolong & Zhang, Fode & Zhang, Jianchuan & Liu, Wen & Zhou, Kuang, 2023. "A flexible RUL prediction method based on poly-cell LSTM with applications to lithium battery data," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    6. Wenying Zeng & Songbai Song & Yan Kang & Xuan Gao & Rui Ma, 2022. "Response of Runoff to Meteorological Factors Based on Time-Varying Parameter Vector Autoregressive Model with Stochastic Volatility in Arid and Semi-Arid Area of Weihe River Basin," Sustainability, MDPI, vol. 14(12), pages 1-12, June.
    7. Jin, Yuxue & Geng, Jie & Lv, Chuan & Chi, Ying & Zhao, Tingdi, 2023. "A methodology for equipment condition simulation and maintenance threshold optimization oriented to the influence of multiple events," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    8. Raydonal Ospina & João A. M. Gondim & Víctor Leiva & Cecilia Castro, 2023. "An Overview of Forecast Analysis with ARIMA Models during the COVID-19 Pandemic: Methodology and Case Study in Brazil," Mathematics, MDPI, vol. 11(14), pages 1-18, July.
    9. Yan, Weian & Xu, Xiaofan & Bigaud, David & Cao, Wenqin, 2023. "Optimal design of step-stress accelerated degradation tests based on the Tweedie exponential dispersion process," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    10. Haiping Ren & Xue Hu, 2023. "Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution," Mathematics, MDPI, vol. 11(11), pages 1-16, May.
    11. Alotaibi, Naif M. & Scarf, Philip & Cavalcante, Cristiano A.V. & Lopes, Rodrigo S. & de Oliveira e Silva, André Luiz & Rodrigues, Augusto J.S. & Alyami, Salem A., 2023. "Modified-opportunistic inspection and the case of remote, groundwater well-heads," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    12. Ding, Wanmeng & Li, Jimeng & Mao, Weilin & Meng, Zong & Shen, Zhongjie, 2023. "Rolling bearing remaining useful life prediction based on dilated causal convolutional DenseNet and an exponential model," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    13. Zhang, Shuyi & Zhai, Qingqing & Li, Yaqiu, 2023. "Degradation modeling and RUL prediction with Wiener process considering measurable and unobservable external impacts," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    14. Essam A. Ahmed & Mahmoud El-Morshedy & Laila A. Al-Essa & Mohamed S. Eliwa, 2023. "Statistical Inference on the Entropy Measures of Gamma Distribution under Progressive Censoring: EM and MCMC Algorithms," Mathematics, MDPI, vol. 11(10), pages 1-30, May.
    15. Wang, Han & Liao, Haitao & Ma, Xiaobing, 2022. "Stochastic Multi-phase Modeling and Health Assessment for Systems Based on Degradation Branching Processes," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    16. Huda M. Alshanbari & Zubair Ahmad & Hazem Al-Mofleh & Clement Boateng Ampadu & Saima K. Khosa, 2023. "A New Probabilistic Approach: Estimation and Monte Carlo Simulation with Applications to Time-to-Event Data," Mathematics, MDPI, vol. 11(7), pages 1-30, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1414-:d:1389163. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.