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

Jingjing Xu, Qiaobin Yan, Yanhu Pei, Zhifeng Liu, Qiang Cheng, Hongyan Chu and Tao Zhang ()
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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
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

Mathematics, 2024, vol. 12, issue 9, 1-22

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.

Keywords: reliability evaluation; Weibull distribution; multi-state failures; small-sample expansion; fuzzy evaluation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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