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Bare Bones Particle Swarm Applied to Parameter Estimation of Mixed Weibull Distribution

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Soft Computing in Industrial Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 75))

Abstract

An approach for estimating the parameters of mixed Weibull distributions is presented. The problem is formulated as maximization of the likelihood function of the corresponding mixture model. For the solution of the optimization problem, Bare Bones Particle Swarm Optimization (BBPSO) algorithm is applied. Illustrative example for a case study using censored data are provided in order to show the suitability of the BBPSO algorithm for this kind of problem very common in lifetime modelling.

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References

  1. Kececioglu, D.B., Wendai, W.: Parameter estimation for mixed-Weibull distribution. In: Proc. of the Annual Symposium on Reliability and Maintainability, pp. 247–252 (1998)

    Google Scholar 

  2. Patra, K., Dey, D.K.: A multivariate mixture of Weibull distributions in reliability modeling. Statistics and Probability Letters 45, 225–235 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Majeske, K.D.: A mixture model for automobile warranty data. Reliability Engineering and System Safety 81, 71–77 (2003)

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Carta, J.A., Ramírez, P.: Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions. Renewable Energy 32, 518–531 (2007)

    Article  Google Scholar 

  6. Jiang, R., Murthy, D.N.P.: Modeling failure-data by mixture of 2 Weibull distributions: a graphical approach. IEEE Transactions on Reliability 44, 477–488 (1995)

    Article  Google Scholar 

  7. Jiang, S., Kececioglu, D.: Maximum likelihood estimates, from censored data, for mixed-Weibull distributions. IEEE Transactions on Reliability 41, 248–255 (1992)

    Article  MATH  Google Scholar 

  8. Sinha, S.K.: Bayesian estimation of the parameters and reliability function of a mixture of Weibull life distributions. Journal of Statistical Planning and Inference 16, 377–387 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chen, K.-W., Papadopoulos, A.S., Tamer, P.: On Bayes estimation for mixtures of two Weibull distributions under type I censoring. Microelectronics and Reliability 29, 609–617 (1989)

    Article  Google Scholar 

  10. Tan, C.M., Raghavan, N.: An approach to statistical analysis of gate oxide breakdown mechanisms. Microelectronics Reliability 47, 1336–1342 (2007)

    Article  Google Scholar 

  11. Thomas, G.M., Gerth, R., Velasco, T., Rabelo, L.C.: Using real-coded genetic algorithms for Weibull parameter estimation. Computers and Industrial Engineering 29, 377–381 (1995)

    Article  Google Scholar 

  12. Abbasi, B., Jahromi, A.H.E., Arkat, J., Hosseinkouchack, M.: Estimating the parameters of Weibull distribution using simulated annealing algorithm. Applied Mathematics and Computation 183, 85–93 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gong, Z.: Estimation of mixed Weibull distribution parameters using the SCEM-UA algorithm: Application and comparison with MLE in automotive reliability analysis. Reliability Engineering and System Safety 91, 915–922 (2006)

    Article  Google Scholar 

  14. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proc. of the IEEE International Conference on Neural Networks, pp. 1941–1948 (1995)

    Google Scholar 

  15. Kennedy, J., Eberhart, R., Shi, Y.: Swarm intelligence. Morgan Kaufmann Publishers, San Francisco (2001)

    Google Scholar 

  16. Lawless, J.F.: Statistical models and methods for lifetime data. John Wiley and Sons, New York (1982)

    MATH  Google Scholar 

  17. Kennedy, J.: Bare bones particle swarms. In: Proc. of the IEEE Swarm Intelligence Symposium SIS 2003, pp. 80–87 (2003)

    Google Scholar 

  18. Campos, M., Krohling, R.A., Borges, P.: Particle swarm optimization for inference procedures in the generalized gamma family based on censored data. In: Mehnen, J., et al. (eds.) Applications of Soft Computing: From Theory to Praxis. Springer, Heidelberg (2009)

    Google Scholar 

  19. Krohling, R.A., Mendel, E.: Bare bones particle swarm with Gaussian and Cauchy jumps. In: Proc. of the IEEE Congress on Evolutionary Computation CEC 2009, pp. 3285–3291 (2009)

    Google Scholar 

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Krohling, R.A., Campos, M., Borges, P. (2010). Bare Bones Particle Swarm Applied to Parameter Estimation of Mixed Weibull Distribution. In: Gao, XZ., Gaspar-Cunha, A., Köppen, M., Schaefer, G., Wang, J. (eds) Soft Computing in Industrial Applications. Advances in Intelligent and Soft Computing, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11282-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-11282-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11281-2

  • Online ISBN: 978-3-642-11282-9

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