Skip to main content
SpringerLink
Log in

A new inherent reliability modeling and analysis method based on imprecise Dirichlet model for machine tool spindle

  • S.I.: Reliability Modeling with Applications Based on Big Data
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

A Correction to this article was published on 15 October 2019

This article has been updated

Abstract

The factors that influence the inherent reliability of machine tool spindle are a mixture of various uncertainties and it leads that the reliability modeling and analysis of machine tool spindle can’t be dealt with by one mathematical theory. Meanwhile, the reliability data of the machine tool spindle for reliability modeling and analysis is often insufficient, and data of different types such as accumulated historical data, expert opinions, simulation data, etc. are used to make up for the lack of data. Thus, the unified quantification of mixed uncertainties and the data characterization of different types are the major premises for reliability modeling and analysis of machine tool spindle. By considering this, this paper makes use of the advantage of imprecise probability theory in quantizing the multiple types of data and the advantage of the Bayes theory in data fusion, and proposes a new inherent reliability modeling and analysis method based on imprecise Dirichlet model. In the proposed method, imprecise probability theory is used to quantify mixed uncertainties, imprecise Dirichlet model is built to characterize the different types of reliability data. After analyzing the inherent reliability variation regularity, an inherent reliability model is built, and the proposed method is verified by the inherent reliability calculation of a certain heavy-duty CNC machine tool’s milling spindle. This study can provide new method, theory and reference for reliability modeling and analysis when there are various uncertainties mixed and multiple data existed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Change history

References

  • Bernard, J. M. (2005). An introduction to the imprecise Dirichlet model for multinomial data. International Journal of Approximate Reasoning, 39(2–3), 123–150.

    Article  Google Scholar 

  • Dey, S., Sharma, V. K., Anis, M. Z., & Yadav, B. (2017). Assessing lifetime performance index of Weibull distributed products using progressive type II right censored samples. International Journal of System Assurance Engineering and Management, 8(2), 318–333.

    Google Scholar 

  • Fox, C., & Parker, A. (2017). Accelerated Gibbs sampling of normal distributions using matrix splittings and polynomials. Bernoulli, 23(4B), 3711–3743.

    Article  Google Scholar 

  • Guo, T., & Xu, Z. L. (2018). Data fusion of multi-scale representations for structural damage detection. Mechanical Systems and Signal Processing, 98, 1020–1033.

    Article  Google Scholar 

  • Gupta, Y. P., & Somers, T. M. (1989). Availability of CNC machines: Multiple-input transfer-function modeling. IEEE Transactions on Reliability, 38(3), 285–295.

    Article  Google Scholar 

  • Huang, H. Z., Liu, Z., Peng, W., Li, Y. F., & Mi, J. H. (2015). Study on reliability evaluation index system of NC machine tools. Manufacturing Technology & Machine Tool, 7, 71–77.

    Google Scholar 

  • Jana, N., Kumar, S., & Chatterjee, K. (2016). Bayes estimation for exponential distributions with common location parameter and applications to multi-state reliability models. Journal of Applied Statistics, 43(15), 2697–2712.

    Article  Google Scholar 

  • Jia, Z. X., Zhang, H. B., & Xi, A. M. (2011). Expanding reliability data of NC machine tool based on neural network. Journal of Jilin University, 41(2), 403–407.

    Google Scholar 

  • Kun, K., & Li, X. G. (2014). Bayesian evaluation method for binomial system reliability growth. Journal of Beijing University of Aeronautics and Astronautics, 40(9), 1312–1316.

    Google Scholar 

  • Lee, D., & Pan, R. (2018). A nonparametric Bayesian network approach to assessing system reliability at early design stages. Reliability Engineering & System Safety, 171, 57–66.

    Article  Google Scholar 

  • Li, G. Y., Wu, Q. G., & Zhao, Y. H. (2002). On Bayesian analysis of binomial reliability growth. Journal of the Japan Statistical Society, 32(1), 1–14.

    Article  Google Scholar 

  • Li, H., Huang, H. Z., Li, Y. F., Zhou, J., & Mi, J. H. (2018a). Physics of failure-based reliability prediction of turbine blades using multi-source information fusion. Applied Soft Computing, 72, 624–635.

    Article  Google Scholar 

  • Li, X. P., Huang, H. Z., Li, F. Q., & Chen, L. (2017). A new method for astronautically phased mission system reliability assessment based on multi-source data fusion. In New York (Ed.), Proceedings of 2017 prognostics and system health management conference.

  • Li, X. Y., Huang, H. Z., & Li, Y. F. (2018b). Reliability analysis of phased mission system with non-exponential and partially repairable components. Reliability Engineering & System Safety, 175, 119–127.

    Article  Google Scholar 

  • Li, Y. F., Mi, J. H., Liu, Y., Yang, Y. J., & Huang, H. Z. (2015). Dynamic fault tree analysis based on continuous-time Bayesian networks under fuzzy numbers. Proceedings of the Institution of Mechanical Engineers, Part O, Journal of Risk and Reliability, 229(6), 530–541.

    Article  Google Scholar 

  • Liu, X. C., & Luger, R. (2017). Markov-switching quantile autoregression: A Gibbs sampling approach. Studies in Nonlinear Dynamics & Econometrics, 22(2), 1–10.

    Google Scholar 

  • Liu, Z., & Liu, X. (2018). An improved approach by introducing copula functions for structural reliability analysis under hybrid uncertainties. Advances in Mechanical Engineering, 10(7), 1–10.

    Google Scholar 

  • Mi, J. H., Li, Y. F., Peng, W., & Huang, H. Z. (2018). Reliability analysis of complex multi-state system with common cause failure based on evidential networks. Reliability Engineering & System Safety, 174, 71–81.

    Article  Google Scholar 

  • Mi, J. H., Li, Y. F., Yang, Y. J., Peng, W., & Huang, H. Z. (2016). Reliability assessment of complex electromechanical systems under epistemic uncertainty. Reliability Engineering & System Safety, 152, 1–15.

    Article  Google Scholar 

  • Ming, Z. M. (2009). Research on reliability synthetical assessment and qualification based on Bayes analysis of dynamic distribution parameter. Changsha: National University of Defense Technology.

    Google Scholar 

  • Ming, Z. M., Ling, X. D., & Bai, X. S. (2016). The Bayesian reliability assessment and prediction for radar system based on new Dirichlet prior distribution. Journal of Physics: Conference Series, 679, 1–11.

    Google Scholar 

  • Utkin, L. V., & Coolen, F. P. A. (2007). Imprecise reliability: An introductory overview. Computational Intelligence in Reliability Engineering, 40, 261–306.

    Article  Google Scholar 

  • Zhang, H. B., Jia, Y. Z., & Zhou, G. W. (2005). Time between failures distribution model of CNC system. Journal of Harbin Institute of Technology, 37(2), 198–200.

    Google Scholar 

  • Zhang, J. P., Cui, S. C., Cai, J., Pei, J. Z., & Jia, Y. S. (2018a). Life-cycle reliability evaluation of semi-rigid materials based on modulus degradation model. KSCE Journal of Civil Engineering, 22(6), 2043–2054.

    Article  Google Scholar 

  • Zhang, K. N. (2015a). Research on modeling and applications of life circle failure process of CNC machine. Chongqing: Chongqing University.

    Google Scholar 

  • Zhang, X. G. (2016). Research on reliability data related technology of CNC machine tools. Chongqing: Chongqing University.

    Google Scholar 

  • Zhang, X., Gao, H., Huang, H. Z., Li, Y. F., & Mi, J. (2018b). Dynamic reliability modeling for system analysis under complex load. Reliability Engineering & System Safety, 180, 345–351.

    Article  Google Scholar 

  • Zhang, Z. H. (2015b). Visualization playback of historical data and reliability evaluation of CNC machine tools. Wuhan: Huazhong University of Science and Technology.

    Google Scholar 

  • Zhu, S. P., Liu, Q., Peng, W., & Zhang, X. C. (2018a). Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks. International Journal of Mechanical Sciences, 142–143, 502–517.

    Article  Google Scholar 

  • Zhu, S. P., Liu, Q., Zhou, J., & Yu, Z. Y. (2018b). Fatigue reliability assessment of turbine discs under multi-source uncertainties. Fatigue and Fracture of Engineering Materials and Structures, 41(6), 1291–1305.

    Article  Google Scholar 

Download references

Acknowledgements

The research of Prof. Zhongwei Liang was supported by the Innovative Academic Team Project of Guangzhou Education System (1201610013) and the Innovative Team Project of Guangdong Universities (2017KCXTD025). The research of Dr. Zheng Liu was supported by the Guangzhou University Teaching Reform Project (09-18ZX0309). The research of Dr. Xin Liu was supported by the Guangzhou University Teaching Reform Project (09-18ZX0304). The research of Prof. Pingyu Zhu was supported by Science and Technology Fund of Guangzhou City (201504291326362).

Author information

Authors and Affiliations

  1. Guangzhou University, Guangzhou, 510006, Guangdong, China

    Zheng Liu, Xin Liu, Pingyu Zhu & Zhongwei Liang

  2. University of Electronic Science and Technology of China, Chengdu, 610054, Sichuan, China

    Hong-Zhong Huang

Authors
  1. Zheng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hong-Zhong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pingyu Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhongwei Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xin Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Z., Liu, X., Huang, HZ. et al. A new inherent reliability modeling and analysis method based on imprecise Dirichlet model for machine tool spindle. Ann Oper Res 311, 295–310 (2022). https://doi.org/10.1007/s10479-019-03333-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-019-03333-9

Keywords

Search

Navigation