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Reliability models based on modified Weibull distributions

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Measurement Techniques Aims and scope

The possibility of using modified Weibull distributions for estimation and statistical-physics analysis of the reliability of articles is analyzed. It is proposed that a mixture of distributions – exponential and Weibull distributions – be used.

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References

  1. W. Weibull, “A statistical theory of the strength of materials,” Ingeniers Vetenskaps Akademien Handl., No. 51 (1939).

  2. W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech., 18, 293–297 (1951).

    MATH  Google Scholar 

  3. S. D. Dubey, “Normal and Weibull distributions,” Naval Res. Logist. Quart., 14, No. 1, 69–79 (1967).

    Article  Google Scholar 

  4. M. R. Gurvich, A. T. Dibenedetto, and S. V. Rande, “A new statistical distribution for characterizing the random strength of brittle materials,” Mater. Sci., 32, 2559–2564 (1997).

    Article  ADS  Google Scholar 

  5. C. D. Lai, M. Xie, and D. N. P. Murthy, “Modified Weibull model,” IEEE Trans. Reliabil., 52, 33–37 (2003).

    Article  Google Scholar 

  6. M. Xie,Y. Tang, and T. N. Goh, “A modified Weibull extension with bathtub-shaped failure rate function,” Reliabil. Eng. & Syst. Safety, 76, 279–285 (2002).

    Article  Google Scholar 

  7. J. S. White, “The moments of log-Weibull order statistics,” Technometrics, 11, 373–386 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  8. K. K. Phani, “A new modified Weibull distribution,” Comm. Amer. Ceramic Soc., 70, 182–184 (1987).

    Google Scholar 

  9. J. A. Kies, The Strength of Glass, Report No. 5093, Naval Res. Lab., Washington D.C., (1958).

  10. S. Nadarajah and S. Kotz, “On some recent modifications of Weibull distribution,” IEEE Trans. Reliabil., 34, No. 4, 561–562 (2005).

    Article  Google Scholar 

  11. G. S. Mudholkar, D. K. Srivastava, and M. Freimer, “The exponentiated Weibull family,” Technometrics, 37, 436–445 (1995).

    Article  MATH  Google Scholar 

  12. G. S. Mudholkar and A. D. Hutson, “The exponentiated Weibull distribution: some properties and a flood data application,” Comm. Stat. – Theory and Methods, 25, 3059–3083 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  13. M. M. Nassar and F. H. Eissa, “On the exponentiated Weibull distribution,” Comm. Stat. – Theory and Methods, 32, 1317–1336 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Nadarajah and A. K. Gupta, “On the moments of the exponentiated Weibull distribution,” Comm. Stat. – Theory and Methods, 34, 253–256 (2003).

    MathSciNet  Google Scholar 

  15. H. W. Block, Y. Li, and H. Thomas, “Initial and final behavior of failure rate functions for mixtures and systems,” Appl. Prob., 40, No. 3, 721–740 (2003).

    Article  MATH  Google Scholar 

  16. S. Ya. Grodzensky and V. G. Domrachev, “A universal distribution for component failure times,” Izmer. Tekhn., No. 7, 24–26 (2002); Measur. Techn., 45, No. 7, 710–713 (2002).

  17. S. Ya. Grodzensky and V. G. Domrachev, “Estimation of parameters of universal distribution of moments of failure of products,” Izmer. Tekhn., No. 8, 12–14 (2002); Measur. Techn., 45, No. 8, 799–802 (2002).

  18. S. Ya. Grodzensky and V. G. Domrachev, “Estimation of the parameters of mixture of exponential and Weibull distributions with progressive censoring,” Izmer. Tekhn., No. 11, 10–12 (2002); Measur. Techn., 45, No. 11, 1115–1118 (2002).

  19. S. Ya. Grodzensky, “A statistical-physics method of electronic device reliability testing from working data pages,” Izmer. Tekhn., No. 6, 59–60 (2003); Measur. Techn., 46, No. 6, 616–618 (2003).

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Authors and Affiliations

  1. Moscow State Technical University of Radio Engineering, Electronics, and Automation (MIREA), Moscow, Russia

    S. Ya. Grodzensky

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  1. S. Ya. Grodzensky
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Correspondence to S. Ya. Grodzensky.

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Translated from Izmeritel’naya Tekhnika, No. 7, pp. 27–31, July, 2013.

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Grodzensky, S.Y. Reliability models based on modified Weibull distributions. Meas Tech 56, 768–774 (2013). https://doi.org/10.1007/s11018-013-0280-4

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  • DOI: https://doi.org/10.1007/s11018-013-0280-4

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