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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
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    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).
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