Abstract
Reliability modeling and assessment for a single numerical control (NC) machine tool with zero-failure is a new problem that cannot be solved using classic statistical methods. Thus a Bayesian method is proposed aiming at this problem. In combination with the two-parameter Weibull distribution, the Bayes model of zero-failure problem for a single NC machine tool is built. The method of building the Weibull parameters’ prior distributions is presented. The theoretical formula for the parameter vector’s posterior distribution is derived. In software WinBUGS, the Markov chain Monte Carlo (MCMC) simulation is developed to simulate each parameter’s posterior distribution, solving calculation difficulties in high-dimensional integration and parameter estimation. The proposed method is applied to real data, obtaining the parameter estimators and meant time between failures (MTBF). The result is in consistent with the engineering reality. Given the fact that the actual MTBF cannot be achieved by any means, the proposed method achieves the fusion of the expert experience, multi-source prior information and data. The proposed method is advocated to be a standard solution to the zero-failure reliability assessment for NC machine tools.
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References
Keller, A.Z., Kamath, A.R.R., Perera, U.D.: Reliability analysis of CNC machine tools. Reliab. Eng. 3(6), 449–473 (1982)
Yang, Z.J., Chen, C.H., Chen, F., et al.: Reliability analysis of machining center based on the field data. Eksploatacja i Niezawodność 15(2), 147–155 (2013)
Martz, H.F., Waller, R.A.: A Bayesian zero-failure reliability demonstration testing procedure. J. Qual. Technol. 11, 128–138 (1979)
Coolen, F.P.A., Coolen-Schrijner, P., Rahrouh, M.: Bayesian reliability demonstration for failure-free periods. Reliab. Eng. Syst. Saf. 88(1), 81–91 (2005)
Fan, T.H., Chang, C.C.: A Bayesian Zero-failure reliability demonstration test of high quality electro-explosive devices. Qual. Reliab. Eng. Int. 25(8), 913–920 (2009)
Miller, K.W., Morell, L.J., Noonan, R.E., et al.: Estimating the probability of failure when testing reveals no failures. IEEE Trans. Softw. Eng. 18(1), 33–43 (1992)
Guo, H., Honecker, S., Mettas, A., et al.: Reliability estimation for one-shot systems with zero component test failures. In: 2010 Proceedings-Annual Reliability and Maintainability Symposium, pp. 1–7. IEEE (2010)
Mao, S.S., Xia, J.F.: The hierarchical Bayesian analysis of the zero-failure data. Appl. Math. 7, 411–421 (1992)
Jia, Y.Z., Wang, M.L., Jia, Z.X.: Probability distribution of machining center failures. Reliab. Eng. Syst. Saf. 50(1), 121–125 (1995)
Soland, R.M.: Bayesian analysis of the Weibull process with unknown scale and shape parameters. IEEE Trans. Reliab. 18(4), 181–184 (1969)
Hamada, M.S., Wilson, A.G., Reese, C.S., et al.: Bayesian Reliability. Springer, New York (2008)
Neal, R.M.: Slice sampling. Ann. Stat. 31(3), 705–767 (2003)
Zhang, L.F., Xie, M., Tang, L.C.: A study of two estimation approaches for parameters of Weibull distribution based on WPP. Reliab. Eng. Syst. Saf. 92(3), 360–368 (2007)
Lunn, D., Jackson, C., Best, N., et al.: The BUGS Book: A Practical Introduction to Bayesian Analysis. CRC Press, Boca Raton (2012)
Acknowledgments
The work is supported by The Science and Technology Development Program of Jilin Province(20130302009GX) and Project of Priority Funding for Basic Scientific Research Business of Jilin University(450060521026).
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Li, H., Chen, F., Yang, Z., Kan, Y., Wang, L. (2015). Bayesian Reliability Assessment Method for Single NC Machine Tool Under Zero Failures. In: Niu, W., et al. Applications and Techniques in Information Security. ATIS 2015. Communications in Computer and Information Science, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48683-2_26
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DOI: https://doi.org/10.1007/978-3-662-48683-2_26
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