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Reliability evaluation of the servo turret with accurate failure data and interval censored data based on EM algorithm

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Abstract

The servo turret is a complex electromechanical hydraulic component that is the most likely to fail in a numerical control lathe. Reliability evaluation is used to make statistical inferences about the reliability characteristics of products according to all the information related to product reliability. Failure data is the basis of reliability evaluation; however, it is very difficult to collect many accurate failure data for reliability evaluation. In this paper, the reliability of servo turret is evaluated based on failure data that contains accurate failure data and interval censored data. First, a mixture Weibull distribution is chosen for fitting the reliability model. Then, expectation-maximization algorithm is used for estimating the parameters of the distribution which contains hidden variable, and the confidence interval of parameters is constructed using the delta method. In the simulation, different percentages of accurate data and interval data are used and compared with data containing only accurate data. The accuracy of this method is evaluated by mean square error. Finally, the method is applied to the failure data of servo turret and the parameters of mixture Weibull distribution are determined. For possibly simplifying the mixed Weibull distribution, the hypothesis of shape or scale parameters being equal is tested. The hazard property and mean time between failure are then estimated and associated 95 % confidence intervals are obtained.

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Abbreviations

FMECA :

Failure mode, effects and criticality analysis

CNC :

Computer numerical control

EM :

Expectation-maximization

MTBF :

Mean time between failure

MLE :

Maximum likelihood estimate

MSE :

Mean square error

CI :

Confidence Intervals

CDF :

Cumulative distribution function

PDF :

Probability density function

N :

Sample size

p a :

Percentage of accurate data

p c :

Percentage of interval censored data

References

  1. C. Duan, C. Deng and N. Li, Reliability assessment for CNC equipment based on degradation data, The International Journal of Advanced Manufacturing Technology, 100 (1-4) (2019) 421–434.

    Article  Google Scholar 

  2. H. Li, Z. Yang, B. Xu, C. Chen, Y. Kan and G. Liu, Reliability evaluation of NC machine tools considering working conditions, Mathematical Problems in Engineering (2016).

    Google Scholar 

  3. X. He, Recent development in reliability analysis of NC machine tools, The International Journal of Advanced Manufacturing Technology, 85 (1-4) (2016) 115–131.

    Article  Google Scholar 

  4. L. ChAngyou, W. Wei, Z. Yimin, G. Song, L. Zhenyuan and Q. Changshuai, Indexing accuracy reliability sensitivity analysis of power tool turret, Eksploatacja i Niezawodność, 17 (2015).

  5. Y. Wang, R. C. Yam, M. J. Zuo and P. Tse, A comprehensive reliability allocation method for design of CNC lathes, Reliability Engineering & System Safety, 72(3) (2001) 247–252.

    Article  Google Scholar 

  6. Z. Yang, C. Chen, F. Chen and G. Li, Progress in the research of reliability technology of machine tools, Journal of Mechanical Engineering, 49(20) (2013) 130–139.

    Article  Google Scholar 

  7. J. Yazhou, W. Molin and J. Zhixin, Probability distribution of machining center failures, Reliability Engineering & System Safety, 50(1) (1995) 121–125.

    Article  Google Scholar 

  8. D. Chen, T. Wang and H. Wei, Sectional model involving two Weibull distributions for CNC lathe failure probability, Journal of Beijing University of Aeronautics and Astronautics, 31(7) (2005) 766–769.

    Google Scholar 

  9. Y. Dai, Y. F. Zhou and Y. Z. Jia, Distribution of time between failures of machining center based on type I censored data, Reliability Engineering & System Safety, 79(3) (2003) 377–379.

    Article  Google Scholar 

  10. N. Balakrishnan and D. Mitra, Left truncated and right censored Weibull data and likelihood inference with an illustration, Computational Statistics & Data Analysis, 56(12) (2012) 4011–4025.

    Article  MathSciNet  Google Scholar 

  11. S. Maximov, V. H. Coria, F. Rivas-Davalos, R. Escarela-Perez and J. C. Olivares-Galvan, New analytical method for estimating mean life of electric power equipment based on complete and right-censored failure data, Electric Power Systems Research, 154 (2018) 311–318.

    Article  Google Scholar 

  12. X. Bai, Y. Shi, Y. Liu and B. Liu, Reliability estimation of stress-strength model using finite mixture distributions under progressively interval censoring, Journal of Computational and Applied Mathematics, 348 (2019) 509–524.

    Article  MathSciNet  Google Scholar 

  13. E. F. Alsina, M. Chica, K. Trawiński and A. Regattieri, On the use of machine learning methods to predict component reliability from data-driven industrial case studies, The International Journal of Advanced Manufacturing Technology, 94 (5-8) (2018) 2419–2433.

    Article  Google Scholar 

  14. Y. N. Kan, Z. J. Yang, G. F. Li, J. L. He, Y. K. Wang and H. Z. Li, Bayesian zero-failure reliability modeling and assessment method for multiple numerical control (NC) machine tools, Journal of Central South University, 23(11) (2016) 2858–2866.

    Article  Google Scholar 

  15. P. Schlattmann, Estimating the number of components in a finite mixture model: The special case of homogeneity, Computational Statistics & Data Analysis, 41 (3–4) (2003) 441–451.

    Article  MathSciNet  Google Scholar 

  16. T. Zhan, I. Chevoneva and B. Iglewicz, Generalized weighted likelihood density estimators with application to finite mixture of exponential family distributions, Computational Statistics & Data Analysis, 55(1) (2011) 457–465.

    Article  MathSciNet  Google Scholar 

  17. Y. Abdel-Aty, Bayesian prediction of future number of failures based on finite mixture of general class of distributions, Statistics, 46(1) (2012) 111–122.

    Article  MathSciNet  Google Scholar 

  18. J. F. Castet and J. H. Saleh, Single versus mixture Weibull distributions for nonparametric satellite reliability, Reliability Engineering & System Safety, 95(3) (2010) 295–300.

    Article  Google Scholar 

  19. S. Bi, M. Broggi and M. Beer, The role of the Bhattacharyya distance in stochastic model updating, Mechanical Systems and Signal Processing, 117 (2019) 437–452.

    Article  Google Scholar 

  20. N. Balakrishnan and S. Pal, Expectation maximization-based likelihood inference for flexible cure rate models with Weibull lifetimes, Statistical Methods in Medical Research, 25(4) (2016) 1535–1563.

    Article  MathSciNet  Google Scholar 

  21. J. He, S. Wang, G. Li, Z. Yang, L. Hu and K. Wu, Compilation of NC lathe dynamic cutting force spectrum based on twodimensional mixture models, The International Journal of Advanced Manufacturing Technology, 98 (1–4) (2018) 251–262.

    Article  Google Scholar 

  22. S. Kotz, N. Balakrishnan and N. L. Johnson, Continuous Multivariate Distributions, Volume 1: Models and Applications (Vol. 1), John Wiley & Sons (2004) 407–412.

    Google Scholar 

  23. S. F. Ateya, Maximum likelihood estimation under a finite mixture of generalized exponential distributions based on censored data, Statistical Papers, 55(2) (2014) 311–325.

    Article  MathSciNet  Google Scholar 

  24. G. McLachlan and T. Krishnan, The EM Algorithm and Extensions, John Wiley & Sons, 382 (2007) 66–77.

    Google Scholar 

  25. Y. Liu, Y. Shi, X. Bai and P. Zhan, Reliability estimation of a NMcold-standby redundancy system in a multicomponent stress-strength model with generalized half-logistic distribution, Physica A: Statistical Mechanics and its Applications, 490 (2018) 231–249.

    Article  MathSciNet  Google Scholar 

  26. D. Karlis and E. Xekalaki, Choosing initial values for the EM algorithm for finite mixtures, Computational Statistics & Data Analysis, 41 (3-4) (2003) 577–590.

    Article  MathSciNet  Google Scholar 

  27. C. Biernacki, G. Celeux and G. Govaert, Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models, Computational Statistics & Data Analysis, 41 (3-4) (2003) 561–575.

    Article  MathSciNet  Google Scholar 

  28. Y. Z. Zhang, S. Zheng, G. X. Shen, R. Zheng, D. W. Gu and X. L. Niu, Criticality analysis for CNC turret adopting importance and fuzzy reasoning, Journal of Jilin University (Engineering and Technology Edition), 42(5) (2012) 1157–1162.

    Google Scholar 

  29. K. Lin, Y. Chen and D. Xu, Reliability assessment model considering heterogeneous population in a multiple stresses accelerated test, Reliability Engineering & System Safety, 165 (2017) 134–143.

    Article  Google Scholar 

  30. C. Zhang, Y. Shi, X. Bai and Q. Fu, Inference for constantstress accelerated life tests with dependent competing risks from bivariate Birnbaum-Saunders distribution based on adaptive progressively hybrid censoring, IEEE Transactions on Reliability, 66(1) (2017) 111–122.

    Article  Google Scholar 

Download references

Acknowledgments

The research was supported by the National Science and Technology Major Project of China under Grant 2018ZX0 4039001; JLU Science and Technology Innovative Research Team; Science and Technology Development Plan Project of Jilin Province under Grant 20180520068JH; Jilin Province Education Department's thirteenth five-year plan Science and Technology project under Grant JJKH20180079KJ; Project of the Graduate Innovation Fund of Jilin University under Grant 101832018C190, and was carried out when the first author made a research visit to McMaster University, Canada, thanks to Professor N. Balakrishnan for his guidance during this period.

Author information

Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Jilin University, Changchun, Jilin, 130022, China

    Bo Sun, Fei Chen, Binbin Xu & Zhaojun Yang

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    Narayanaswamy Balakrishnan

  3. Sino-german College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen, Guangdong, 518118, China

    Fei Chen & Binbin Xu

  4. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shanxi, 710072, China

    Yiming Liu

Authors
  1. Bo Sun
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  2. Narayanaswamy Balakrishnan
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  3. Fei Chen
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  4. Binbin Xu
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  5. Zhaojun Yang
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  6. Yiming Liu
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Corresponding author

Correspondence to Binbin Xu.

Additional information

Recommended by Editor Chongdu Cho

Bo Sun received the M.S. degree in mechanical engineering from Yanshan University, Qinhuangdao, Hebei, China in 2016, and he is currently pursuing the Ph.D. degree under the supervision of Prof. Zhanjun Yang with the School of Mechanical and Aerospace Engineering, Jilin University, Changchun, Jilin, China. He is also a visiting student with McMaster University, Hamilton, Ontario Canada. His research interests include reliability evaluation and test of machine tools.

Narayanaswamy Balakrishnan is a Distinguish Professor at McMaster University, Hamilton, Ontario, Canada. He received his B.Sc. and M.Sc. degrees in Statistics from University of Madras, India, in 1976 and 1978, respectively. He finished his Ph.D. in Statistics from Indian Institute of Technology, Kanpur, India, in 1981. He is a Fellow of the American Statistical Association, and a Fellow of the Institute of Mathematical Statistics. He is currently the Editor-in-Chief of Communications in Statistics, and Executive Editor of Journal of Statistical Planning and Inference. His research interests include distribution theory, ordered data analysis, censoring methodology, reliability, survival analysis, and statistical quality control.

Fei Chen is a Professor with the School of Mechanical and Aerospace Engineering, Jilin University, Changchun, Jilin, China. She received her Ph.D. degree in Mechanical Engineering from the Jilin University in 2009. Her main research interests are reliability theory, application technology of NC equipment, and system fault diagnosis. She is a committee member of reliability branch of Chinese Mechanical Engineering Society, committee member of reliability branch of Systems Engineering Society of China, trustee of testing machine branch of China Instrument and Control Society.

Binbin Xu an Associate Professor with the School of Mechanical and Aerospace Engineering, Jilin University, Changchun, Jilin, China. She received her Ph.D. degree in Mechanical Engineering from the Jilin University in 2011. Her main research interests are reliability theory and application technology of high-end manufacturing equipment and its functional parts, system fault diagnosis and prediction technology. She is a senior member of the Chinese Mechanical Engineering Society, and member of Chinese society of Aeronautics and Astronautics.

Zhaojun Yang received the Ph.D. degree in Mechanical Engineering from the Jilin University of Technology in 1995. He is currently a Professor with the School of Mechanical Science and Engineering, Jilin University. His main research interests are reliability theory and technology of computer numerical control equipment. He is granted as the Changbai Mountain Scholars Distinguished Professor and enjoys special government allowances from the State Council of China. He has been in charge of over 30 projects involving national science and technology major projects and published over 100 papers of reliability field.

Yiming Liu is working toward the Ph.D. degree in the Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, China, working on his Ph.D. thesis under the supervision of Prof. Y. Shi. He is also a visiting student with McMaster University, Hamilton, Ontario, Canada. His research interests include reliability analysis and competing risk.

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Sun, B., Balakrishnan, N., Chen, F. et al. Reliability evaluation of the servo turret with accurate failure data and interval censored data based on EM algorithm. J Mech Sci Technol 34, 1503–1513 (2020). https://doi.org/10.1007/s12206-020-0312-3

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  • DOI: https://doi.org/10.1007/s12206-020-0312-3

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