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Bayesian reliability modeling and assessment solution for NC machine tools under small-sample data

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Abstract

Although Markov chain Monte Carlo(MCMC) algorithms are accurate, many factors may cause instability when they are utilized in reliability analysis; such instability makes these algorithms unsuitable for widespread engineering applications. Thus, a reliability modeling and assessment solution aimed at small-sample data of numerical control(NC) machine tools is proposed on the basis of Bayes theories. An expert-judgment process of fusing multi-source prior information is developed to obtain the Weibull parameters’ prior distributions and reduce the subjective bias of usual expert-judgment methods. The grid approximation method is applied to two-parameter Weibull distribution to derive the formulas for the parameters’ posterior distributions and solve the calculation difficulty of high-dimensional integration. The method is then applied to the real data of a type of NC machine tool to implement a reliability assessment and obtain the mean time between failures(MTBF). The relative error of the proposed method is 5.8020×10-4 compared with the MTBF obtained by the MCMC algorithm. This result indicates that the proposed method is as accurate as MCMC. The newly developed solution for reliability modeling and assessment of NC machine tools under small-sample data is easy, practical, and highly suitable for widespread application in the engineering field; in addition, the solution does not reduce accuracy.

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Author information

Authors and Affiliations

  1. College of Mechanical Science and Engineering, Jilin University, Changchun, 130025, China

    Zhaojun Yang, Yingnan Kan, Fei Chen, Binbin Xu, Chuanhai Chen & Chuangui Yang

  2. Key Laboratory of CNC Equipment Reliability Technique of Machinery Industry, Jilin University, Changchun, 130025, China

    Zhaojun Yang, Yingnan Kan, Fei Chen, Binbin Xu & Chuanhai Chen

Authors
  1. Zhaojun Yang
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  2. Yingnan Kan
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  3. Fei Chen
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  4. Binbin Xu
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  5. Chuanhai Chen
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  6. Chuangui Yang
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Corresponding author

Correspondence to Fei Chen.

Additional information

Supported by Research on Reliability Assessment and Test Methods of Heavy Machine Tools, China(State Key Science & Technology Project High-grade NC Machine Tools and Basic Manufacturing Equipment, Grant No. 2014ZX04014-011), Reliability Modeling of Machining Centers Considering the Cutting Loads, China(Science & Technology Development Plan for Jilin Province, Grant No. 3D513S292414), and Graduate Innovation Fund of Jilin University, China(Grant No. 2014053)

YANG Zhaojun, born in 1956, is currently a professor at College of Mechanical Science and Engineering, Jilin University, China. He received his PhD degree from Jilin University, China, in 1995. His research interests include reliability techniques and theories of CNC equipment.

KAN Yingnan, born in 1985, is currently a PhD candidate at College of Mechanical Science and Engineering, Jilin University, China. He received his master’s degree from Jilin University, China, in 2009. His research interests include reliability modeling methods of CNC equipment and Bayesian reliability theory.

CHEN Fei, born in 1970, is currently an associate professor at College of Mechanical Science and Engineering, Jilin University, China. She received her PhD degree from Jilin University, China, in 2009. Her research interests include reliability techniques and theories of CNC equipment.

XU Binbin, born in 1982, is currently a lecturer at Jilin University, China. She received her PhD degree from Jilin University, China, in 2011. Her research interests include reliability techniques and theories of CNC equipment.

CHEN Chuanhai, born in 1983, is currently a lecturer at Jilin University, China. He received his PhD degree from Jilin University, China, in 2013. His research interests include reliability techniques and theories of CNC equipment.

YANG Chuangui, born in 1987, is currently a master candidate at College of Mechanical Science and Engineering, Jilin University, China. He received his bachelor’s degree from Jilin University, China, in 2012.

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Yang, Z., Kan, Y., Chen, F. et al. Bayesian reliability modeling and assessment solution for NC machine tools under small-sample data. Chin. J. Mech. Eng. 28, 1229–1239 (2015). https://doi.org/10.3901/CJME.2015.0707.088

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